Atom-based closed-loop control for electromagnetic radiation measurement, communication, and information processing

Abstract

To improve EM sensing, detection, measurement, imaging, reception, communication, and source generation by extending capabilities beyond those achievable with conventional sensor technologies and using atom-based quantum sensor technologies.SOLUTION: A method for atom-based closed-loop control includes exciting atoms of a gas into one or more Rydberg states, applying one or more signal processing functions to the one or more Rydberg states, and adjusting characteristics of the applied one or more signal processing functions based at least in part on a response of the one or more Rydberg states to the one or more signal processing functions. A system for internal quantum state space interferometry includes an atomic receiver, an interference path, and a detector. The interferometer includes an atomic vapor having a first atomic state and a second atomic state. The interference path from an RF phase between the first and second atomic states is closed by a quantum state space. The detector is configured to detect a readout of an interference signal.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. Provisional Application No. 63 / 032,041, filed May 29, 2020, and U.S. Provisional Application No. 63 / 077,244, filed September 11, 2020. Both applications are incorporated herein by reference in their entirety.

[0002]

[0002] The present disclosure relates to atom-based devices, systems, and methods, such as atom-based closed-loop devices, systems, and methods. [Background technology]

[0003]

[0003] Sensors and measurement devices for electromagnetic (EM) radiation primarily rely on antenna technology. However, conventional antenna and / or solid-state technology impose fundamental limitations on the achievable accuracy, precision, and performance of EM probes and detectors. Atom-based quantum sensor technology can achieve capabilities beyond conventional sensor technology. In quantum mechanics, a Rydberg atom is an excited atom with one or more loosely bound electrons with a high principal quantum number that exhibits large polarizability and electric dipole moment. Atom-based sensors that utilize individual atoms in highly excited Rydberg states can provide improved sensing, measurement, and imaging for EM radiation measurement, communication, and / or information processing. Summary of the Invention

[0004]

[0004] Therefore, there is a need to extend capabilities beyond those achievable with conventional sensor technologies and improve EM sensing, detection, measurement, imaging, reception, communication, and source generation using atom-based quantum sensor technologies.

[0005] In some embodiments, the atom-based closed-loop control system includes a compartment, a device, a detector, and a controller. In some embodiments, the compartment encloses a gas of excited atoms including one or more Rydberg states. In some embodiments, the device is configured to apply an input signal to the one or more Rydberg states. In some embodiments, the detector is configured to detect a response of the one or more Rydberg states due to an interaction of the one or more Rydberg states with electromagnetic radiation. In some embodiments, the controller is configured to adjust a characteristic of the applied input signal based at least in part on the detected response of the one or more Rydberg states to the electromagnetic radiation.

[0006] In some embodiments, the controller is further configured to adjust a characteristic of the applied input signal based on a characteristic of the electromagnetic radiation. In some embodiments, the characteristic of the electromagnetic radiation includes frequency, amplitude, phase, polarization, power, direction of arrival, angle of arrival, and / or combinations thereof. In some embodiments, the controller is further configured to adjust the control signal and / or the processing signal based on the detected response of one or more Rydberg states to the electromagnetic radiation.

[0007] In some embodiments, the controller is further configured to adjust the characteristic based on differential feedback between the detected response and the setpoint. In some embodiments, the controller is further configured to adjust the characteristic based on one or more detector sensitivity parameters.

[0008] In some embodiments, the detected response of the one or more Rydberg states is further based on a temperature of the gas, a pressure of the gas, an electric field applied to the gas, a magnetic field applied to the gas, and / or an auxiliary RF waveform applied to the gas. In some embodiments, the device includes a mechanical device, an electrical device, and / or an optical device.

[0009] In some embodiments, the applied input signal comprises an electromagnetic field, an electric field, and / or a magnetic field, and the characteristic comprises a parameter of the applied electromagnetic field, an electric field, and / or a magnetic field. In some embodiments, the controller is further configured to automatically adjust the characteristic based on the detected response. In some embodiments, the controller includes hardware or software configured to automatically adjust the characteristic to a set point.

[0010] In some embodiments, the device includes an RF generator or RF source, and the applied input signal includes an RF electromagnetic wave, an RF electronic signal, an electric field, and / or a magnetic field. In some embodiments, the detected response includes an optical transmission, optical absorption, or scattering signal from the excited atoms.

[0011] In some embodiments, the device is further configured to apply a reference RF electromagnetic wave or a reference local oscillator wave. In some embodiments, the applied input signal comprises multiple electric fields for multi-field modulation of one or more Rydberg states. In some embodiments, the applied input signal comprises a laser beam and the characteristics comprise parameters of the laser beam.

[0012] In some embodiments, the characteristic and the detected response comprise phase-encoded signals. In some embodiments, the characteristic and the detected response are electronically synchronized, frequency-locked, and / or phase-locked.

[0013] In some embodiments, the controller is further configured to determine an electromagnetic spectrum, and in some embodiments, the detected response is further based on multidimensional Doppler matching of parameters of multiple laser beams for Doppler-free Rydberg spectroscopy in a gas of excited atoms at or near a homogeneous Rydberg linewidth.

[0014] In some embodiments, a system for detecting radio frequency (RF) signals includes a stripline, a device, an excited atomic gas, a detector, and a controller. In some embodiments, the stripline is configured to receive an input RF signal and a reference signal. In some embodiments, the device is configured to apply the reference signal. In some embodiments, the excited atomic gas includes one or more Rydberg states and is disposed within the stripline within a vacuum enclosure. In some embodiments, the detector is configured to detect responses of the one or more Rydberg states due to interaction of the one or more Rydberg states with electromagnetic radiation inside or adjacent to the stripline based on the input RF signal and / or the applied reference signal. In some embodiments, the controller is configured to determine parameters of the input RF signal based at least in part on the detected responses of the one or more Rydberg states to the electromagnetic radiation. In some embodiments, the controller is configured to adjust characteristics of the applied reference signal based at least in part on the detected responses of the one or more Rydberg states to the electromagnetic radiation.

[0015] In some embodiments, the controller is further configured to adjust a characteristic of the applied reference signal based on a second characteristic of the electromagnetic radiation, the input RF signal, and / or the applied reference signal. In some embodiments, the second characteristic of the electromagnetic radiation, the input RF signal, and / or the applied reference signal includes frequency, amplitude, phase, polarization, power, direction of arrival, angle of arrival, and / or combinations thereof. In some embodiments, the controller is further configured to adjust the control signal and / or the processing signal based on the detected response of one or more Rydberg states to the electromagnetic radiation.

[0016] In some embodiments, the applied reference signal comprises a reference RF signal. In some embodiments, the input RF signal comprises an electrical signal, an optical signal, and / or an electromagnetic wave. In some embodiments, the stripline comprises one or more electrodes, a waveguide, and / or a vapor cell compartment.

[0017] In some embodiments, the device includes a controller configured to vary a parameter of the input RF signal. In some embodiments, the reference signal includes a reference RF signal included in modulating a parameter of a laser beam interacting with one or more Rydberg states. In some embodiments, the stripline is further configured to receive one or more modulation RF signals for multi-field modulation of the one or more Rydberg states.

[0018] In some embodiments, the system for detecting RF signals further includes a multiplexer configured to parallelize or multiplex one or more combinations of the optical and RF electromagnetic fields, interference paths, and / or interference signals of one or more Rydberg states. In some embodiments, the multiplexer is configured to apply space, time, and / or frequency multiplexing. In some embodiments, the multiplexer is configured to provide an increased detected RF bandwidth.

[0019] In some embodiments, the stripline includes a pair of electrodes and the parameter of the input RF signal is the power or field equivalent voltage across the pair of electrodes. In some embodiments, the parameter of the input RF signal is a characteristic of an applied reference signal.

[0020] In some embodiments, the controller is further configured to determine the electromagnetic spectrum.

[0021] In some embodiments, the controller is further configured to determine power, voltage, communication signal, direction of arrival, and / or combinations thereof. In some embodiments, the detected response is further based on multidimensional Doppler matching of parameters of multiple laser beams for Doppler-free Rydberg spectroscopy in a gas of excited atoms at or near a homogeneous Rydberg linewidth. In some embodiments, the multidimensional Doppler matching of parameters of multiple laser beams includes at least two laser beams positioned at angles that suppress Doppler shifts in one, two, and / or three dimensions. In some embodiments, three laser beams are non-collinear to achieve Doppler matching in two degrees of freedom. In some embodiments, four laser beams are non-collinear to achieve Doppler matching in three degrees of freedom.

[0022]

[0022] In some embodiments, a method for atom-based closed-loop control includes exciting atoms of a gas into one or more Rydberg states, applying one or more signal processing functions to the one or more Rydberg states, and adjusting characteristics of the applied one or more signal processing functions based at least in part on the response of the one or more Rydberg states to the one or more signal processing functions.

[0023] In some embodiments, the one or more signal processing functions include a phase-locked loop. In some embodiments, the one or more signal processing functions include a Costas loop. In some embodiments, the characteristic includes electromagnetic field frequency, amplitude, polarization, phase, and / or combinations thereof. In some embodiments, the one or more signal processing functions include injection locking with an injection-locked oscillator (ILO) for radio frequencies. In some embodiments, exciting the atoms includes exciting the atoms to a lower-lying excited state. In some embodiments, the characteristic includes laser frequency, phase, amplitude, and / or polarization involved in exciting or interacting with the atoms. In some embodiments, the one or more signal processing functions include automatic level control of a modulated signal from the response of one or more Rydberg states. In some embodiments, adjusting includes performing baseband or modulated signal processing for retrieval of analog or digital information from the response of one or more Rydberg states.

[0024] In some embodiments, a system for quantum state space interferometry includes an atomic receiver containing an atomic vapor having a first atomic state and a second atomic state, an interference path, and a detector. The first atomic state is coupled by a radio frequency (RF) modulated radio frequency electromagnetic field (RF-EM). The second atomic state is coupled by a second radio frequency (RF) modulated optical electromagnetic field (O-EM). The RF phase interference path between the first and second atomic states is closed by a quantum state space. The detector is configured to detect a readout including an interference signal from the quantum state space. The detected readout is configured to provide RF interferometry in the optical and / or quantum domains. This system can be described as atomic RF interferometry. The phase and amplitude of either the RF field or the O-EM field can be detected and measured for implementation in optical RF phase sensing or optical RF phase detection mediated by an atomic RF interferometer.

[0025] In some embodiments, RF is in the range from DC (0 Hertz) to THz (Terahertz, or 10 12 In some embodiments, the O-EM includes a range of colors from ultraviolet to infrared wavelengths. In some embodiments, the second atomic state includes at least one Rydberg state. In some embodiments, the RF phase interference pathway is configured to be modified by atomic changes, atomic excitations, interactions of the first atomic state with other atoms, interactions of the second atomic state with other atoms, the first atomic state, the second atomic state, RF-EM, O-EM, another external field, a perturbation, and / or some combination thereof.

[0026] In some embodiments, the system further includes a transceiver coupled to the detector and configured to transmit and / or receive communication signals. In some embodiments, the interference signal includes optical detection, measurement, and / or imaging of the phase, frequency, amplitude, polarization, direction or angle of arrival, and / or some combination thereof of the RF electromagnetic wave. In some embodiments, the readout of the interference signal includes an electromagnetic signal, an optical signal, a charge signal, or an electronic signal.

[0027]

[0027] In some embodiments, a method for performing quantum state space interferometry includes coupling a first atomic state with RF-EM modulated at a first RF, coupling a second atomic state with O-EM modulated at a second RF, forming an RF phase interference path between the first atomic state and the second atomic state enclosed by the quantum state space, and detecting an interference signal from the quantum state space.

[0028] In some embodiments, the method further includes parallelizing or multiplexing one or more combinations of optical and radio frequency electromagnetic fields, interference paths, and / or interference signals. In some embodiments, the multiplexing includes spatial multiplexing and time multiplexing. In some embodiments, the detecting includes optical interference signals carrying radio frequency modulation, information, or communication signals.

[0029] In some embodiments, a system for atom-based RF signal waveform detection, imaging, and / or processing includes a gas of excited atoms comprising one or more Rydberg states, an RF signal waveform interacting with the gas of excited atoms, and a detector configured to detect a readout from the gas of excited atoms based on the RF signal waveform, the detected readout being configured to provide a characteristic of the RF signal waveform.

[0030] In some embodiments, the readout comprises a time domain signal or a frequency domain signal. In some embodiments, the system further comprises a processor coupled to the detector, the processor configured to analyze the modulated RF signal and the wave pattern of the detected readout comprising a communication protocol, a Doppler shift, and / or a frequency chirp.

[0031]

[0031] In some embodiments, a method for atom-based RF signal detection, reception, imaging, and processing includes exciting atoms of a gas into one or more Rydberg states, interacting at least one applied electromagnetic field with the excited atoms of the gas to form a structured Rydberg level, interacting at least one RF signal wave with the structured Rydberg level, and detecting at least one RF signal wave from the excited atoms.

[0032]

[0032] In some embodiments, the method further includes analyzing the modulated radio frequency signal and the wave pattern comprising the communication protocol, Doppler shift, and frequency chirp.

[0033] In some embodiments, a system for detecting RF signals includes an atomic gas contained within an RF stripline in a vacuum enclosure or an RF stripline contained within the atomic gas, an electrical feedthrough coupled to the stripline and configured to inject one or more RF signals into the stripline, and a detector configured to detect a readout of the atomic response to the RF signals in the stripline. The detected readout is configured to increase the detection sensitivity of the RF signal and provide a means for applying one or more RF fields, including for structuring Rydberg levels, using RF phase detection and interferometry, and for integration into conventional RF electronic systems.

[0034] In some embodiments, an atom-based closed-loop control system includes an atomic receiver, a control signal, and a feedback loop. The atomic receiver is configured to receive an input signal and includes one or more Rydberg atoms. The control signal is based on a response of the one or more Rydberg atoms to the input signal. The feedback loop is coupled to the control signal and the atomic receiver. The feedback loop regulates one or more process variables of the atomic receiver to a predetermined state or set point.

[0035] In some embodiments, an atomic automatic level control (AALC) system includes an atomic receiver, a control signal, and a controller. The atomic receiver is configured to receive an input signal and includes one or more Rydberg atoms. The control signal includes a baseband signal and / or a carrier signal based on a response of the one or more Rydberg atoms to the input signal. The controller is coupled to the control signal and the atomic receiver and is configured to adjust one or more laser parameters based on the carrier signal for automatic level control of the baseband and / or carrier signals.

[0036] In some embodiments, an atomic phase-locked loop (PLL) system includes an atomic receiver, a feedback signal, and an oscillator. The atomic receiver is configured to receive an input signal and one or more reference signals, and the atomic receiver includes one or more Rydberg atoms. The feedback signal is based on a response of the one or more Rydberg atoms to the input signal and the one or more reference signals. The oscillator is coupled to the feedback signal and the atomic receiver and configured to adjust the frequency and / or phase of the one or more reference signals to form the phase-locked loop.

[0037] In some embodiments, a quantum state-space interferometry method includes an atomic receiver, a closed internal-state interference loop, and a detector. The atomic receiver is configured to receive a first input signal and a second input signal, the atomic receiver including one or more Rydberg atoms. The closed internal-state interference loop is based on a first coupling of the first input signal with the one or more Rydberg atoms and a second coupling of the second input signal with the one or more Rydberg atoms. The detector detects an optical readout based on a response of the one or more Rydberg atoms to the first and second input signals. The second input signal includes a modulated optical beam.

[0038] In some embodiments, the atomic transducer includes an antenna, a connector, an atomic receiver, and a detector. The antenna is configured to collect an input signal. The connector is coupled to the antenna and configured to transfer the input signal. The atomic receiver is coupled to the connector via electrodes and configured to receive the input signal, the atomic receiver including one or more Rydberg atoms. The detector is configured to detect a readout based on a response of the one or more Rydberg atoms to the input signal. The antenna, connector, atomic receiver, and detector form a single unit.

[0039] In some embodiments, an atomic receiver with an antenna includes an antenna, an atomic receiver, an optical input / output (I / O), and an electrical I / O. The antenna is configured to collect an input signal. The atomic receiver is coupled to the antenna and configured to receive the input signal, the atomic receiver including one or more Rydberg atoms. The optical I / O is coupled to the atomic receiver, the optical I / O including atom-based closed-loop feedback control based on a response of the one or more Rydberg atoms to the input signal. The electrical I / O is coupled to the atomic receiver, the electrical I / O including atom-based closed-loop feedback control based on a response of the one or more Rydberg atoms to the input signal.

[0040] In some embodiments, the atom imager includes an atom receiver, an optoelectronic converter, and a signal processor. The atom receiver is configured to receive an input signal, the atom receiver including one or more Rydberg atoms. The optoelectronic converter is coupled to the atom receiver and configured to receive an optical readout from the atom receiver. The optical readout has an atom-based closed-loop feedback control based on a response of the one or more Rydberg atoms to the input signal. The signal processor is coupled to the optoelectronic converter and configured to receive an electrical readout from the optoelectronic converter. The electrical readout includes an atom-based closed-loop feedback control based on a response of the one or more Rydberg atoms to the input signal.

[0041] In some embodiments, an atomic hybrid detector with a stripline includes an asymmetric, symmetric, or two-electrode stripline and an atomic receiver. The stripline is configured to receive an input signal and a reference signal, the stripline including a first electrode and a second electrode, both of which are connected to a symmetric pair of separated RF connectors. An atomic vapor is disposed between the first and second electrodes connected to the pair of RF connectors, and the atomic receiver includes one or more Rydberg atoms. The stripline is configured to increase a local field by compression of the input signal and the reference signal in the atomic receiver to provide an optical readout based on a response of the one or more Rydberg atoms to the input signal and / or the reference signal.

[0042] In some embodiments, an atomic hybrid detector having one or more striplines with one or more RF connectors is configured for homodyne amplitude and phase measurement, heterodyne amplitude and phase measurement, heterodyne parametric signal amplification, communication, and wireless signal reception and processing. In some embodiments, the atomic hybrid detector can be configured as a spectrum analyzer.

[0043] In some embodiments, the multi-field modulation system includes an atomic receiver and a detector. The atomic receiver is configured to receive an input signal, a reference signal, and an adjustment signal, the atomic receiver including one or more Rydberg atoms. The detector is configured to detect a readout based on a response of the one or more Rydberg atoms to the input signal and the reference signal. The adjustment signal is configured to adjust the Rydberg level structure of the one or more Rydberg atoms for resonant detection of the input signal.

[0044] In some embodiments, a Rydberg field probe includes a probe, an atom receiver, a detector, and a control unit. The probe includes a probe tip. The atom receiver is disposed within the probe tip and configured to receive an input signal, the atom receiver including one or more Rydberg atoms. The detector is configured to detect a readout based on a response of the one or more Rydberg atoms to the input signal. The control unit is coupled to the probe and the detector, the control unit configured to provide a control signal to the atom receiver and to receive the detected readout. The probe, the detector, and the control unit may be portable.

[0045] In some embodiments, the atomic waveform sampler and spectrum analyzer includes an atomic receiver and a photodetector array. The atomic receiver is configured to receive an input signal and a site-selective signal, and the atomic receiver includes one or more Rydberg atoms. The photodetector array is configured to detect optical readouts based on responses of the one or more Rydberg atoms to the input signal and the site-selective signal generated by a space- or time-varying perturbation in the atomic sample. The photodetector array is configured to perform spatial and / or time multiplexing of the detected optical readouts to provide a sampled waveform based on the input signal. In some embodiments, the atoms can provide an instantaneous bandwidth of up to 10 MHz or more, multiplexed to 1 GHz or more.

[0046] In some embodiments, an atom-based raster imager for RF-EM field and phase at high speed and high resolution includes an atomic vapor, a raster-scanned O-EM laser beam, and a detector. The raster imager is configured to spatially scan an O-EM beam to selectively read out the phase and amplitude of one or more RF-EM fields emitted from one or more sources, such as an antenna or antenna array, from Rydberg atoms located in 1D or 2D. The raster imager has the capability to include subwavelength spatial imaging over distances and areas larger than allowed by the O-EM beam size, which is typically limited to about 1 mm or less due to requirements such as high Coupler-Rabi frequencies in Rydberg spectroscopy, far-subwavelength resolution of microwave phase and amplitude in the O-EM beam at selectable regions in space, and physical separation between the front-end detector atoms and the back-end laser source and other hardware for remote sensing and imaging, such as for microwave measurements and imaging in anechoic chambers, base stations, or other remote locations. Atom-based electromagnetic field and phase imaging was previously described in U.S. Application No. 16 / 222,384, filed December 17, 2018, which is incorporated herein by reference in its entirety.

[0047] In some embodiments, atom-based raster imagers may be effected by geometric scanning of one or more optical imaging beams using electro-optical or opto-mechanical scanning elements. In some embodiments, subgroups of pixels may be interrogated in parallel (e.g., simultaneously). In some embodiments, subgroups of pixels may be interrogated with a combination of scanning and parallel computation. In some embodiments, scanning may be performed by opto-mechanical, electro-optical, and / or MEMS-based actuators.

[0048]

[0048] In some embodiments, an atom-based RF-EM source and transceiver includes an atomic pump medium excited to one or more Rydberg states, one or more EM cavities, an RF-EM field output, and an atomic receiver.

[0049]

[0049] Further features and exemplary aspects of the embodiments, as well as the structure and operation of various embodiments, are described in detail below with reference to the accompanying drawings. It should be noted that the embodiments are not limited to the specific embodiments described herein. Such embodiments are presented herein for illustrative purposes only. Additional embodiments will be apparent to those skilled in the art based on the teachings contained herein. [Brief explanation of the drawings]

[0050]

[0050] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments and, together with the specification, serve to explain the principles of the embodiments and to enable those skilled in the art to make and use the embodiments.

[0051] [Figure 1]

[0051] FIG. 1 is a schematic cross-sectional view of an atomic receiver according to an exemplary embodiment. [Figure 2]

[0052] FIG. 1 is a schematic diagram of an atom-based closed-loop control system in accordance with an illustrative embodiment; [Figure 3A]

[0053] FIG. 1 is a schematic diagram of an atomic automatic level control (AALC) system in accordance with an exemplary embodiment. [Figure 3B] FIG. 1 is a schematic diagram of an atomic automatic level control (AALC) system in accordance with an exemplary embodiment. [Figure 3C]

[0054] 3C is a plot of the electrical readout of the AALC system shown in FIG. 3B according to an exemplary embodiment. [Figure 4A]

[0055] FIG. 1 is a schematic diagram of an atomic phase-locked loop (PLL) system in accordance with an example embodiment. [Figure 4B]FIG. 1 is a schematic diagram of an atomic phase-locked loop (PLL) system in accordance with an exemplary embodiment. [Figure 4C] FIG. 1 is a schematic diagram of an atomic phase-locked loop (PLL) system in accordance with an exemplary embodiment. [Figure 5A]

[0056] 1 is a schematic diagram of a quantum state space interferometer according to an example embodiment; [Figure 5B]

[0056] FIG. 1 is a schematic diagram of a quantum state space interferometer according to an exemplary embodiment. [Figure 5C]

[0057] 5C is a plot of an optical readout of the quantum state space interferometer shown in FIGS. 5A and 5B, according to an example embodiment. [Figure 6A]

[0058] 1 is a schematic diagram of an atomic transducer in accordance with an illustrative embodiment; [Figure 6B]

[0058] FIG. 1 is a schematic diagram of an atomic transducer according to an exemplary embodiment. [Figure 6C]

[0059] 6C is a plot of the electric field dependence as a function of distance from the electrical readout of the atomic transducer shown in FIGS. 6A and 6B, according to an exemplary embodiment. [Figure 6D]

[0060] 6C is a plot of electric field dependence as a function of tilt angle from an electrical readout of the atomic transducer shown in FIGS. 6A and 6B, according to an exemplary embodiment. [Figure 7]

[0061] 1 is a schematic diagram of an atomic receiver with an antenna in accordance with an exemplary embodiment; [Figure 8]

[0062] FIG. 1 is a schematic diagram of an atom imager in accordance with an exemplary embodiment. [Figure 9A]

[0063] FIG. 1 is a schematic diagram of an atomic hybrid detector with striplines, according to an example embodiment; [Figure 9B]

[0063] FIG. 1 is a schematic diagram of an atomic hybrid detector with striplines according to an exemplary embodiment. [Figure 10A]

[0064] FIG. 1 is a schematic diagram of a multi-field conditioning system in accordance with an illustrative embodiment. [Figure 10B]

[0065] 10B is a plot of optical excitation intensity from an optical readout of the multi-field modulation system shown in FIG. 10A according to an exemplary embodiment. [Figure 10C]

[0066] 10B is a plot of baseband transition intensity from an optical readout of the multi-field modulation system shown in FIG. 10A according to an exemplary embodiment. [Figure 11A]

[0067] FIG. 1 is a schematic diagram of a Rydberg field probe in accordance with an exemplary embodiment; [Figure 11B]

[0067] FIG. 1 is a schematic diagram of a Rydberg field probe according to an exemplary embodiment. [Figure 11C]

[0068] 11C is a plot of a time domain signal from a readout of the Rydberg field probe shown in FIGS. 11A and 11B, according to an exemplary embodiment. [Figure 11D]

[0069] 11C is a plot of a time domain signal from a readout of the Rydberg field probe shown in FIGS. 11A and 11B, according to an exemplary embodiment. [Figure 11E]

[0070] 11C is a plot of a time domain signal from a readout of the Rydberg field probe shown in FIGS. 11A and 11B, according to an exemplary embodiment. [Figure 11F]

[0071] 11C is a plot of a time domain signal from a readout of the Rydberg field probe shown in FIGS. 11A and 11B, according to an exemplary embodiment. [Figure 12]

[0072] FIG. 1 is a schematic diagram of an atomic waveform sampler in accordance with an exemplary embodiment. [Figure 13A]

[0073] FIG. 1 is a schematic diagram of an atomic raster imager in accordance with an exemplary embodiment; [Figure 13B]

[0073] A schematic diagram of an atomic raster imager according to an exemplary embodiment. [Figure 14]

[0074] 1 is a plot of three-photon Rydberg electromagnetically induced transparency (EIT) Autler-Townes (AT) spectra of three in-plane beams according to an example embodiment. [Figure 15]

[0075] 1 is a plot of rubidium (Rb) lifetime as a function of Rydberg state in accordance with an illustrative embodiment. [Figure 16]

[0076] 1 is a plot of a four-photon Doppler corrected Rydberg EIT spectrum according to an example embodiment. [Figure 17A]

[0077] FIG. 1 is a schematic diagram of an atomic energy level diagram of a two-photon Rydberg EIT optical readout for cesium vapor according to an example embodiment. [Figure 17B]

[0078] 1 is a plot of optical readout from an atomic vapor of a Rydberg EIT resonance as a function of laser frequency offset according to an example embodiment. [Figure 18]

[0079] FIG. 1 is a schematic diagram of a Rydberg field measurement system (RFMS) having a Rydberg field probe (RFP) and a mainframe control unit in accordance with an exemplary embodiment. [Figure 19]

[0080] 19 is a plot of spectroscopic and optical signals as a function of laser frequency detuning simultaneously collected by the RFMS shown in FIG. 18 according to an exemplary embodiment. [Figure 20A]

[0081] 19 is a plot of optical atomic spectra as a function of laser frequency detuning for the RFP shown in FIGS. 11A, 11B, and 18, according to an exemplary embodiment. [Figure 20B]

[0082] 19 is a plot of the non-resonant AC Stark shift as a function of laser frequency detuning for the RFP shown in FIGS. 11A, 11B, and 18, according to an exemplary embodiment. [Figure 21A]

[0083] 19 is a plot of E-field patterns for a single axis rotation angle of the RFP shown in FIGS. 11A, 11B, and 18, according to an exemplary embodiment. [Figure 21B]

[0083] Figure 19 is a plot of the electric field patterns for a single axis rotation angle of the RFP shown in Figures 11A, 11B, and 18, according to an exemplary embodiment. [Figure 21C]

[0083] Figure 19 is a plot of the electric field patterns for a single axis rotation angle of the RFP shown in Figures 11A, 11B, and 18, according to an exemplary embodiment. [Figure 22A]

[0084] 19 is a plot of polarization patterns with peak height ratio R for a single axis rotation angle of the RFP shown in FIGS. 11A, 11B, and 18 according to an exemplary embodiment. [Figure 22B]

[0084] FIG. 19 is a plot of polarization patterns with peak height ratios R for single axis rotation angles of the RFP shown in FIGS. 11A, 11B, and 18, according to an exemplary embodiment. [Figure 22C]

[0084] FIG. 19 is a plot of polarization patterns with peak height ratios R for single axis rotation angles of the RFP shown in FIGS. 11A, 11B, and 18, according to an exemplary embodiment. [Figure 23A]

[0085] 19 is a plot of atomic spectral output for single axis rotation angles of the RFP shown in FIGS. 11A, 11B, and 18 according to an exemplary embodiment. [Figure 23B]

[0085] Figure 19 is a plot of atomic spectral output for single axis rotation angles of the RFP shown in Figures 11A, 11B, and 18, according to an exemplary embodiment. [Figure 23C]

[0085] Figure 19 is a plot of atomic spectral output for single axis rotation angles of the RFP shown in Figures 11A, 11B, and 18, according to an exemplary embodiment. [Figure 24A]

[0086] 19 is a plot of E-field patterns for a single axis rotation angle of the RFP shown in FIGS. 11A, 11B, and 18, according to an exemplary embodiment. [Figure 24B]

[0086] Figure 19 is a plot of the electric field patterns for a single axis rotation angle of the RFP shown in Figures 11A, 11B, and 18, according to an exemplary embodiment. [Figure 25A]

[0087] 19 is a plot of the total RF E-field in three planes of the RFP shown in FIGS. 11A, 11B, and 18 according to an exemplary embodiment. [Figure 25B]

[0087] Figure 19 is a plot of the total RF E-field in three planes for the RFP shown in Figures 11A, 11B, and 18, according to an exemplary embodiment. [Figure 25C]

[0087] Figure 19 is a plot of the total RF E-field in three planes for the RFP shown in Figures 11A, 11B, and 18, according to an exemplary embodiment. [Figure 26]

[0088] 1 is a plot of RF E-field probability distribution in RFP atomic vapor along a light beam path according to an example embodiment. [Figure 27]

[0089] 1 is a schematic diagram of a Rydberg atomic radio frequency (THz) maser in accordance with an example embodiment; [Figure 28A]

[0090] 1 is a plot of Rydberg versus potential as a function of internuclear axis in accordance with an illustrative embodiment; [Figure 28B]

[0090] A plot of Rydberg pair potential as a function of internuclear axis according to an exemplary embodiment. [Figure 29A]

[0091] 1 is a plot of absorption coefficient as a function of laser frequency detuning in accordance with an illustrative embodiment. [Figure 29B] 10 is a plot of absorption coefficient as a function of laser frequency detuning according to an exemplary embodiment. [Figure 30]

[0092] 1 is a schematic diagram of a Rydberg atomic radio frequency (THz) transceiver in accordance with an example embodiment; [Figure 31]

[0093] FIG. 1 is a schematic diagram of a Rydberg atom RF phase detector and receiver according to an example embodiment. [Figure 32]

[0094] FIG. 32 is a schematic diagram of an atomic energy level diagram for the Rydberg atomic RF phase detector and receiver shown in FIG. 31 according to an exemplary embodiment. [Figure 33]

[0095] 32 is a plot of optical phase as a function of laser frequency detuning for the Rydberg atom RF phase detector and receiver shown in FIG. 31 in accordance with an exemplary embodiment. [Figure 34]

[0096] 1 is a plot of an AM baseband signal as a function of time for a Rydberg-based atomic detector in accordance with an illustrative embodiment. [Figure 35A]

[0097] 1 is a plot of transmission over time as a function of coupler laser frequency for a Rydberg-based atomic detector in accordance with an illustrative embodiment. [Figure 35B]

[0097] Figure 10 is a plot of transmission over time as a function of coupler laser frequency for a Rydberg-based atomic detector according to an exemplary embodiment. [Figure 36A]

[0098] 1 is a plot of measured EIT probe transmission over time as a function of relative coupler laser frequency according to an exemplary embodiment. [Figure 36B]

[0099] FIG. 1 is a schematic diagram of an EIT level diagram according to an exemplary embodiment. [Figure 37A]

[0100] 1 is a plot of an EIT signal as a function of time according to an example embodiment. [Figure 37B] 10 is a plot of an EIT signal as a function of time according to an exemplary embodiment. [Figure 38A]

[0101] 10 is a plot of EIT transmission over time as a function of coupler laser frequency with varying probe laser power, according to an example embodiment. [Figure 38B]

[0101] A plot of EIT transmission over time as a function of coupler laser frequency with varying probe laser power, according to an exemplary embodiment. [Figure 39A]

[0102] 10 is a plot of EIT transmission over time as a function of coupler laser frequency with varying cell temperature, according to an example embodiment. [Figure 39B]

[0102] A plot of EIT transmission over time as a function of coupler laser frequency with varying cell temperature, according to an exemplary embodiment. [Figure 40A]

[0103] 10 is a plot of EIT transmission over time as a function of coupler laser frequency with varying cell temperature, according to an example embodiment. [Figure 40B]

[0103] A plot of EIT transmission over time as a function of coupler laser frequency with varying cell temperature, according to an exemplary embodiment. [Figure 41A]

[0104] 10 is a plot of EIT formation over time as a function of coupler laser frequency for a constant probe and a pulsed coupler, according to an example embodiment. [Figure 41B]

[0104] A plot of EIT formation over time as a function of coupler laser frequency for a constant probe and a pulsed coupler, according to an exemplary embodiment. [Figure 41C]

[0104] A plot of EIT formation over time as a function of coupler laser frequency for a constant probe and a pulsed coupler, according to an exemplary embodiment. [Figure 42A-42B]

[0105] 1 is a plot of EIT transmission over time as a function of coupler laser frequency for an RF pulse at resonance, according to an example embodiment. [Figure 43A-43B]

[0106] 1 is a plot of EIT transmission over time as a function of coupler laser frequency for an EIT pulse and an RF pulse, according to an example embodiment. [Figure 44A]

[0107] 1 is a schematic diagram of a Rydberg radio receiver in accordance with an exemplary embodiment; [Figure 44B]

[0108] 1 is a schematic diagram of a Rydberg radio receiver in accordance with an exemplary embodiment; [Figure 45]

[0109] 1 is a schematic diagram of an MVA air-cooled generator according to an exemplary embodiment; [Figure 46A]

[0110] 46 is a schematic diagram of excess flux damage in the MVA air-cooled generator shown in FIG. 45 according to an exemplary embodiment. [Figure 46B]

[0110] Figure 46 is a schematic diagram of excess flux damage in the MVA air-cooled generator shown in Figure 45 according to an exemplary embodiment. [Figure 47A]

[0111] FIG. 1 is a schematic diagram of an atom probe and control unit according to an exemplary embodiment. [Figure 47B]

[0111] A schematic diagram of an atom probe and control unit according to an exemplary embodiment. [Figure 48A]

[0112] FIG. 1 is a schematic diagram of an atom RF interferometer for optical RF phase and amplitude sensing according to an example embodiment. [Figure 48B]

[0112] FIG. 1 is a schematic diagram of an atom RF interferometer for optical RF phase and amplitude sensing according to an exemplary embodiment. [Figure 48C]

[0112] FIG. 1 is a schematic diagram of an atom RF interferometer for optical RF phase and amplitude sensing according to an exemplary embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0052]

[0113] Features and exemplary aspects of the embodiments will become more apparent from the following detailed description when read in conjunction with the drawings, in which like reference numerals identify corresponding elements throughout. In the drawings, like reference numerals generally indicate identical, functionally similar, and / or structurally similar elements. Furthermore, the leftmost digit(s) of a reference number generally identifies the drawing in which the reference number first appears. Unless otherwise indicated, the drawings provided throughout this disclosure should not be construed as drawings to scale.

[0053]

[0114] This specification discloses one or more embodiments incorporating features of the present disclosure. The disclosed embodiment or embodiments are merely exemplary of the present disclosure. The scope of the present disclosure is not limited to the disclosed embodiment or embodiments. The present disclosure is defined by the claims appended hereto.

[0054]

[0115] References to one or more described embodiments, and to "one embodiment," "an embodiment," "an example embodiment," "an exemplary embodiment," or "an exemplary embodiment" herein, indicate that one or more described embodiments may include a particular feature, structure, or characteristic, but each embodiment does not necessarily include that particular feature, structure, or characteristic. Moreover, such phrases do not necessarily refer to the same embodiment. Furthermore, when a particular feature, structure, or characteristic is described in connection with one embodiment, it is understood that it is within the knowledge of one of ordinary skill in the art to implement such feature, structure, or characteristic in connection with other embodiments, whether or not explicitly described.

[0055]

[0116] Spatially relative terms such as "beneath," "below," "lower," "above," "on," "upper," and the like may be used herein for ease of description to describe the relationship of one element or feature to another element or features shown in the figures. Spatially relative terms are intended to encompass various orientations of the device in use or operation in addition to the orientation shown in the figures. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein may be similarly interpreted accordingly.

[0056]

[0117] As used herein, the terms "about" or "substantially" or "approximately" refer to a given quantity value that may vary based on a particular technique, which may indicate that the value of the given quantity varies within a range of, for example, 1 to 15% of that value (e.g., ±1%, ±2%, ±5%, ±10%, or ±15% of that value).

[0057]

[0118] The disclosed embodiments may be implemented in hardware, firmware, software, or any combination thereof. The disclosed embodiments may also be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (e.g., a computing device). For example, machine-readable media may include read-only memory (ROM), random-access memory (RAM), magnetic disk storage media, optical storage media, flash memory devices, electrical, optical, acoustic, or other forms of propagated signals (e.g., carrier waves, infrared signals, digital signals, etc.), and others. Furthermore, firmware, software, routines, and / or instructions may be described herein as performing certain actions. However, it should be understood that such description is merely for convenience and that such actions may actually result from a computing device, processor, controller, or other device executing the firmware, software, routines, instructions, etc.

[0058]

[0119] Aspect 1 of the present specification: An atom-based closed-loop control system, the system including: a compartment enclosing a gas of excited atoms including one or more Rydberg states; a device configured to apply an input signal to the one or more Rydberg states; a detector configured to detect a response of the one or more Rydberg states due to an interaction of the one or more Rydberg states with electromagnetic radiation; and a controller configured to adjust a characteristic of the applied input signal based at least in part on the detected response of the one or more Rydberg states to the electromagnetic radiation.

[0059]

[0120] Aspect 2 of the Present Invention The system of aspect 1, wherein the controller is further configured to adjust a characteristic of the applied input signal based on a characteristic of the electromagnetic radiation.

[0060]

[0121] Aspect 3 of the Present Description: The system of aspect 2, wherein the characteristics of the electromagnetic radiation include frequency, amplitude, phase, polarization, power, direction of arrival, angle of arrival, and / or combinations thereof.

[0061]

[0122] Aspect 4 of the Present Invention The system of aspect 1, wherein the controller is further configured to adjust the control signal and / or the processing signal based on the detected response of the one or more Rydberg states to the electromagnetic radiation.

[0062]

[0123] Aspect 5 of the present specification. The system of aspect 1, wherein the controller is further configured to adjust the characteristic based on differential feedback between the detected response and the set point.

[0063]

[0124] Aspect 6 of the present specification. The system of aspect 1, wherein the controller is further configured to adjust the characteristics based on one or more detector sensitivity parameters.

[0064]

[0125] Aspect 7 of the present specification: The system of aspect 1, wherein the detected response of the one or more Rydberg states is further based on a temperature of the gas, a pressure of the gas, an electric field applied to the gas, a magnetic field applied to the gas, and / or a supplemental RF waveform applied to the gas.

[0065]

[0126] Aspect 8 of the Present Description The system of aspect 1, wherein the device comprises a mechanical device, an electrical device, and / or an optical device.

[0066]

[0127] Aspect 9 of the Present Description The system of aspect 1, wherein the applied input signal comprises an electromagnetic field, an electric field, and / or a magnetic field, and the characteristics comprise parameters of the applied electromagnetic field, an electric field, and / or a magnetic field.

[0067]

[0128] Aspect 10 of the present specification. The system of aspect 1, wherein the controller is further configured to automatically adjust the characteristic based on the detected response.

[0068]

[0129] Aspect 11 of the present specification: The system of aspect 1, wherein the controller includes hardware or software configured to automatically adjust the characteristic to a set point.

[0069]

[0130] Embodiment 12 of the present specification. The system of embodiment 1, wherein the device comprises an RF generator or RF source, and the applied input signal comprises an RF electromagnetic wave, an RF electronic signal, an electric field, and / or a magnetic field.

[0070]

[0131] Aspect 13 of the present specification. The system of aspect 1, wherein the detected response comprises a light transmission, light absorption, or scattering signal from the excited atoms.

[0071]

[0132] Embodiment 14 of the present specification. The system of embodiment 1, wherein the device is further configured to apply a reference RF electromagnetic wave or a reference local oscillator wave.

[0072]

[0133] Embodiment 15 of the Present Invention The system of embodiment 1, wherein the applied input signal comprises multiple fields for multi-field modulation of one or more Rydberg states.

[0073]

[0134] Embodiment 16 of the present specification. The system of embodiment 1, wherein the applied input signal comprises a laser beam and the characteristics comprise parameters of the laser beam.

[0074]

[0135] Aspect 17 of the present specification. The system of aspect 1, wherein the characteristics and the detected responses include phase-encoded signals.

[0075]

[0136] Aspect 18 of the present specification. The system of aspect 1, wherein the characteristics and detected responses are electronically synchronized, frequency locked, and / or phase locked.

[0076]

[0137] Aspect 19 of the present specification. The system of aspect 1, wherein the controller is further configured to determine the electromagnetic spectrum.

[0077]

[0138] Aspect 20 of the present specification. The system of aspect 1, wherein the detected response is further based on multidimensional Doppler matching of parameters of multiple laser beams for Doppler-free Rydberg spectroscopy in a gas of excited atoms at or near a homogeneous Rydberg linewidth.

[0078]

[0139] Aspect 21 of the present specification: A system for detecting a radio frequency (RF) signal, the system including: a stripline configured to receive an input RF signal and a reference signal; a device configured to apply the reference signal; a gas of excited atoms including one or more Rydberg states and disposed within the stripline within a vacuum enclosure; a detector configured to detect responses of the one or more Rydberg states due to interaction of the one or more Rydberg states with electromagnetic radiation inside or adjacent to the stripline based on the input RF signal and / or the applied reference signal; and a controller configured to determine parameters of the input RF signal based at least in part on the detected responses of the one or more Rydberg states to the electromagnetic radiation, and to adjust characteristics of the applied reference based at least in part on the detected responses of the one or more Rydberg states to the electromagnetic radiation.

[0079]

[0140] Aspect 22 of the present specification: The system of aspect 21, wherein the controller is further configured to adjust a characteristic of the applied reference signal based on a second characteristic of the electromagnetic radiation, the input RF signal, and / or the applied reference signal.

[0080]

[0141] Aspect 23 of the present specification: The system of aspect 22, wherein the second characteristic of the electromagnetic radiation, the input RF signal, and / or the applied reference signal includes frequency, amplitude, phase, polarization, power, direction of arrival, angle of arrival, and / or combinations thereof.

[0081]

[0142] Aspect 24 of the present specification. The system of aspect 21, wherein the controller is further configured to adjust the control signal and / or the processing signal based on the detected response of the one or more Rydberg states to the electromagnetic radiation.

[0082]

[0143] Embodiment 25 of the present specification. The system of embodiment 21, wherein the applied reference signal comprises a reference RF signal.

[0083]

[0144] Aspect 26 of the present specification: The system of aspect 21, wherein the input RF signal comprises an electrical signal, an optical signal, and / or an electromagnetic wave.

[0084]

[0145] Embodiment 27 of the present specification. The system of embodiment 21, wherein the stripline comprises one or more electrodes, waveguides, and / or vapor cell compartments.

[0085]

[0146] Embodiment 28 of the present specification The system of embodiment 21, wherein the device includes a controller configured to vary a parameter of the input RF signal.

[0086]

[0147] Embodiment 29 of the present specification. The system of embodiment 21, wherein the reference signal comprises a reference RF signal included in modulating a parameter of a laser beam that interacts with one or more Rydberg states.

[0087]

[0148] Embodiment 30 of the present specification. The system of embodiment 21, wherein the stripline is further configured to receive one or more modulation RF signals for multi-field modulation of one or more Rydberg states.

[0088]

[0149] Embodiment 31 of the present specification. The system of embodiment 21, further comprising a multiplexer configured to parallelize or multiplex one or more combinations of the optical and RF electromagnetic fields, interference paths, and / or interference signals of the one or more Rydberg states.

[0089]

[0150] Aspect 32 of the present specification. The system of aspect 31, wherein the multiplexer is configured to apply space, time, and / or frequency multiplexing.

[0090]

[0151] Aspect 33 of the present specification. The system of aspect 31, wherein the multiplexer is configured to provide an increased detected RF bandwidth.

[0091]

[0152] Embodiment 34 of the present specification The system of embodiment 21, wherein the stripline includes a pair of electrodes, and the parameter of the input RF signal is power or field equivalent voltage across the pair of electrodes.

[0092]

[0153] Embodiment 35 of the present specification The system of embodiment 21, wherein the parameter of the input RF signal is a characteristic of the applied reference signal.

[0093]

[0154] Aspect 36 of the present specification: The system of aspect 21, wherein the controller is further configured to determine the electromagnetic spectrum.

[0094]

[0155] Aspect 37 of the present specification. The system of aspect 36, wherein the controller is further configured to determine power, voltage, communication signal, direction of arrival, and / or combinations thereof.

[0095]

[0156] Aspect 38 of the present specification. The system of aspect 21, wherein the detected response is further based on multidimensional Doppler matching of parameters of multiple laser beams for Doppler-free Rydberg spectroscopy in a gas of excited atoms at or near a homogeneous Rydberg linewidth.

[0096]

[0157] Aspect 39 of the present specification: The system of aspect 38, wherein the multidimensional Doppler matching of parameters of the multiple laser beams includes at least two laser beams positioned at angles that suppress Doppler shift in one, two, and / or three dimensions.

[0097]

[0158] Aspect 40 of the present specification: The system of aspect 39, wherein three laser beams are non-collinear to achieve Doppler matching in two degrees of freedom, or four laser beams are non-collinear to achieve Doppler matching in three degrees of freedom.

[0098]

[0159] Aspect 41 of the present specification: A method for atom-based closed-loop control, the method including: exciting atoms of a gas into one or more Rydberg states; applying one or more signal processing functions to the one or more Rydberg states; and adjusting characteristics of the applied one or more signal processing functions based at least in part on a response of the one or more Rydberg states to the one or more signal processing functions.

[0099]

[0160] Aspect 42 of the present specification. The method of aspect 41, wherein the one or more signal processing functions include a phase-locked loop.

[0100]

[0161] Aspect 43 of the present specification. The method of any one of aspects 41 to 42, wherein the one or more signal processing functions include a Costas loop.

[0101]

[0162] Aspect 44 of the present specification. The method of any one of aspects 41 to 43, wherein the characteristics include electromagnetic field frequency, amplitude, polarization, phase, and / or combinations thereof.

[0102]

[0163] Embodiment 45 of the present specification. The method of any one of embodiments 41 to 44, wherein the one or more signal processing functions include injection locking.

[0103]

[0164] Embodiment 46 of the present specification The method of any one of embodiments 41 to 45, wherein exciting the atom comprises exciting the atom to a lower-lying excited state.

[0104]

[0165] Embodiment 47 of the present specification The method of any one of embodiments 41 to 46, wherein the property comprises a laser frequency, amplitude, and / or polarization involved in exciting or interacting with the atom.

[0105]

[0166] Embodiment 48 of the present specification The method of any one of embodiments 41 to 47, wherein the one or more signal processing functions include automatic level control of the modulated signal from the response of the one or more Rydberg states.

[0106]

[0167] Aspect 49 of the present specification The method of any one of aspects 41 to 48, wherein the adjusting includes effecting processing of baseband or modulated signals for retrieval of analog or digital information from the response of one or more Rydberg states.

[0107]

[0168] Aspect 50 of the present specification is a system for internal quantum state space interference, the system including: an atomic receiver including an atomic vapor having a first atomic state and a second atomic state, the first atomic state coupled by a radio frequency (RF) modulated radio frequency electromagnetic field (RF-EM) and the second atomic state coupled by a second radio frequency (RF) modulated optical electromagnetic field (O-EM); an RF phase interference path between the first and second atomic states bounded by the quantum state space; and a detector configured to detect a readout including an interference signal from the quantum state space, the detected readout configured to provide RF interferometry in the optical and / or quantum domains.

[0108]

[0169] Aspect 51 of the present specification. The system of aspect 50, wherein the first and second radio frequencies comprise a range from DC to THz.

[0109]

[0170] Embodiment 52 of the present specification. The system of any one of embodiments 50 to 51, wherein the second atomic state comprises at least one Rydberg state.

[0110]

[0171] Aspect 53 of the present specification. The system of any one of aspects 50 to 52, wherein the RF phase interference path is configured to be modified by atomic changes, atomic excitations, interactions of the first atomic state with other atoms, interactions of the second atomic state with other atoms, the first atomic state, the second atomic state, RF-EM, O-EM, and / or some combination thereof.

[0111]

[0172] Embodiment 54 of the present specification The system of any one of embodiments 50 to 53, further comprising a transceiver coupled to the detector and configured to transmit and / or receive communication signals.

[0112]

[0173] Aspect 55 of the present specification: The system of any one of aspects 50 to 54, wherein the interference signal comprises optical detection, measurement, and / or imaging of phase, frequency, amplitude, polarization, direction, and / or some combination thereof, of RF electromagnetic waves.

[0113]

[0174] Aspect 56 of the present specification The system of any one of aspects 50 to 55, wherein the interference signal readout comprises an electromagnetic signal, an optical signal, a charge signal, or an electronic signal.

[0114]

[0175] Aspect 57 of the present specification: A method for performing internal quantum state space interference, the method comprising: coupling a first atomic state by a radio frequency (RF) modulated radio frequency electromagnetic field (RF-EM); coupling a second atomic state by a second radio frequency (RF) modulated optical electromagnetic field (O-EM); forming an RF phase interference path between the first and second atomic states that are enclosed by the quantum state space; and detecting an interference signal from the quantum state space.

[0115]

[0176] Embodiment 58 of the present specification. The method of embodiment 57, further comprising parallelizing or multiplexing one or more combinations of optical and radio frequency electromagnetic fields, interference paths, and / or interference signals.

[0116]

[0177] Aspect 59 of the present specification. The method of aspect 58, wherein the multiplexing comprises spatial multiplexing and / or time multiplexing.

[0117]

[0178] Aspect 60 of the present specification The method of any one of aspects 57 to 59, wherein the detecting comprises an optical interference signal carrying a radio frequency modulation, information, or communication signal.

[0118]

[0179] Aspect 61 of the present specification: A system for detecting, imaging, and / or processing atom-based radio frequency (RF) signal waveforms, the system including: a gas of excited atoms comprising one or more Rydberg states; an RF signal waveform interacting with the gas of excited atoms; and a detector configured to detect a readout from the gas of excited atoms based on the RF signal waveform, wherein the detected readout is configured to provide a characteristic of the RF signal waveform.

[0119]

[0180] Aspect 62 of the present specification. The system of aspect 61, wherein the readout comprises a time domain signal or a frequency domain signal.

[0120]

[0181] Aspect 63 of the present specification: The system of any one of aspects 61 to 62, further comprising a processor coupled to the detector, the processor configured to analyze the modulated RF signal and the wave pattern of the detected readout, including the communication protocol, Doppler shift, and / or frequency chirp.

[0121]

[0182] Aspect 64 of the present specification: A method for detecting, receiving, imaging, and processing atom-based radio frequency (RF) signals, the method comprising: exciting atoms of a gas into one or more Rydberg states; interacting at least one electromagnetic field with the excited atoms of the gas to form a structured Rydberg level; interacting at least one RF signal wave with the structured Rydberg level; and detecting the at least one RF signal wave from the excited atoms.

[0122]

[0183] Aspect 65 of the present specification. The method of aspect 64, further comprising analyzing the modulated radio frequency signal and wave patterns including communication protocols, Doppler shifts, and frequency chirps.

[0123]

[0184] Aspect 66 of the present specification: A system for detecting radio frequency (RF) signals, the system comprising: an atomic gas contained within an RF stripline within a vacuum enclosure; an electrical feedthrough coupled to the stripline and configured to inject one or more RF signals into the stripline; and a detector configured to detect a readout of an atomic response to the RF signal in the stripline, the detected readout configured to increase the detection sensitivity of the RF signal.

[0124]

[0185] Aspect 67 of the present specification is an atom-based closed-loop control system, the system including: an atomic receiver configured to receive an input signal, the atomic receiver including one or more Rydberg atoms; a control signal based on a response of the one or more Rydberg atoms to the input signal; and a feedback loop coupled to the control signal and the atomic receiver, the feedback loop regulating one or more process variables of the atomic receiver to a predetermined state or set point.

[0125]

[0186] Aspect 68 of the present specification is an atomic automatic level control (AALC) system, the system including: an atomic receiver configured to receive an input signal, the atomic receiver including one or more Rydberg atoms; a control signal based on a response of the one or more Rydberg atoms to the input signal, the control signal including a baseband signal and / or a carrier signal; and a controller coupled to the control signal and the atomic receiver, the controller configured to adjust one or more laser parameters based on the carrier signal for automatic level control of the baseband signal.

[0126]

[0187] Aspect 69 of the present specification is an atomic phase-locked loop (PLL) system, the system including: an atomic receiver configured to receive an input signal and one or more reference signals, the atomic receiver including one or more Rydberg atoms; a feedback signal based on a response of the one or more Rydberg atoms to the input signal and the one or more reference signals; and an oscillator coupled to the feedback signal and the atomic receiver, the oscillator configured to adjust a frequency and / or a phase of the one or more reference signals to form a phase-locked loop.

[0127]

[0188] Aspect 70 of the present specification is a quantum state space interferometer, comprising: an atomic receiver configured to receive a first input signal and a second input signal, the atomic receiver comprising one or more Rydberg atoms; a closed internal state interference loop based on a first coupling of the first input signal with the one or more Rydberg atoms and a second coupling of the second input signal with the one or more Rydberg atoms; and a detector configured to detect an optical readout based on a response of the one or more Rydberg atoms to the first and second input signals, the second input signal comprising a modulated optical beam.

[0128]

[0189] Aspect 71 of the present specification is an atomic transducer comprising: an antenna configured to collect an input signal; a connector coupled to the antenna and configured to transfer the input signal; an atomic receiver coupled to the connector via an electrode and configured to receive the input signal, the atomic receiver comprising one or more Rydberg atoms; and a detector configured to detect a readout based on a response of the one or more Rydberg atoms to the input signal, wherein the antenna, connector, atomic receiver, and detector comprise a single unit.

[0129]

[0190] Aspect 72 of the present specification: An atomic receiver comprising: an atomic receiver having an antenna, the antenna configured to collect an input signal; an atomic receiver coupled to the antenna and configured to receive the input signal, the atomic receiver comprising one or more Rydberg atoms; an optical input / output (I / O) coupled to the atomic receiver, the optical I / O comprising atom-based closed-loop feedback control based on a response of the one or more Rydberg atoms to the input signal; and an electrical I / O coupled to the atomic receiver, the electrical I / O comprising atom-based closed-loop feedback control based on a response of the one or more Rydberg atoms to the input signal.

[0130]

[0191] Aspect 73 of the present specification is an atomic imager, comprising: an atomic receiver configured to receive an input signal, the atomic receiver comprising one or more Rydberg atoms; an optoelectronic converter coupled to the atomic receiver and configured to receive an optical readout from the atomic receiver, the optical readout comprising an atom-based closed-loop feedback control based on a response of the one or more Rydberg atoms to the input signal; and a signal processor coupled to the optoelectronic converter and configured to receive an electrical readout from the optoelectronic converter, the electrical readout comprising an atom-based closed-loop feedback control based on a response of the one or more Rydberg atoms to the input signal.

[0131]

[0192] Aspect 74 of the present specification relates to an atomic hybrid detector having a stripline, the atomic hybrid detector comprising: a symmetric stripline configured to receive an input signal and a reference signal, the symmetric stripline including a first electrode and a second electrode; and an atomic receiver disposed between the first and second electrodes, the atomic receiver including one or more Rydberg atoms, the symmetric stripline configured to increase local field compression of the input signal and the reference signal at the atomic receiver to provide an optical readout based on a response of the one or more Rydberg atoms to the input signal.

[0132]

[0193] Aspect 75 of the present specification is a multi-field modulation system, comprising: an atomic receiver configured to receive an input signal, a reference signal, and an adjustment signal, the atomic receiver including one or more Rydberg atoms; and a detector configured to detect a readout based on a response of the one or more Rydberg atoms to the input signal and the reference signal, the adjustment signal configured to adjust a Rydberg level structure of the one or more Rydberg atoms for resonant detection of the input signal.

[0133]

[0194] Aspect 76 of the present specification is a Rydberg field probe comprising: a probe including a probe tip; an atomic receiver disposed within the probe tip and configured to receive an input signal, the atomic receiver including one or more Rydberg atoms; a detector configured to detect a readout based on a response of the one or more Rydberg atoms to the input signal; and a control unit coupled to the probe and the detector, the control unit configured to provide control signals to the atomic receiver and to receive the detected readout, wherein the probe, the detector, and the control unit are portable.

[0134]

[0195] Aspect 77 of the present specification is an atomic waveform sampler and spectrum analyzer, comprising: an atomic receiver configured to receive an input signal and a site-selective signal, the atomic receiver comprising one or more Rydberg atoms; and a photodetector array configured to detect optical readouts based on responses of the one or more Rydberg atoms to the input signal and the site-selective signal, the photodetector array configured to perform spatial and / or temporal multiplexing of the detected optical readouts to provide a sampled waveform based on the input signal.

[0135]

[0196] Atom-based quantum sensor technologies offer capabilities beyond those achievable with conventional sensor technologies. Advances in utilizing the properties of individual atoms in Rydberg states using electromagnetically induced transparency (EIT) in atomic gases have provided novel capabilities, for example, in electromagnetic radiation sensing (e.g., detection, measurement, imaging, reception, analog / digital communication, etc.) as well as source generation.

[0136]

[0197] For radio frequency (RF) applications, Rydberg atom-based electromagnetic (EM) radiation detection can provide a combination of performance capabilities beyond those possible with conventional antennas and other solid-state RF detectors, such as ultra-wideband RF detection from DC to sub-THz, a dynamic field range of over 120 dB (e.g., from a field detection threshold of less than 10 mV / m to high-intensity RF fields exceeding 5 kV / m with atomic ionization limits at the MV / m level), and high-resolution RF amplitude, phase, and polarization measurements and imaging.

[0137]

[0198] Over a wide range of RF field amplitudes and frequencies, Rydberg-based measurement methods are rooted in a physical model of atomic-field interactions that relies on invariant atomic parameters and fundamental constants. This allows for a measurement uncertainty of less than 1% for atomic RF fields, with the Planck constant (h = 6.62607015 × 10 -34This enables self-calibrating electric field measurements that are directly traceable to the RF field (J s). This is nearly an order of magnitude improvement over existing antenna standards and has the potential to become the new international atomic RF measurement standard for national metrology institutes around the world.

[0138]

[0199] Hybrid devices that combine conventional RF techniques with Rydberg atom-based EIT detection for enhanced capabilities and novel applications in RF sensing and metrology can also be realized, for example, Rydberg EIT-based communications, including both analog amplitude and frequency modulation and digital communications, as well as pulsed RF detection and measurement.

[0139]

[0200] Advances to date using Rydberg atomic gases and EIT for electromagnetic sensing are based on obtaining an optical (or electrical) readout (e.g., output signal and / or signal beam) of the atomic response to an external electromagnetic radiation field, and from this readout, obtaining information about the external field of interest or relative changes in parameters of the external field.

[0140]

[0201] As described herein, a "readout" is an optical and / or electrical output signal from one or more Rydberg levels (e.g., in an atomic vapor or atomic cell) resulting from the response of the one or more Rydberg levels to an external EM radiation field (e.g., an RF and / or modulated optical field). For example, an "optical readout" is a laser beam or optical signal beam from one or more Rydberg levels resulting from the response of the one or more Rydberg levels to an external EM radiation field (e.g., an RF and / or modulated optical field), which "optical readout" can be detected by a detector (e.g., via a photodetector) and / or transferred and / or converted to an "electrical readout" (e.g., via a photoelectric detector).

[0141]

[0202] The present disclosure demonstrates and develops atomic-based closed-loop devices, systems, and methods for electromagnetic sensing based on using atomic response readout or a derivative thereof to regulate the atomic readout process itself and provide a readout signal for autonomous or semi-autonomous operation with minimal or no human interaction.

[0142]

[0203] An atom-based closed loop includes a set of hardware and / or software functions that can regulate a process variable (e.g., a characteristic of a process) to a desired state or setpoint based on the response of a quantum system or atomic gas. An atom-based closed loop enables the ability to automate sub-functions that can operate a Rydberg atom-based device, such as laser frequency tracking (e.g., "detection") of atomic resonances caused by atoms induced by changing external electromagnetic radiation environments. An atom-based closed loop can also provide new or enhanced performance capabilities in atom-based devices that implement, for example, atomic phase-locked loops (PLLs) and RF frequency tuners.

[0143]

[0204] The present disclosure relates to atomic-based closed-loop apparatus, systems, and methods for electromagnetic radiation measurement, communication, and information processing. For example, an atomic-based closed-loop control system includes a set of hardware and / or software functions that automatically adjust a process variable (e.g., a characteristic of a process) to a desired state or set point based on the response of a quantum system or atomic gas, without any human interaction. Atomic-based closed-loop control can provide new or enhanced performance capabilities in atomic-based devices.

[0144]

[0205] Implementations of atom-based closed-loop control devices, systems, and methods for, for example, electromagnetic radiation detection, measurement, imaging, modulated signal reception, demodulation, and processing with atoms are described in the following embodiments. Exemplary embodiments include atom-based PLLs, in-phase and quadrature (I / Q) frequency and phase recovery loops (Costas loops), atom-based injection locking, automatic baseband level control, modulated baseband processing, and automatic spectral line tracking for atom-based devices.

[0145]

[0206] Implementations in atom-based device hardware automation, such as laser frequency and laser power adjustment, are also presented. Also, quantum state-space interferometers for RF interferometry (DC to THz) in the optical and / or quantum domains are described and demonstrated. Methods and processes for combining atom-based closed-loop control with quantum state-space interferometry, also referred to as atomic RF interferometry, are described, such as RF photonics and optical communications, and radar with subwavelength near-field RF phase and amplitude measurement and imaging, direction finding (RF angle of arrival), and Rydberg atom-based RF phase detection.

[0146]

[0207] Various related atom-based concepts, methods, processes, and systems are also presented, such as atomic automatic level control (AALC), baseband processing, atomic modems (AMODEMs), atom-based RF amplitude, frequency, and / or phase (e.g., for power and / or voltage transducers), and atomic standards. Atom-based closed-loop control devices and implementations may include, for example, atom-based electromagnetic receivers with antenna feeds, atom-based electromagnetic imagers / detectors with closed-loop control for autonomous operation, hybrid atom-based detectors with striplines (e.g., for implementing field compression, multi-field conditioning, parametric amplification, superheterodynes, etc.), and RF waveform samplers and / or spectrum analyzers (e.g., based on atoms using spatial and / or temporal multiplexing of atomic responses to electromagnetic fields).

[0147]

[0208] This disclosure also relates, in part, to AMODEM, including AALC and / or Atomic Baseband Processor (ABP), for conversion and transmission of analog or digital information using, for example, RF-to-optical or RF-to-electrical conversion in atomic gases.

[0148]

[0209] Throughout this disclosure, "RF" can refer to EM radiation at frequencies from DC to THz, and "light" can refer to EM radiation at frequencies above THz to ultraviolet (eg, PHz).

[0149]

[0210] Unlike conventional antenna and receiver technologies, atomic receivers include RF amplitude, frequency, and phase domains specific to the spectroscopic response of atoms (e.g., Rydberg) to incident EM waves. Atomic receivers also accommodate different receiver operating parameters, such as laser frequency and laser power. For example, when extracting a modulated RF signal, the carrier amplitude of the incident modulated RF field may vary with the receiver location due to changes in atmospheric attenuation, the relative distance between the source and receiver, etc. These variations can shift or change the location of the Rydberg line or the laser frequency operating point on the Rydberg line. To account for this, the laser frequency may need to be adjusted according to the atomic response (e.g., AC shift of the line due to carrier field changes) to maintain receiver sensitivity to the signal.

[0150]

[0211] An exemplary implementation of atom-based closed-loop control is an AALC that controls or maintains the output signal level of an atomic receiver. The AALC operates by extracting the signal strength of the incident electromagnetic RF wave from the atomic response and automatically adjusting receiver parameters (e.g., laser frequency, etc.) to maintain the operating point and baseband signal output level within acceptable limits.

[0151]

[0212] In another exemplary implementation of atom-based closed-loop control, the ABP can manage the baseband processing functions of the atomic receiver (e.g., processing the atomic and optical outputs, extracting RF waveforms, extracting signal information from the atomic and optical outputs, etc.) For example, the ABP can extract signal information from the atomic and / or optical outputs by demodulation, such as analog demodulation (e.g., amplitude demodulation (AM), frequency demodulation (FM), phase demodulation (PM), quadrature phase amplitude demodulation (QAM), etc.), digital demodulation (e.g., frequency shift keying (FSK), asymmetric frequency shift keying (AFSK), phase shift keying (PSK), QAM, etc.), hierarchical demodulation (e.g., QAM), spread spectrum waveforms, etc.

[0152]

[0213] The ABP may also provide feedback regarding reference RF modulation parameters of local oscillators (e.g., voltage controlled oscillators (VCOs)) implemented in holographic / heterodyne RF reception for, for example, signal RF wave demodulation, channel selection, analog (e.g., atomic / spectroscopic) and / or digital encoding / decoding, filtering, etc. Holographic / heterodyne RF reception from atom-based devices was previously described in U.S. Application No. 16 / 222,384, filed December 17, 2018, which is incorporated herein by reference in its entirety.

[0153]

[0214] Unlike classical baseband processors, ABPs can perform operations (1) in the atomic medium itself (e.g., direct atom-mediated demodulation of baseband from a modulated RF carrier prior to conversion to an electrical signal or demodulation of the electrical signal), (2) electronically through analog or digital signal processing of the electronic signal from the atomic-EM interaction, or (3) using a combination of the two. Generally, in atomic receivers and transceivers, RF carrier detection and baseband modulation / demodulation can occur in the atomic and optical domains as well as the electronic domain. As a result, certain tasks and controls via AMODEM can be shared and synchronized between the AALC and the ABP.

[0154]

[0215] 1 shows a diagram of an atomic receiver 100. In some embodiments, the atomic receiver 100 can include an atomic cell 106 that encapsulates an atom 107 (e.g., a Rydberg atom), as described in U.S. Application No. 16 / 222,384, filed December 17, 2018, and International Application No. PCT / US2018 / 066006, filed December 17, 2018. These applications are incorporated herein by reference in their entireties.

[0155]

[0216] 2 shows a diagram of an atom-based closed-loop control system 200. The atom-based closed-loop control system 200 can generate a control signal 220 from the response of atoms 107 in the atomic receiver 100 to one or more input signals 210 (e.g., RF signals). The control signal 220 adjusts a process variable 222, which is fed back to the atomic receiver 100 to close the loop. The atom-based closed-loop control system 200 produces an output signal 250 that contains information about the input signals 210 based on the response of the atoms 107 of the atomic receiver 100.

[0156]

[0217] Figure 3A shows a general example implementation of an AALC system 300 for automatic laser parameter adjustment (e.g., frequency and / or power) of an atomic-based device operating based on a control signal 320 from the atomic receiver 100's response to an input signal 310. Figures 3B and 3C show example implementations of an AALC system 300 with automatic laser parameter adjustment of atomic automatic level control in AM baseband reception at the atomic receiver 100.

[0157]

[0218] 4A-4C illustrate example implementations of an atomic PLL system 400, eg, an automatic frequency and / or power level control, a PLL, and a Costas loop, respectively.

[0158]

[0219] 5A-5C show an exemplary implementation of a quantum state-space interferometer 500, e.g., quantum state-space optical RF interferometry, and optical detection and measurement of RF phase using Rydberg EIT in an atomic receiver 100 with cesium atomic vapor.

[0159]

[0220] 6A-6D show exemplary implementations of atomic transducers 600 (eg, RF power / voltage transducers and sensors).

[0160]

[0221] FIG. 7 shows an exemplary implementation of an atomic receiver (eg, an RF receiver) with an antenna 700 with closed-loop control.

[0161]

[0222] FIG. 8 shows an exemplary implementation of an atomic imager 800 (eg, an RF imager / detector) with closed-loop control.

[0162]

[0223] 9A and 9B show an example implementation of a stripline atomic hybrid detector 900 incorporating a symmetric stripline 920 suitable for field compression and increased RF detection sensitivity via atom-based control loops for implementing, for example, PLLs, AALCs, multiple field adjustments, etc.

[0163]

[0224] 10A-10C illustrate an exemplary embodiment of a multi-field tuning system 1000 for multi-field engineering / tuning of Rydberg levels of atom-based RF signal reception for high sensitivity long wavelength (e.g., less than 3 cm) RF reception and reception / imaging of composite RF signal transmissions.

[0164]

[0225] 11A-11F show an exemplary implementation of a Rydberg field probe 1100 for RF waveform imaging and detection with atom-based closed-loop control.

[0165]

[0226] FIG. 12 shows an exemplary implementation of an atomic waveform sampler 1200 for atom-based RF waveform sampling or spectrum analysis using spatial and / or temporal multiplexing of atomic responses to electromagnetic fields.

[0166]

[0227] 13A and 13B show an exemplary implementation of an atomic raster imager 1300 that spatially scans (e.g., rasters) an O-EM beam to selectively read out the phase and / or amplitude of one or more input RF-EM fields from an atomic cell (e.g., from Rydberg atoms located in 1D or 2D). Figure 13A shows a partial top view of the atomic raster imager 1300, and Figure 13B shows a cross-sectional view of the atomic raster imager 1300.

[0167] Exemplary Atomic Receiver

[0228] 1 illustrates an atom receiver 100 according to various exemplary embodiments. The atom receiver 100 can be configured to detect an incident EM field (e.g., an RF / microwave field) and to output a readout signal based on the interaction of the incident EM field with one or more atoms (e.g., Rydberg atoms) within the atom receiver 100. As shown in FIG. 1 , the atom receiver 100 can include an entrance port 102, a probe laser beam 103, a coupler laser beam 104, an atom cell 106, an active measurement volume 110, a fiber 120, a lens 122, a dichroic mirror 130, a beam block 132, a signal beam 134, a quarter-wave plate 140, a polarizing optic 150, and / or a detector (e.g., a photodiode) 160. In some embodiments, the atom cell 106 can encapsulate atoms 107 (e.g., Rydberg atoms) within the vapor cell volume 108, as described in U.S. Application No. 16 / 222,384, filed December 17, 2018 (issued as U.S. Patent No. 10,823,775), and International Application No. PCT / US2018 / 066006, filed December 17, 2018, which are incorporated herein by reference in their entireties.

[0168]

[0229] According to certain embodiments of the present disclosure, a single-sided optically coupled RF sensing element (also referred to herein as an “atom receiver,” “cell,” “vapor cell,” and “atomic vapor cell”) is provided, generally designated by the numeral 100 and described with reference to FIG. 1 . The pen-like linear sensor design shown in FIG. 1 provides for the use of a single inlet port 102 to fiber-optically couple a probe laser beam 103 and a coupler laser beam 104 into and out of a vapor cell volume 108 contained within an atom cell 106. The vapor cell volume 108 contains an atomic or molecular gas (e.g., cesium (Cs), rubidium (Rb), etc.). The region of gas within the vapor cell volume 108 is probed by the probe laser beam 103 and the coupler laser beam. In some embodiments, the atoms 107 may include one or more highly excited Rydberg atoms. In some embodiments, the probe laser beam 103 may have an optical wavelength (λ) of about 780 nm, and the coupler laser beam 104 may have an optical wavelength (λ) of about 480 nm.

[0169]

[0230] 1 leaves the active measurement volume 110 unobstructed to incident EM fields 112 (e.g., RF / microwave fields) from all sides except one, when the atom receiver 100 enters the active measurement volume 110 from a single side. In some embodiments, as shown in FIG. 1, the linearly polarized probe laser beam 103 and coupler laser beam 104 are sent through a single polarization-maintaining fiber 120 and collimated by a lens 122 to a full width at half maximum (FWHM) of approximately 200 μm within the atom cell 106. The probe laser beam 103 and coupler laser beam 104 co-propagate through the atom cell 106, with the probe laser beam 103 then selectively reflected back through the atom cell 106 by a dichroic mirror 130 (e.g., a short-pass dichroic mirror coating), while the coupler laser beam 104 passes through and is blocked by a beam block 132 (e.g., a thin dielectric absorber beam block).

[0170]

[0231] The signal beam 134 (e.g., the retro-reflected probe beam) retraces its path, overlaps with the outgoing coupler laser beam 104, and is recombined back into the fiber 120 by the lens 122. In some embodiments, a quarter-wave plate 140 can be positioned before the retroreflection (e.g., between the lens 122 and the atomic cell 106 in FIG. 1 ) to ensure that the linearly polarized incoming probe laser beam 103 is rotated 90 degrees on the signal beam 134 (e.g., the retro-reflected outgoing beam) so that the signal beam 134 can be selectively separated by a polarization-selective element 150 (e.g., a polarizing beam splitter) after the polarization-maintaining fiber 120 for readout (e.g., optical readout, electrical readout, etc.). For example, the atomic receiver 100 can output the signal beam 134 as an optical input signal (e.g., optical readout) to another device and / or system. For example, as shown in FIG. 1, a detector (eg, a photodiode) 160 can receive the signal beam 134 and output an electrical signal 162 (eg, an electrical readout) based on the received optical signal (eg, the signal beam 134).

[0171]

[0232] The atomic receiver 100 shown in FIG. 1 can offer several advantages over other implementations of vapor cell EIT. First, the linear, single-sided design allows for a compact, low-profile probe tip and sensor element with a small dielectric footprint. This design also eliminates the need for optical elements to redirect the light beam from the fiber into the cell. Utilizing a single lens for input and output coupling of larger beam diameters compared to other implementations of vapor cell EIT can improve measurement accuracy and sensitivity by providing less interaction time spread and higher achievable spectral resolution, as well as improve operational stability by reducing device sensitivity to misalignment by back-coupling the readout probe beam into the same fiber.

[0172] Exemplary Atom-Based Closed-Loop Control System and Method

[0233] 2 illustrates an atom-based closed-loop control system 200 according to various exemplary embodiments. The atom-based closed-loop control system 200 can be configured to automatically adjust one or more process variables 222 to a desired state or states or setpoints based on the response of the atoms 107 of the atomic receiver 100. The atom-based closed-loop control system 200 further produces an output signal 250 that includes information about the input signal 210 (e.g., an EM / RF field) based on the response of the atoms 107 of the atomic receiver 100.

[0173]

[0234] 2, atom-based closed-loop control system 200 can include an input signal 210 (e.g., an EM / RF field), an atomic receiver 100 having an optical readout 134 and / or an electrical readout 162, a control signal 220, a process variable 222, and / or an output signal 250 (e.g., an EM / RF field). In some embodiments, process variable 222 can include frequency, amplitude, polarization, phase, power, and / or some combination thereof. For example, process variable 222 can include a laser process variable (e.g., probe laser beam 103, coupler laser beam 104, etc.), an EM field (e.g., RF) process variable (e.g., input signal 210, etc.), and / or some combination thereof.

[0174]

[0235] In some embodiments, the atom-based closed-loop control system 200 can include an RF input signal 210 and an RF output signal 250. For example, the atom-based closed-loop control system 200 can automatically adjust one or more process variables 222 to a desired state or states or setpoints based on the response of the atoms 107 of the atomic receiver 100 to achieve an RF output signal 250 that is informative about the RF input signal 210.

[0175]

[0236] In an atomic receiver (e.g., atomic receiver 100), there are RF carrier amplitude, frequency, and phase regions that are characteristic of the spectroscopic response of atoms (e.g., atoms 107) to an incident wave (e.g., RF input signal 210) and correspond to different linearity ranges, laser, and / or hardware operating parameters. In an exemplary embodiment, atom-based closed-loop control system 200 can use the spectroscopic atomic response such that, for a weak carrier wave (e.g., RF input signal 210), atom-based closed-loop control system 200 can operate the laser frequency (e.g., probe laser beam 103) of atomic receiver 100 at an operating point where baseband sensitivity is maximized. For example, as the carrier field increases, atom-based closed-loop control system 200 can automatically adjust the operating point of the laser frequency (e.g., probe laser beam 103) of atomic receiver 100 via the control signal 220 and process variable 222 feedback loop to where the same baseband sensitivity remains maximized. In this manner, atom-based closed-loop control system 200 can increase baseband bandwidth, sensitivity, and / or dynamic range.

[0176]

[0237] In some embodiments, other parameters of atomic receiver 100 may also be adjusted by atom-based closed-loop control system 200 to obtain and control baseband signal levels for RF carrier field amplitude, frequency, and / or phase dependent spectral responses. For example, atom-based closed-loop control system 200 may adjust laser center frequency, laser modulation, RF modulation, AM, FM, PM, power, atomic gas temperature and / or density, amplifier gain in electronic baseband processing components, and / or some combination thereof.

[0177]

[0238] In some embodiments, the atom-based closed-loop control system 200 can provide control of parameters of the atomic receiver 100 for simultaneous signal searching on one or more carriers. In some embodiments, the atom-based closed-loop control system 200 can control laser parameter (e.g., amplitude, frequency, phase) modulation, shifting, switching, spatial and / or frequency multiplexing (e.g., to access different atoms or atomic states in a multi-channel signal reception operation), and / or some combination thereof.

[0178]

[0239] In some embodiments, the atomic receiver 100 can include an aerogel atomic vapor cell for atomic electromagnetic field sensing applications. For example, the atomic cell 106 of the atomic receiver 100 can incorporate atoms 107 (e.g., atomic gas or vapor) within an aerogel to provide storage of the atoms 107 in an optically transparent medium. In some embodiments, the aerogel of the atomic cell 106 can be configured for Rydberg spectroscopy, where there is minimal variation in the dielectric constant of the material at RF wavelengths throughout the structure. In some embodiments, the aerogel of the atomic cell 106 can be configured to provide structural stability for embedded applications.

[0179] Exemplary Atomic Automatic Level Control (AALC) Systems and Methods

[0240] 3A-3C illustrate an AALC system 300 according to an example embodiment. The AALC system 300 can be configured to provide atomic-based device operation and automatic level control in the atomic receiver 100. The AALC system 300 can further be configured to adjust the baseband signal 323 and automatically adjust laser parameters 332 (e.g., frequency and / or power) for automatic level control in AM baseband signal reception. In some embodiments, the AALC system 300 can include an atomic receiver such as that described in "An atomic receiver for AM and FM radio communication," David A. Anderson et al., arXiv:1808.08589v1, published August 26, 2018, pages 1-6 (see Appendix L), which is incorporated herein by reference in its entirety. In some embodiments, the AALC system 300 can be similar to the atomic-based closed-loop control system 200 shown in FIG. 2.

[0180]

[0241] As shown in FIG. 3A , the AALC system 300 can include an input signal 310 (e.g., an EM / RF field), an atomic receiver 100 having an optical readout 134 and / or an electrical readout 162, a control signal 320, a laser controller 330, a laser process variable 332 (e.g., frequency and / or power), and / or an output signal 350 (e.g., an EM / RF field). In some embodiments, the laser controller 330 can receive the control signal 320 and adjust one or more laser process variables 332, such as the laser frequency and laser power (e.g., the probe laser beam 103, the coupler laser beam 104, etc.). In some embodiments, the control signal 320 can be derived from the response of the atoms 107 of the atomic receiver 100 to the input signal 310. For example, the laser frequency 332 can be adjusted by the laser controller 330 for automatic level control in AM baseband signal reception using the atomic receiver 100.

[0181]

[0242] 3B, the control signal 320 may include a high-pass filter 321, a low-pass filter 322, a baseband signal 323, a carrier signal 324, an amplifier 325 (e.g., gain), a linearizer 326 (e.g., to increase efficiency and / or power), and / or linearized baseband signals 327, 328. In some embodiments, the linearizer 326 may send the linearized baseband signal 327 to the amplifier 325 and send the linearized baseband signal 328 to the laser controller 330.

[0182]

[0243] The AALC system 300 can accept an electrical readout 162 from the signal beam 134 of the atomic receiver 100 (e.g., via a detector (e.g., photodiode) 160). In some embodiments, the electrical signal 162 can be obtained directly from the detector (e.g., photodiode) 160 of the atomic receiver 100, or after additional signal pre-amplification or conditioning. The AALC system 300 can split the electrical readout 162 through a high-pass (AC) filter 321 and a low-pass (DC) filter 322 to separate the baseband signal 323 (AC) and carrier signal 324 (DC) components, respectively. In some embodiments, the electrical readout 162 (e.g., the optical input signal) can be filtered, e.g., by a Δ 510 = 0MHz (e.g., Cesium (Cs) 47S 1 / 2 From 47 pages 1 / 2 Laser detuning of resonance Δ 510 3C for a fixed laser operating point 332 at 37.4 GHz (37.4 GHz). For example, the electrical readout 162 can be filtered into separate signal channels, a baseband signal 323 and a carrier signal 324, by high-pass filter 321 and low-pass filter 322, respectively.

[0183]

[0244] In some embodiments, the carrier signal 324 may be sent through a linearizer 326 to convert the nonlinear carrier signal 324 across different carrier intensity ranges of the atomic response to an amplifier 325 for adjustment (e.g., gain adjustment) of the baseband signal 323 in the output amplification stage. For example, the linearizer 326 may receive the carrier signal 324 and search for carrier-dependent baseband gain (e.g., changes in the carrier signal 358) that can result in an increase in amplifier performance (e.g., linearized baseband signal 327) in the baseband signal 323, which may affect automatic level control (ALC).

[0184]

[0245] 3C, the electrical readout 162 may include the baseband signal 323, the carrier signal 324, the laser operating point 332, the measured optical signal 352, the laser detuning 354, the Rydberg spectral line 356, and / or the carrier signal change 358. The electrical readout 162 may include the Cs47S signal in the atomic receiver 100. 1 / 2 The optical signal 352 (e.g., amplitude) is shown versus laser detuning 354 around the Rydberg EIT line. Three outputs 356, 324, and 323 are shown versus frequency offset 354 (e.g., laser detuning) of one of the atom probe lasers 103 and 104. The RF-free Rydberg spectral line (black) is labeled 356, and the Cs47S 1 / 2 From 47 pages 1 / 2 The Rydberg spectral line (blue) with an unmodulated 37.4 GHz RF carrier at a fixed field intensity resonance resonant with the transition 232 to 37.4 GHz is labeled 324, and the Rydberg spectral line 222 (red) with a carrier amplitude modulated (AM) at a baseband frequency of 1 kHz with a modulation depth of + / - 25% is labeled 323. The dot indicates the laser frequency operating point 332. Also shown is the carrier signal variation 358 at the center laser frequency point 332 due to an input signal 310 (e.g., a carrier RF signal) having an electric field of, for example, 5.9 V / m.

[0185]

[0246] In one exemplary embodiment, the AALC system 300 may be configured to detect, for example, cesium (Cs) 47S. 1 / 2From 47 pages 1 / 2 This can be used to perform AM audio reception on a 37.4 GHz carrier using an atomic receiver 100 operating at the Rydberg transition to . For example, as shown in Figure 3C, electrical readout 162 can be derived from the optical readout (e.g., signal beam 134) of an atomic receiver 100 (e.g., a room temperature Cs atomic vapor cell receiver) operating at a fixed laser power as a function of laser frequency (e.g., via laser controller 330) for a particular 37.4 GHz RF carrier field and an AM transmitted 1 KHz baseband signal.

[0186] Exemplary Atomic Phase Locked Loop (PLL) Systems and Methods

[0247] 4A-4C illustrate an atomic PLL system 400 according to various exemplary embodiments. The atomic PLL system 400 may be configured to provide automatic frequency and / or power level control to an oscillator 420. The atomic PLL system 400 may further be configured to form a phase-locked loop (PLL) for synchronous FM and / or PM signal reception. The atomic PLL system 400 may further be configured to form a Costas loop for carrier frequency and phase recovery.

[0187]

[0248] 4A , the atomic PLL system 400 may include an input signal 410 (e.g., an EM / RF field), an atomic receiver 100 having an optical readout 134 and / or an electrical readout 162, an oscillator 420, an oscillator variable 422, and / or an output signal 450 (e.g., a voltage signal). In some embodiments, the oscillator 420 may be a voltage-controlled oscillator (VCO). In some embodiments, the oscillator variable 422 may include a frequency, an amplitude, a voltage, a phase, a power, and / or some combination thereof. For example, the oscillator variable 422 may include a frequency, an amplitude, a voltage, and / or some combination thereof.

[0188]

[0249] In some embodiments, the atomic PLL system 400 can include an RF input signal 410 and a voltage output signal 450. For example, the atomic PLL system 400 can automatically adjust one or more oscillator variables 422 to one or more desired states or one or more set points based on derived responses of the atoms 107 of the atomic receiver 100 to achieve a voltage output signal 450 that renders information about the RF input signal 410.

[0189]

[0250] 4B, oscillator 420 may include a reference wave 422, a VCO 424, an amplifier 426, a difference signal 427, and / or a filter 428. In some embodiments, oscillator 420 may be configured to form a PLL for synchronous frequency modulated or phase modulated signal reception. Input signal 410 is S(t)=E s cos[ω s t+θ s (t)], and d / dtθ s (t)=2πk s m s (t), where m s (t) = phase change / modulation. The reference wave 422 is r(t) = E r cos[ω r t+θ r (t)], and d / dtθ r (t)=2πk r v r (t), where v r (t)=A G A in cos[Φ(t)]. The input signal 410 and the reference wave 422 can interact with the atoms 107 of the atomic receiver 100, which is the parametric gain of the atoms 107 (e.g., amplified using parametric nonlinearity and the pump wave), a(t)=S(t)+r(t)=E~(E s E r ) 1 / 2For example, atom 107 under the influence of input signal 410 and reference wave 422 can operate as an optical parametric oscillator (e.g., a harmonic oscillator whose parameters oscillate in time).

[0190]

[0251] The optical readout 134 (e.g., a(t)) from the atom 107 contains the difference phase / frequency of S(t) and r(t), defined as v(t). The optical readout 134 can be converted to an electrical readout 162 by a photodetector 160 in the atomic receiver 100. The electrical readout 162 is given by e(t)=A in cos[Φ(t)], and A in =A·(E s E r ) 1 / 2 +Ai and Φ(t)=θ s (t)-θ r (t)-π / 2, where A = electric field (E) to voltage (V) factor, and Ai = signal-to-noise ratio (SNR) from other atomic readout methods. G The difference signal 427 can be defined as v(t)=A G A in cos[Φ(t)]. The difference signal 427 may be sent to a filter 428 (e.g., a loop filter, an adaptive loop filter, a bandpass filter, a notch filter, etc.) that processes the difference signal 427 for adjusting the phase (or frequency) of a voltage controlled oscillator (VCO) 424. The VCO 424 controls the phase (or frequency) of the reference wave 422 at the atom 107, thereby closing the loop. The closed loop outclock output signal 450 is V out (t)=(K / 2πk r )·cos[Φ(t)]=(k s / k r )·m s (t), where K=2πk r A G A in (e.g., loop gain).

[0191]

[0252] In some embodiments, filter 428 can provide various outputs, such as a channel-selectable bandpass AC output for an analog or digitized VCO tuning signal, a baseband modulation signal (e.g., AFSK, FSK, PSK, etc.) included in input signal 410, a low frequency AC output for adjusting the laser frequency to track S(t), atomic spectral lines and / or maintain / level baseband readout of variations in S(t) and r(t), other peripheral atomic-based closed loops, and / or some combination thereof.

[0192]

[0253] In some embodiments, the VCO 424 may have an adjustable output level and, in a closed control loop, adjusts the amplitude (E r This parametric amplification (e.g., amplified using parametric nonlinearity and a pump wave) can be adjusted by, for example, the signal strength of the electrical readout 162, e(t), the optical laser frequency / power, and / or any combination of these and other adjustment signals.

[0193]

[0254] In some embodiments, the atomic PLL system 400 may include modifications and adaptations, for example, incorporating analog and / or digital filtering at the atom 107 location and / or analog and / or digital baseband signal processing, by adjusting process variables, for example, the amplitude, polarization, frequency, and / or phase of a laser (e.g., probe laser beam 103) and / or additional external DC or AC electromagnetic field (e.g., input signal 410) interacting with the atom 107.

[0194]

[0255] In some embodiments, a (square law) photodetector (e.g., detector (e.g., photodiode) 160) measures the optical power change (e.g., E at atom 107). 2 t) can be converted into an electrical readout 162 (e.g., an electronic error signal e(t)). 2and A in ) may be modified accordingly. In some embodiments, the atomic responses to S(t) and r(t), which have a frequency difference of, for example, 1 kHz, may be subject to VCO 424 control and may induce interference responses from atoms 107. In some embodiments, as shown in FIG. 4C, VCO 424 may include reference wave 422a and second reference wave 422b.

[0195]

[0256] 4C, the oscillator 420 may include a reference wave 422a, a second reference wave 422b, a VCO 424, an amplifier 426, a difference signal 427, and / or a filter 428. In some embodiments, the oscillator 420 may be configured to form a Costas loop for carrier frequency and phase recovery. In some embodiments, the atomic PLL system 400 may provide injection locking at the atom 107 (e.g., the second oscillator may capture the first oscillator, so that both have the same frequency). For example, the input signal 410 and the reference wave 422a may undergo injection locking at the atom 107 due to strong coupling and similar reference frequencies.

[0196]

[0257] In some embodiments, the input signal 410 may be demodulated (e.g., mixed down and low-pass filtered) by the atoms 107 using both the in-phase (I) wave r(t) and the quadrature / out-of-phase (Q) wave r(t), respectively, generated by the VCO 424. The optical readout 134 from the atoms 107, including the I / Q demodulated signal, may be detected by the photodetector 160, which combines these signals to generate a control signal for the input signal of the VCO 424, closing the loop.

[0197]

[0258] In some embodiments, the atomic PLL system 400 may be similar to the atomic PLL system 400 shown in FIG. 4B, with the addition of a second reference wave 422b. For example, the input signal 410 may be S(t)=E s cos[ω s t+θ s (t)], and d / dtθs (t)=2πk s m s (t), where m s (t) = phase change / modulation. The reference wave 422a is r(t) = E r cos[ω r t+θ r (t)], and d / dtθ r (t)=2πk r v r (t), where v r (t)=A G A in cos[Φ(t)]. The second reference wave 422b is r2(t)=E r2 sin[ω r t+θ r The input signal 410, the reference wave 422a, and the second reference wave 422b can interact with the atoms 107 of the atomic receiver 100, which can be defined as a r (t)=S(t)+r(t)+r2(t)=E~(E s (E r E r2 ) 1 / 2 ) 1 / 2 The optical readout 134 from the atom 107 (e.g., a r (t)) is v r The optical readout 134 includes the differential phase / frequency of S(t), r(t), and r(t), defined as e(t). The optical readout 134 can be converted to an electrical readout 162 by a photodetector 160 in the atomic receiver 100. The electrical readout 162 is e r (t)=A in cos[Φ(t)]sin[Φ(t)]=(1 / 2)A in 2 sin[2Φ(t)], and A in =A·(E s (E r E r2 ) 1 / 2 ) 1 / 2 +Ai and Φ(t)=θ s (t)-θ r (t)-π / 2. The amplifier 426 is A G, which is the gain. The difference signal 427 is v r (t)=(1 / 2)A G A in 2 sin[2Φ(t)]. The difference signal 427 can be sent to a filter 428 (e.g., equivalent to a specialized loop filter) that processes the difference signal 427 for adjusting the phase (or frequency) of the VCO 424. The VCO 424 controls the phase (or frequency) of the reference wave 422a and the second reference wave 422b at the atom 107, thereby closing the loop.

[0198]

[0259] In some embodiments, using the principles of the atomic PLL system 400 described above, injection locking (e.g., the second oscillator captures the first oscillator, so that both have the same frequency) of two signals (e.g., S(t), r(t), r2(t)) mediated by the atomic response in a closed loop naturally follows. For example, injection locking and / or injection pulling can occur between the two signals S(t) and r(t), whereby the atomic PLL system 400 locks and / or pulls the frequency of r(t) to match the frequency of S(t) through the atomic response. As injection locking occurs, pulling and pushing of the S(t) and r(t) signal frequencies occurs due to the cross-coupling of the two oscillators by the atoms 107 and the parameters of the filter 428 in the atomic PLL system 400.

[0199] Exemplary quantum state-space interferometer

[0260] 5A-5C illustrate a quantum state space interferometer 500 according to various exemplary embodiments. The quantum state space interferometer 500 can be configured to provide radio frequency (DC to THz) interferometry in the optical and / or quantum domains. The quantum state space interferometer 500 can also be configured to provide optical RF phase detection and measurement with Rydberg atomic vapor. In some embodiments, the quantum state space interferometer 500 can use a fiducial reference phase (e.g., from a second electromagnetic wave, e.g., an RF wave or an optical beam with RF phase modulation) and atomic gas for RF phase detection as described in International Application No. PCT / US2018 / 066006, filed December 17, 2018, which is incorporated herein by reference in its entirety.

[0200]

[0261] As shown in FIG. 5A, quantum state-space interferometer 500 can include a first input signal 510 (e.g., an EM / RF field), an atom receiver 100, a second input signal 520 (e.g., an EM / RF modulated optical beam), a third input signal 530 (e.g., an EM / RF field or an EM / RF modulated optical beam), and / or an optical readout 550. In some embodiments, quantum state-space interferometer 500 can utilize all-optical RF phase detection, which can use a closed interference loop within the internal state space of the atoms. For example, the driving field can be a modulated optical field (e.g., second input signal 520) with a reference phase (e.g., a predetermined or selected) and an external RF field (e.g., first input signal 510) whose phase and amplitude are to be detected or measured. The closed interference loop exhibits quantum interference between two optical excitation paths (e.g., an interference path of RF phase 515) within the Rydberg state space. Thus, the EIT response of the atoms senses the signal phase and amplitude, allowing for an all-optical readout (eg, optical readout 550) of the RF phase and amplitude.

[0201]

[0262] In some embodiments, the second input signal 520 may comprise an RF wave modulated with respect to optical phase (e.g., an RF-modulated probe laser beam 103). In some embodiments, the quantum state space interferometer 500 may be based on the interaction of the first RF wave 510 and the second reference RF wave 520 with the atoms 107 of the atomic receiver 100 to produce an optical readout 550 from the atoms 107.

[0202]

[0263] In some embodiments, closed-loop control can be implemented between different combinations of the atomic receiver 100, the optical readout 550, the first input signal 510, and / or the second input signal 520 for different purposes. For example, an atom-based PLL (e.g., similar to the atomic PLL system 400 shown in FIGS. 4A-4C ) can be realized by controlling the RF phase modulation of the optical beam of the second input signal 520 using a VCO drive signal (e.g., the reference wave 422 from the VCO 424) that is modulated by a control signal derived from the optical readout 550 from the atomic receiver 100. For example, as shown in FIG. 5A , the RF signal of the first input signal 510 can be modulated by the optical readout 550 from the atomic receiver 100. In some embodiments, the RF signal of the first input signal 510, the RF signal of the second input signal 520, and / or other signal fields can be modulated and / or synchronized with each other and / or with the optical readout 550 that provides the output from the loop. For example, as shown in FIG. 5A, quantum state space interferometer 500 may include a third input signal 530 that may interact with atoms 107 of atomic receiver 100.

[0203]

[0264] 5B, quantum state space interferometer 500 can utilize a first atomic state |1>501, a second atomic state |2>502, a third atomic state |3>503, a fourth atomic state |4>504, and / or a zeroth atomic state |0>505. Atomic states |2>502 and |3>503, and atomic states |3>503 and |4>504, are each electric dipoles coupled by a radio frequency electromagnetic field (e.g., first input signal 510). Atomic states |1>501 and |2>502, and atomic states |1>501 and |4>504, are each coupled by an optical electromagnetic field that is phase modulated near a radio frequency (e.g., third input signal 520). Interference paths of RF phase 515 closed by the quantum state space are formed between atomic states |1> 501, |2> 502, and |4> 504 (e.g., |1> to |2>, |1> to |4>, |2> to |1>, |2> to |4>, |4> to |1>, |4> to |2>). An optical field (e.g., optical readout 134 of atomic receiver 100) coupling atomic state |0> to |1> can provide an optical readout 550 from quantum state space interferometer 500.

[0204]

[0265] 5C, the optical readout 550 can include a laser frequency offset 552, a phase angle 554, and / or a transmission change 556. In some embodiments, as shown in FIG. 5C, the quantum state space interferometer 500 can employ the optical domain for all-optical RF phase and frequency detection (e.g., for applications in the RF domain) and / or optical RF phase and frequency detection (e.g., for applications in the optical domain). For example, the RF reference phase is mediated via a modulated laser beam (e.g., second input signal 520) rather than via an RF reference wave.

[0205]

[0266] In some embodiments, the optical readout 550 can provide optical detection and measurement of the phase of the RF field. For example, as shown in FIG. 5C , a plot shows the optical (EIT) readout 550 from Cs Rydberg atoms in a vapor cell to which an external 5 GHz RF signal field is applied versus the optical laser frequency (vertical axis) and the optical RF phase at 5 GHz (horizontal axis) generated by electro-optic phase modulation of the optical laser beam. This plot shows that the optical (EIT) readout 550 at a specific fixed frequency of the EIT laser (e.g., probe laser beam 103) exhibits a strong modulation that reveals the phase of the RF-modulated optical phase relative to the fixed external RF phase. Similarly, external RF phase changes can be detected relative to the fixed RF-modulated optical phase.

[0206]

[0267] In some embodiments, quantum state-space interferometer 500 can exploit the sensitivity of Rydberg atoms to RF electric fields across the electromagnetic spectrum from DC to THz to realize new capabilities in RF and atom-based quantum RF field sensors and devices. For example, quantum state-space interferometer 500 can be configured as an all-optical RF phase detector based on Rydberg atomic vapor. In some embodiments, quantum state-space interferometer 500 can provide an RF E-field standard, a broadband SI-traceable absolute (atomic) standard for RF electric fields at national metrology institutes. For example, quantum state-space interferometer 500 can be implemented in commercially available RF detection and measurement equipment (e.g., near-field / far-field mapping, synthetic aperture radar (SAR), communications, phased array antenna characterization, 5G receivers, phase detection, heterodyning, phase referencing, parametric amplification, etc.).

[0207]

[0268] In some embodiments, quantum state space interferometer 500 can employ an effective RF reference via appropriate electro-optic modulation of a laser beam used to read out the Rydberg atom's response to the measured field. For example, a modulated laser field is employed in Rydberg atom RF detection (e.g., atom receiver 100), providing the atoms with an efficient means of using the same optical field as the RF reference carrier, eliminating the need for any external RF source, such as an antenna. In some embodiments, quantum state space interferometer 500 can provide the atoms with a phase-stable, interference-free RF reference. For example, quantum state space interferometer 500 can operate without an antenna.

[0208]

[0269] In some embodiments, the quantum state space interferometer 500 may include a spatially selective optical RF phase reference on a sub-mm length scale. For example, a dense grid of sensor atoms (e.g., atoms 107) may be probed with an optical reference beam (e.g., second input signal 520) that varies from one grid point to the next. In some embodiments, the quantum state space interferometer 500 may include optical spatial resolution for broadband RF phase and amplitude sensing. For example, the quantum state space interferometer 500 may implement parallelization and / or miniaturization based on the optical spatial resolution.

[0209] Exemplary Atomic Transducers

[0270] 6A-6D illustrate an atomic transducer 600 according to various exemplary embodiments. The atomic transducer 600 can be configured to detect and measure incident EM fields (e.g., RF fields) based on atomic spectroscopy of field-sensitive atomic states in the atomic receiver 100, or physical quantities derived from measurements of RF fields, such as DC or AC voltages across parallel-plate electrodes 620 precisely positioned at a fixed, known distance. The electrode distance can be actively stabilized to a known, accurate, and precise set distance by an optical interferometric positioning system relative to the atomic transition wavelength of a reference laser, resulting in an all-atom voltage standard. The atomic transducer 600 can be further configured to provide ultra-high bandwidth (e.g., DC to THz) and absolute (atomic) measurements of RF power and / or voltage. The atomic transducer 600 can be further configured to provide high-sensitivity RF signal detection, for example, in a compact unit easily adaptable to various RF receivers and circuits. The atomic transducer 600 can be further configured to provide voltage or power measurements and standards traceable to atomic properties and fundamental constants.

[0210]

[0271] As shown in FIG. 6A , atomic transducer 600 may include atomic receiver 100, electrode 620, connector 630, absorber 640, antenna 650 for detecting radiation 652, detector (e.g., photodiode) 660, and / or electrical readout 670. In some embodiments, atomic receiver 100 of atomic transducer 600 may include a small, cylindrical cesium (Cs) vapor cell (e.g., similar to atomic cell 106) having an integral internal electrode 620 with, for example, a wire connection to connector 630. In some embodiments, electrodes 620 may be spaced apart (e.g., 4 mm apart) thick rings (e.g., 0.5 mm thick), each fused to the cell body (e.g., atomic cell 106), with, for example, one electrode side disposed inside the cell and another electrode side disposed outside the cell (e.g., outside the cell window). For example, the total path length through the cell may be approximately 5 mm. In some embodiments, the inner and outer diameters of the cell may be approximately 3.4 mm and 5 mm, respectively, while the inner and outer diameters of the electrode rings 620 may be approximately 2 mm and 5 mm, respectively. For example, two 0.7 mm thick ring electrodes 620 may be embedded within the vapor cell to provide external electrical connections to connectors 630 (e.g., SMA connectors).

[0211]

[0272] In some embodiments, detection of radiation 652 (e.g., microwave) can be performed via spectroscopic measurement of Autler-Townes (AT) splitting (e.g., dynamic Stark effect) in atomic receiver 100. AT splitting occurs when an oscillating electric field (e.g., laser) is tuned to a resonance (or near-resonance) of a spectral line, which changes the shape (e.g., splits) of the absorption / emission spectrum. For example, a probe laser beam 103 having a wavelength (λ) of about 852 nm, a power of about 8 mW, and a FWHM of about 333 microns counter-propagates with a coupler laser beam 104 having a wavelength (λ) of about 510 nm, a power of about 100 mW, and a FWHM of about 394 microns. The probe laser beam 103 is 6S 1 / 2 F=4→6P 3 / 2 The coupler laser beam 104 can be tuned to a cyclic transition of F'=5 while the coupler laser beam 104 is tuned to a 6P3 / 2 →39D 5 / 2 This beam configuration induces EIT in the atomic receiver 100, which can be read out (e.g., electrical readout 670) by monitoring absorption in the probe laser beam 103 using a detector (e.g., photodiode) 660. 5 / 2 →40P 3 / 2 The presence of 12.599 GHz microwaves 652 resonating with the transition can induce AT splitting in the spectroscopic signal.

[0212]

[0273] In some embodiments, microwaves 652 may be generated by signal generator 632 and transmitted by microwave horn antenna 654. In some embodiments, a microwave amplifier 634 (e.g., 45 dB) may be inserted in line before microwave horn 654 for most measurements. For example, the output of signal generator 632 may be set to −4 dBm (near the saturation point of amplifier 634). In some embodiments, amplifier 634 may be omitted. For example, the output of signal generator 632 may be set to +24 dBm.

[0213]

[0274] In some embodiments, microwaves 652 can propagate through free space, where they can be detected by a second receiving antenna 650. As shown in Figure 6A, antenna 650 can be connected to electrode 620 in atomic receiver 100 (e.g., a Cs vapor cell) via connector 630 (e.g., an SMA cable). In some embodiments, atomic receiver 100 can be placed inside absorber 640 (e.g., a microwave-absorbing foam box) to shield the atomic Cs vapor from external microwaves incident on the vapor cell, such that only microwaves 652 collected by receiving horn 650 and transmitted through SMA cable 630 are introduced into the atomic vapor.

[0214]

[0275] As shown in FIG. 6B, the atomic transducer 600 can be implemented in a compact unit. For example, the atomic receiver 100 can be integrated with a connector 630, such as an SMA connector. In some embodiments, to make the connection, a wire is wrapped around the circumference of each electrode 620 and glued in place using conductive ink. For example, a wire attached to one electrode 620 can be connected to a signal pin 631, while the other is connected to a ground pin 633 of the SMA connector 630.

[0215]

[0276] In some embodiments, atomic transducer 600 may include an atom-based optical RF power / voltage transducer and sensor and remote detection. In some embodiments, atomic transducer 600 may use an atomic vapor integrated with electrodes 620, RF waveguides, or similar structures for injection and / or field-mode compression of an RF signal of interest into the vapor, from which the RF electric field is detected or measured via field-sensitive atomic state spectroscopy. In some embodiments, atomic transducer 600 may provide direct conversion of an RF electrical signal to an atom-mediated readout 670. In some embodiments, atomic transducer 600 may provide ultra-high bandwidth (DC to THz) absolute (atomic) measurement of RF power or voltage. In some embodiments, atomic transducer 600 may provide high-sensitivity RF signal detection in a compact unit easily adaptable to a variety of RF receivers and circuits. In some embodiments, atomic transducer 600 may be employed in remote detection of microwaves 652. 6A, the atomic receiver 100 can consist of a cesium vapor cell with an integrated electrode 620 attached directly to a microwave horn receive antenna 650 via SMA cables 631, 633. For example, a spectroscopic Rydberg EIT readout 670 of the vapor cell can be used to determine the field equivalent power of the microwaves 652 detected by the horn 650.

[0216]

[0277] As shown in FIG. 6C, the electrical readout 670 of the atomic transducer 600 can detect the electric field dependence 676 of the atomic transducer 600 as a function of the distance 674 between the transmitting antenna 654 and the receiving antenna 650 to test the remote detection of the atomic transducer 600. For example, the receiving antenna 650 may be mounted in a fixed position and connected to the vapor cell electrode 620 with an SMA cable 630, while the transmitting antenna 654 may be on a movable stand pointed directly at the receiving antenna 650. The distance 674 can be varied, for example, from 10 cm to 220 cm, between the two horns 650, 654. The AT splitting can be detected at the atomic receiver 100, and based on the splitting, the microwave power transmitted by the receiving antenna 650 to the atomic receiver 100 can be calculated. As shown in FIG. 6C, the electric field 672 decreases as the distance 674 increases, as expected (e.g., according to Coulomb's inverse square law: E~1 / d 2 ).

[0217]

[0278] As shown in FIG. 6D , the electrical readout 670 of the atomic transducer 600 can detect the electric field dependence 677 of the atomic transducer 600 as a function of the angle 675 of tilt between the transmitting antenna 654 and the receiving antenna 650 to test the directional dependence of the atomic transducer 600. For example, zero degrees is interpreted as when the antennas 650, 654 are aligned with each other and the microwave horn antennas 650, 654 are placed 100 cm apart. The transmitting horn 654 can be aligned with the receiving horn 650 so that they are approximately coaxial, and then adjusted until a maximum in detected microwaves is found, indicating perfect alignment between the antennas (e.g., this would be considered a 0-degree tilt between the antennas). The transmitting antenna 654 can then be rotated along the microwave polarization axis from 0 to 90 degrees in 2.5-degree increments. The detected angular dependence 677 decreases as expected as the transmit antenna 654 is tilted away from the receive antenna 650 (e.g., radiation pattern directivity: E~tilt angle, maximum at 0 degrees).

[0218]

[0279] In some embodiments, AT splitting can be observed at tilts 675 between antennas 650, 654 up to 55 degrees, but for tilt angles greater than 30 degrees, the splitting will be too small to derive accurate field measurements. For example, this low splitting can be attributed to the particular Cs(vapor) transition chosen. In some embodiments, higher n states can be chosen for accurate measurements of weaker microwave fields.

[0219]

[0280] In some embodiments, with a 100 cm separation between the antennas 650, 654, a piece of pressboard (e.g., 25 mm thick and with an area much larger than the antenna aperture) may be placed several centimeters in front of the transmitting antenna 654 (e.g., to simulate microwave transmission through a wall). For example, an electric field of 31.7 V / m may be measured without the pressboard, but 24.8 V / m may be measured with the pressboard, indicating that the pressboard attenuates the electric field by 22% but does not prevent detection. In some embodiments, the atomic transducer 600 can even detect microwaves transmitted through a wall.

[0220]

[0281] In some embodiments, a comparison can be made between the detection of microwaves 652 at receive antenna 650 and the detection of microwaves 652 directly incident on atomic receiver 100. For example, amplifier 634 can be removed from microwave transmission system 632, and transmit antenna 654 can be placed 10 cm from receive antenna 650 to measure electric field 672. Cell electrode 620 can then be disconnected from receive antenna 650, microwave absorbing foam 640 can be removed, and transmit antenna 654 can be placed 10 cm from atomic receiver 100. Measurements can be made with transmit antenna 654 oriented so that the microwave polarization is both parallel and perpendicular to the axis of atomic receiver 100. For antenna-to-antenna transmission, an electric field of 21.7 V / m is measured. When microwaves are directly incident on the atomic receiver 100, a microwave field of 19.4 V / m is measured for polarization parallel to the axis of the electrode 620, while a microwave field of 47.0 V / m is measured for polarization perpendicular to the axis of the electrode 620.

[0221]

[0282] In some embodiments, assuming the microwave signal is transmitted through SMA cable 630 using electrode 620 as a small antenna and then into atomic receiver 100, the polarization in this case is likely to be perpendicular to the cell axis, and therefore vertical polarization measurements provide a better comparison to antenna-to-antenna measurements. For example, approximately 46% of the microwave power incident on receive horn 650 can be detected by Cs atoms in atomic receiver 100.

[0222]

[0283] In some embodiments, a comparative measurement can be made by applying the transmit antenna 654 directly to the receive antenna 650 (e.g., measuring an electric field of 75.0 V / m). Both antennas 650, 654 can then be disconnected, and the electrode 620 can be connected directly to the signal generator 632 via a microwave cable, an SMA barrel, an SMA cable, and finally an SMA connector 630 attached to the electrode. With this directional connection, an electric field of 166.9 V / m is measured, which represents 45% of the microwave power incident on the receive horn 650, consistent with the previous measurement.

[0223]

[0284] In some embodiments, atomic transducer 600 with integrated electrode 620 can be used for direct measurement of microwaves from a source without the need for intermediate free-space transmission or detection. For example, atomic transducer 600 can include a microwave isolator to allow for impedance matching.

[0224] Exemplary Atomic Receiver with Antenna

[0285] FIG. 7 illustrates an antenna-equipped atomic receiver 700 according to various exemplary embodiments. The antenna-equipped atomic receiver 700 may be configured to provide electromagnetic (e.g., RF) field collection and / or field compression via atom-based closed-loop control (e.g., atomic PLL, AALC, ABP, etc.) for autonomous operation. The antenna-equipped atomic receiver 700 may further be configured to provide atomic readout parameters (e.g., atomic transitions, laser frequency, power, scheme, etc.). In some embodiments, the antenna-equipped atomic receiver 700 may include atom-based RF amplitude and phase detection as described in International Application No. PCT / US2018 / 066006, filed December 17, 2018, which is incorporated herein by reference in its entirety.

[0225]

[0286] 7, the atomic receiver with antenna 700 can include an input signal 710 (e.g., an EM / RF field), an atomic receiver 100, an antenna 720, an optical I / O 730, and / or an electrical I / O 740. The atomic receiver with antenna 700 can include three operating parts: (1) field collection (e.g., antenna 720), (2) field compression (e.g., reducing the cross-sectional area of ​​the cable and / or stripline through which the signal propagates, such as the atomic hybrid detector 900 with striplines as shown in FIGS. 9A and 9B), and (3) atomic readout parameters (e.g., atomic transitions, laser frequency, power, scheme, etc.).

[0226]

[0287] In some embodiments, the antenna-equipped atomic receiver 700 may include optical coupling 732, electrical coupling 742, optoelectronic coupling 744, and / or source coupling 750, e.g., based on atom-based closed-loop control (e.g., atomic PLL, AALC, ABP, etc.), to improve signal response, precision, and accuracy for detection, communication, and processing of the input signal 710. In some embodiments, the antenna 720 may include an inductor 722 (e.g., coil) and / or a compressor 724 (e.g., capacitor, power feed) to improve signal reception. In some embodiments, the electrical I / O 740 may include additional inputs and / or outputs to and / or from the atomic receiver 100 (e.g., reference local oscillator, DC offset, electrical readout from the atoms, digital signal processor, CPU, etc.).

[0227]

[0288] In some embodiments, optical I / O 730 may be coupled to optical coupling 732 and / or optoelectronic coupling 744 to enhance signal detection via atom-based closed-loop control systems and methods, as described herein. In some embodiments, electrical I / O 740 may be coupled to electrical coupling 742 and / or optoelectronic coupling 744 to enhance signal detection via atom-based closed-loop control systems and methods, as described herein. In some embodiments, input signal 710 may be coupled to source coupling 750 to enhance signal detection via atom-based closed-loop control systems and methods, as described herein.

[0228] Exemplary Atomic Imager

[0289] 8 illustrates an atomic imager 800 according to various exemplary embodiments. The atomic imager 800 may be configured to provide electromagnetic (e.g., RF) field collection and / or field imaging with atomic-based closed-loop control (e.g., atomic PLL, AALC, ABP, etc.) for autonomous operation. In some embodiments, the atomic imager 800 may include atomic-based RF imaging as described in International Application No. PCT / US2018 / 066006, filed December 17, 2018, which is incorporated herein by reference in its entirety.

[0229]

[0290] 8, the atom imager 800 may include an input signal 810 (e.g., an EM / RF field), an atom receiver 100, an optical readout 134, an optoelectronic converter 820 (e.g., a CCD, CMOS, photodetector, etc.), and / or a signal processor 830 (e.g., a microprocessor, an embedded processor, a dedicated or general-purpose CPU, etc.). In some embodiments, the atom imager 800 may include an optical coupling 832, an electrical coupling 834, an optoelectronic coupling 836, and / or a source coupling 850, for example, based on atom-based closed-loop control (e.g., atomic PLL, AALC, ABP, etc.), to improve signal response, precision, and accuracy for detection and imaging of the input signal 810.

[0230]

[0291] In some embodiments, the optical readout 134 may be coupled to the optical coupling 832 and / or the optoelectronic coupling 836 to enhance signal detection and / or imaging via atom-based closed-loop control systems and methods, as described herein. In some embodiments, the electrical readout 162 may be coupled to the electrical coupling 834 and / or the optoelectronic coupling 836 to enhance signal detection and / or imaging via atom-based closed-loop control systems and methods, as described herein. In some embodiments, the input signal 810 may be coupled to the source coupling 850 to enhance signal detection and / or imaging via atom-based closed-loop control systems and methods, as described herein.

[0231] Exemplary Atomic Hybrid Detector with Stripline

[0292] 9A and 9B illustrate a stripline atomic hybrid detector 900 according to various exemplary embodiments. FIG. 9B is a schematic cross-sectional view of the stripline atomic hybrid detector 900 shown in FIG. 9A . The stripline atomic hybrid detector 900 can be configured to increase field compression and enhance detection sensitivity through atomic-based closed-loop control (e.g., atomic PLL, AALC, ABP, etc.) for multiple field tuning. The stripline atomic hybrid detector 900 can also be configured to maximize the peak intensity and / or the ratio of transmitted power along the cable cross-section (e.g., by reducing the cable cross-section) to create a stronger local field at the spectroscopic cell 910. In some embodiments, the stripline atom hybrid detector 900 can be configured as a spectrum analyzer based on, for example, homodyne measurements (e.g., phase, amplitude, frequency, polarization, etc.), heterodyne measurements (e.g., phase, amplitude, frequency, polarization, etc.), heterodyne parametric signal amplification, processing, atoms using spatial and / or temporal multiplexing of atomic responses to electromagnetic fields (e.g., similar to the atomic waveform sampler 1200 shown in FIG. 12), and / or multiplexing of optical beams for atomic readout (e.g., similar to the atomic waveform sampler 1200 shown in FIG. 12). Optical beam multiplexing and / or modulation may be implemented using, for example, a spatial light modulator or adaptive optics.

[0232]

[0293] 9A and 9B , an atomic hybrid detector 900 with a stripline may include a spectroscopic cell 910 (e.g., similar to the atomic cell 106 or atomic receiver 100 shown in FIG. 1 ), a probe laser beam 913 (e.g., similar to the probe laser beam 103 shown in FIG. 1 ), a coupler laser beam 914 (e.g., similar to the coupler laser beam 104 shown in FIG. 1 ), an atomic cell 916 (e.g., similar to the atomic cell 106 shown in FIG. 1 ), an atom 917 (e.g., similar to the atom 107 shown in FIG. 1 ), a stripline 920, and / or an insulator 930 (e.g., glass). The stripline 920 may include a trace electrode 922, a trace input 924 (e.g., an RF input signal), a ground electrode 926, and a ground input 928 (e.g., an RF reference signal). An input signal 942 (e.g., an EM / RF input field) may be coupled to the trace input 924, and a reference signal 944 (e.g., an EM / RF reference field) may be coupled to the ground input 928. The stripline 920 may be configured to increase or maximize the induction field 946 within the atomic cell 916 between the trace electrode 922 and the ground electrode 926. In some embodiments, the stripline 920 may be symmetrical and include, as shown in FIG.

[0233]

[0294] In some embodiments, the input signal 942 may be received from an antenna. In some embodiments, the reference signal 944 may include an RF reference signal and / or additional signals for multi-field adjustment. In some embodiments, the trace input 924 and the ground input 928 may be inductively coupled to the input signal 942 and the reference signal 944, respectively, to reduce (e.g., eliminate) electrical connections (e.g., conduction) between the atomic readouts (e.g., similar to the readouts 134, 162 of the atomic receiver 100) and the input signal 942 and / or external RF electronics.

[0234]

[0295] In some embodiments, the stripline-equipped atomic hybrid detector 900 may include a symmetric stripline 920 with an embedded atomic gas 917 for optical readout from the atoms 917 of field parameters of a signal (e.g., input signal 942, reference signal 944) injected into the stripline 920. For example, the stripline 920 may increase field compression (e.g., induced field 946) at the location of the detector atoms 917 for a given input signal to the stripline 920. In some embodiments, the optical readout signal from the atoms 917 (e.g., similar to the optical readout 134 of the atomic receiver 100) may be converted to an electronic signal by an optical detector (e.g., similar to the detector (e.g., photodiode) 160 and electrical readout 162). For example, the electronic signal may be used to realize one or more electronic-based control loops, e.g., for implementing a PLL, an ALC, and / or multiple field modulation.

[0235] Exemplary Multi-Field Modulation Systems and Methods

[0296] 10A-10C illustrate a multi-field conditioning system 1000 according to various exemplary embodiments. The multi-field conditioning system 1000 can be configured to provide multi-field engineering and / or conditioning of Rydberg levels for atom-based RF signal reception, such as high-sensitivity long-wavelength (<c / 10 GHz) RF reception and reception of combined RF signal transmission (e.g., spread spectrum schemes). The multi-field conditioning system 1000 can further be configured to structure the Rydberg level structure and corresponding available atomic dipole RF resonances, for example, to suit the type of input signal (e.g., EM / RF field) being detected and / or received. The multi-field conditioning system 1000 can further be configured to provide at least one additional EM field to the EIT field and the RF signal field. In some embodiments, the multi-field modulation system 1000 can use a fiducial reference phase (e.g., by a second electromagnetic wave, e.g., an RF wave or a light beam with RF phase modulation) and an atomic gas for RF phase detection as described in International Application No. PCT / US2018 / 066006, filed December 17, 2018, which is incorporated herein by reference in its entirety.

[0236]

[0297] 10A , a multi-field modulation system 1000 may include a first input signal 1010 (e.g., an EM / RF field), an atomic receiver 100, a second input signal 1020 (e.g., an EM / RF field or an EM / RF modulated optical beam or an O-EM optical beam), a third input signal 1030 (e.g., an EM / RF field or an EM / RF modulated optical beam), and / or an optical readout 1050. In some embodiments, the third input signal 1030 may comprise one or more additional fields, which may be DC or AC, depending on the application. In some embodiments, a device (e.g., a detector, receiver, imager, etc.) may be tuned by the additional field parameters (e.g., amplitude, phase, frequency, polarization, etc.) of the third input signal 1030 and / or the response of the atomic receiver 100 to the field parameters of the third input signal 1030 in an atom-based closed loop (e.g., a PLL, an AALC, an ABP, etc.).

[0237]

[0298] In some embodiments, a microwave field (e.g., third input signal 1030) couples two Rydberg levels, and the E field level can be used to control the resulting AT splitting of the two dressed states. For example, as the E field of this control microwave field (e.g., third input signal 1030) changes, the transition frequency between one of the controlled AT split states (e.g., a mixed S and P state) and another nearby Rydberg state (e.g., a D state) changes as well and can be tuned to resonantly couple an RF signal field (e.g., second input signal 1020) with a longer (or shorter) wavelength than the control microwave field (e.g., third input signal 1030). In some embodiments, states can be selected and / or field properties (e.g., large field amplitude) can be controlled to mix states in the Floquet regime (e.g., many-body localization) for more avoided crossings and a richer RF transition level structure. For example, states can be selected and / or field properties can be controlled so that the transition frequency is small and reaches a minimum at the avoided crossing of the AT state with another state.

[0238]

[0299] In some embodiments, a third input signal 1030 (e.g., a control microwave field) can prepare and control the atomic level structure for reception on a desired RF carrier frequency. For example, as shown in Figures 10B and 10C, the multi-field modulation system 1000 can use a strong microwave field at a frequency of 5.037 GHz resonating on a strong microwave dipole transition in Cs to generate a rich level structure in the atomic receiver 100 with electric dipole resonances between Floquet states at much longer wavelengths. In some embodiments, the multi-field modulation system 1000 can tune the quantum structure of the Rydberg atoms to enable sensitive reception of low-frequency RF (MHz) fields with moderate quantum number Rydberg states accessible to laser preparation in alkali vapor cells. 10B and 10C, the RF (MHz) transition frequency 1052 can be adjusted or selected by varying the electric field strength of the tuning microwave (GHz) field (e.g., third input signal 1030), whereby a change in microwave amplitude (e.g., electric field of dressing field amplitude 1054) along the x-axis results in a change in the RF resonance frequency 1052 between the Floquet-Rydberg levels prepared by the microwave dressing field. In some embodiments, the launch level of the RF wave reception can be selected by choosing the appropriate laser frequency 1052 of the Rydberg atom pump laser (y-axis).

[0239]

[0300] As shown in Figure 10B, the optical readout 1050 of the multi-field conditioning system 1000 can include, for example, a Floquet level structure setup in rubidium vapor using a 5.037 GHz dressing field. 1 / 2The Rydberg levels near the level may have a labeled Floquet level structure, which can be used as an operating platform for resonant RF reception at wavelengths much longer than the wavelength of the dressing field. As shown in Figure 10C, the optical readout 1050 of the multi-field modulation system 1000 may include a frequency 1052 for the electric field of the dressing field amplitude 1055 and a line strength (dot size) of the RF field reception. It can be seen that the Floquet level structure provides multiple strong RF transitions (e.g., transition 1056) in the sub-200 MHz range that are frequency tunable via the dressing field amplitude.

[0240]

[0301] In some embodiments, the control field (e.g., third input signal 1030) of the multi-field modulation system 1000 can serve as a process variable in an atom-based closed loop and atom-based receiver synchronous communication scheme. For example, in the implementation described above and shown in FIGS. 10B and 10C , the control field strength process variable can dynamically switch between two or more E-field values ​​to resonantly tune the atomic state to two or more RF carrier frequencies in the sub-GHz frequency range, based on, for example, a preset algorithm for implementing the atomic receiver in synchronous frequency-hopping spread-spectrum reception or the atomic response itself. For example, the laser frequency for optical EIT readout 1050 of the atomic response to the RF signal field can be line-tracked using an atom-based closed loop when switching / hopping to different control microwave E-fields to maintain an operating point on the Rydberg line required for continuous reception of the transmitted signal (e.g., atom-based feedback, PLL, AALC, ABP, laser controller 330, VCO 424, etc.).

[0241]

[0302] In some embodiments, the multi-field conditioning system 1000 may include RF signal phase / frequency reception (e.g., first and second input signals 1010, 1020) with the addition of a reference RF signal field (e.g., third input signal 1030) as a local oscillator applied for carrier selection, channel tuning, parametric amplification, and / or any combination thereof. For example, the multi-field conditioning system 1000 may utilize atom-based closed loop control (e.g., PLL, AALC, ABP, etc.).

[0242] Exemplary Rydberg field probe

[0303] 11A through 11F illustrate a Rydberg field probe 1100 according to various exemplary embodiments. The Rydberg field probe 1100 can be configured to provide a Rydberg atom-based RF signal waveform imager and receiver with closed-loop control for RF waveform imaging and detection. The Rydberg field probe 1100 can further be configured to be a portable Rydberg atom-based RF E-field probe and control unit for intrinsic absolute standard (atomic) broadband RF E-field measurements over a wide dynamic range from MHz to sub-THz using a single sub-wavelength detector. In some embodiments, the Rydberg field probe 1100 may include a Rydberg field probe and control unit as described in "A self-calibrating SI-traceable broadband Rydberg atom-based radio-frequency electric field probe and measurement instrument," David A. Anderson et al., arXiv:1910.07107v2, published October 18, 2019, pages 1-12 (see Appendix A), which is incorporated herein by reference in its entirety.

[0243]

[0304] 11A and 11B, Rydberg field probe 1100 may include an input signal 1110 (e.g., an EM / RF field), an atom receiver 100, a probe tip 1120, a probe housing 1130, a readout 1150 (e.g., a fiber optic cable), and / or a control unit 1160. Rydberg field probe 1100 may be based on a method of RF E-field measurement using optical EIT readout of spectral signatures from RF-field-sensitive Rydberg atoms in an atomic vapor (e.g., atom receiver 100). Rydberg field probe 1100 may be a portable probe consisting of a miniature atomic vapor cell sensing element (e.g., atom receiver 100) that is unilaterally fiber-coupled and enclosed in a rugged housing 1130 with a small dielectric footprint. In some embodiments, the Rydberg field probe 1100 may be connected by a fiber link cable (e.g., several meters long) via a software user interface to a portable control unit 1160 (e.g., a mainframe) that contains all the laser and optoelectronics for operation of the Rydberg field probe 1100 and RF E-field readout 1150.

[0244]

[0305] In some embodiments, the Rydberg field probe 1100 can provide high-precision, self-calibrating broadband RF E-field measurements. For example, the Rydberg field probe 1100 can use spectroscopic readout 1150 from the atomic receiver 100 (e.g., in the probe tip 1120), an RF-field-free atomic reference, and active laser frequency calibration to ensure high accuracy (e.g., reaching less than 1% uncertainty) in the spectroscopic output of the atomic RF E-field measurements.

[0245]

[0306] Figures 11C through 11F show signal waveforms 1150 collected in the time domain by the Rydberg field probe 1100 for a time-dependent RF field. The collected signal waveforms 1150 are displayed in linear grayscale (arbitrary units) and are measured versus time 1154 and laser detuning 1152. Figure 11C shows the EIT AC Stark shift response to a square pulse of a 2.5 GHz RF signal with varying pulse lengths of 10 μs, 100 μs, and 200 μs from left to right at a 1 kHz repetition rate, where the RF intensity is constant throughout the pulse. Figure 11D shows the EIT AC Stark shift response to a pulsed signal AM'd within the pulse. Figure 11E shows a continuous AM RF signal with a 2.5 GHz carrier frequency and a 5 kHz AM baseband frequency. Figure 11F shows a continuous FM RF field near the AT resonance with a 12.6 GHz carrier frequency, a 5 kHz FM baseband frequency, and a 160 MHz FM deviation.

[0246] Exemplary Atomic Waveform Sampler

[0307] FIG. 12 illustrates an atomic waveform sampler 1200 according to various exemplary embodiments. The atomic waveform sampler 1200 may be configured to perform atom-based RF waveform sampling or spectrum analysis using spatial and / or temporal multiplexing of atomic responses to EM fields (e.g., RF fields). The atomic waveform sampler 1200 may further be configured to provide an instantaneous bandwidth of over 10 MHz for atom-based RF field detection and reception (e.g., phase, amplitude, frequency, polarization, etc.) using spatial and / or temporal multiplexing of atomic responses to EM fields (e.g., RF fields). The atomic waveform sampler 1200 may further be configured to perform scalable high-speed and high-bandwidth RF waveform sampling over a wide range of carrier frequencies with RF waveform and / or pulse reconstruction and demodulation by electronic signal processing. In some embodiments, the atom-based waveform sampler 1600 may comprise an atomic spectrum analyzer.

[0247]

[0308] To date, the instantaneous bandwidth of RF field detection and reception (including phase, amplitude, frequency, and polarization) using Rydberg EIT is limited to approximately 10 MHz, set primarily by the lifetime or decay rate from the atomic electromagnetic (optical) probing transition. For example, in a Rb ladder Rydberg EIT configuration, the probing laser (780 nm) provides a 5 s 1 / 2 Level 5P 3 / 2 Connect to the level, coupler laser is 5P 3 / 2 to the Rydberg level, which then interacts with RF electromagnetic radiation. 3 / 2 From 5S 1 / 2 The spontaneous decay rate of the probe transition to is approximately 6 MHz, thus setting a fundamental limit on the achievable speed of optical probing readout from RF-interacting atoms, as well as setting a limit on the detectable instantaneous RF bandwidth.

[0248]

[0309] In this discussion, it is useful to clearly distinguish between the definition of instantaneous RF bandwidth (e.g., the baseband bandwidth of a modulated RF carrier driving an atomic transition) and the bandwidth coverage due to an RF carrier (e.g., an RF carrier field driving a substantially different atomic transition, such as the 30S to 30P RF carrier transition in Rydberg atoms). While RF carrier bandwidth coverage due to resonant Rydberg transitions ranges from less than 1 MHz up to THz, as mentioned above, the instantaneous RF bandwidth remains limited to the approximately 10 MHz level due to the relatively long, approximately 10-100 ns, lifetimes of intermediate atomic states.

[0249]

[0310] 12, atom waveform sampler 1200 may include a modulated waveform 1208 (e.g., 1 GHz modulation baseband), an input signal 1210 (e.g., based on modulated waveform 1208), a gradient field 1212 (e.g., for atom site selection), an atom receiver 1220 (e.g., similar to atom receiver 100 shown in FIG. 1), optical elements 1030, and / or a photodetector 1040 (e.g., for atom site selection). Atom receiver 1220 may include a probe laser beam 1223 (e.g., similar to probe laser beam 103), a coupler laser beam 1224 (e.g., similar to coupler laser beam 104), an atom cell 1206 with atoms 1207 (e.g., similar to atom cell 106 with atoms 107), and an optical readout 1228 (e.g., similar to optical readout 134). The photodetector 1040 (eg, CCD, CMOS, etc.) may include a pixel array 1250 (eg, rasterized), a forward raster 1252, a reverse raster 1254, and a sampled waveform 1256.

[0250]

[0311] In some embodiments, the Rydberg EIT probe readout 1228 from the atomic vapor 1227 can be extended onto a high-speed photodetector array 1040, which can provide spatial and temporal information from the optical probing region within the atomic sample. For example, atomic subgroups or sites can be defined by a spatially varying perturbation of the atoms, such as an external gradient field 1212 applied across the atoms 1227 within the probing region. These sites can then be spatially selected and / or readout by the photodetector array 1040, and the temporal response of each site to the RF field can be electronically readout as a sampled waveform 1256.

[0251]

[0312] In some embodiments, although each individual site remains rate-limited by the atomic transition lifetime or decay rate gamma (e.g., for rubidium 5P, lifetime approximately 100 ns and gamma approximately 10 MHz decay rate), readout 1256 from the N-element array 1250 can be performed temporally fast due to the ensemble ultrafast sampling rate of gamma × N. For example, for Rb and a 10 pixel × 10 pixel array, the atomic waveform sampler 1200 can provide RF waveform sampling up to 10 MHz × 100 = 1 GHz, suitable across a wide range of RF carriers given by the Rydberg spectrum (e.g., below 1 MHz up to THz). In some embodiments, RF waveform and / or pulse reconstruction and demodulation can be achieved by electronic signal processing (e.g., the rasterized pixel array 1250 of the photodetector 1240). In some embodiments, analog signal processing by optical and / or atom-optical means can also be implemented using, for example, optical modulation methods (e.g., quantum state-space interferometer 500 shown in Figures 5A-5C, multi-field modulation system 1000 shown in Figures 10A-10C).

[0252]

[0313] In some embodiments, the atomic waveform sampler 1200 can enable scalable high-speed / high-bandwidth RF waveform sampling across a wide range of carrier frequencies, relevant to a wide range of applications (e.g., RF signal reception, analysis, etc.). In some embodiments, the atomic waveform sampler 1200 can utilize RF phase, amplitude, frequency, and / or polarization detection schemes. For example, the atomic waveform sampler 1200 can utilize hybrid devices (e.g., the atomic hybrid detector 900 with striplines shown in FIGS. 9A and 9B), multi-field modulation of Rydberg levels (e.g., the multi-field modulation system 1000 shown in FIGS. 10A-10C), and / or atom-based closed-loop control (e.g., PLL, AALC, ABP, etc.). In some embodiments, the atomic waveform sampler 1200 can include multiplexing (e.g., rastering) of optical beams for atomic readout.

[0253] Exemplary Atomic Raster Imager

[0314] 13A and 13B illustrate an atom raster imager 1300 according to various exemplary embodiments. The atom raster imager 1300 can be configured to spatially scan an O-EM beam to selectively read out the phase and / or amplitude of one or more RF-EM fields emitted from one or more sources (e.g., antennas, antenna arrays, etc.) from Rydberg atoms located in 1D or 2D. The atom raster imager 1300 can be further configured to provide subwavelength spatial imaging over distances and areas greater than those permitted by the O-EM beam size (e.g., greater than about 1 mm). The atom raster imager 1300 can be further configured to provide far-subwavelength resolution of microwave phase and / or amplitude in the O-EM beam in selectable regions in space. The atom raster imager 1300 can also be configured to provide physical spacing between the front-end detector atoms and the back-end laser source and other hardware for remote sensing and / or imaging (e.g., microwave measurements and / or imaging inside an anechoic chamber, e.g., at a base station or other remote location). Atom-based electromagnetic field and phase imaging was previously described in U.S. Application No. 16 / 222,384, filed December 17, 2018, which is incorporated herein by reference in its entirety.

[0254]

[0315] FIG. 13A shows a schematic partial top view of atom raster imager 1300. FIG. 13B shows a schematic cross-sectional view of atom raster imager 1300. As shown in FIG. 13B, atom raster imager 1300 may include an O-EM laser beam 1303, an atom cell 1306 having atoms 1307 (e.g., Rydberg atoms), an input signal 1310 (e.g., an RF-EM field), a rastering mirror 1320, a quarter-wave plate 1330, a lens 1340, a filter 1350, and / or a detector 1360. In some embodiments, a single-spot image area of ​​O-EM laser beam 1303 may be transmitted and adjusted by rastering mirror 1320 within atom cell 1306. For example, the single-spot image area may be approximately 2 mm in diameter. In some embodiments, the side length 1308 of atom cell 1306 may be much larger than the imaging area. For example, the atom cell 1306 may be a rectangular parallelepiped, and the side length 1308 may be approximately 20 mm. In some embodiments, the atom raster imager 1300 may perform polarization mapping at a selected input signal 1310 frequency. For example, as shown in FIG. 13B, the atom raster imager 1300 may include a quarter-wave plate 1330 for polarizing the O-EM laser beam 1303. In some embodiments, the rastering mirror 1320 may scan (e.g., raster) the O-EM laser beam 1303 within the atom cell 1306 at a frequency of approximately 1 Hz to approximately 10 Hz. In some embodiments, the atom raster imager 1300 may be configured for electric field and / or polarization mapping from the near field (e.g., reaction zone and Fresnel zone) to the far field.

[0255]

[0316] Exemplary ultrasensitive potential measurements using Rydberg vapor Figures 14-16 illustrate systems and methods for ultrasensitive potential measurements using Rydberg vapor, according to various exemplary embodiments. Figure 14 is a plot 1400 of three-photon Rydberg electromagnetically induced transparency (EIT) Autler-Townes (AT) spectra of three in-plane beams. Figure 15 is a plot 1500 of the lifetime of rubidium (Rb) as a function of Rydberg state. Figure 16 is a plot 1600 of a four-photon Doppler-corrected Rydberg EIT spectrum.

[0256]

[0317] Atom-based RF field sensing exploits the large transition electric dipole moment of the Rydberg state, a property known since the early days of quantum mechanics. Vapor cell technology and quantum optics methods, such as nonlinear wave mixing in atomic vapors and Rydberg EIT, have recently been used to exploit this property, achieving sensitivity levels that are beginning to approach those of conventional antenna and amplifier technologies. Atom-based sensing offers advantages such as SI-based absolute and recalibration-free measurement capabilities, compact sensing elements, EMI and EMP protection capabilities, and all-optical sensor heads.

[0257]

[0318] To illustrate the potential impact, a target of 0.1 nV / cm in a 1 Hz bandwidth for a 10 GHz RF field is considered. As an example, the historic 1977 Voyager space probes were, from an RF perspective, a collection of science experiments built on the back of a high-gain antenna (HGA) for long-distance space communications. The Voyager probes currently have a target of 2.2 x 10 13 m (about 5 times the distance to Pluto). The HGA has a gain of 48 dBi and can transmit at tens of watts of power in the 8.42 GHz X-band and still be sufficient to communicate with Earth. The receive field is on the order of 0.3 nV / m, or about 1 / 30th the limiting sensitivity (at a 1 Hz bandwidth) of the systems and methods described in this disclosure. Note that NASA will use a 70 m, 34.6 dBi gain dish, so the field of the Voyager signal at the receiver element will be mapped to about twice the ultimate limiting field of the systems and methods described in this disclosure. For further explanation, 2The power of 0.1 nV / cm passing through a vapor cell is approximately -200 dBm, which is far below current civilian and military receiver standards. In short, the impact of instruments reaching the limiting sensitivity of the disclosed systems and methods would be transformative in science and technology, with disruptive and far-reaching implications in defense and commercial RF applications.

[0258]

[0319] RF field sensitivity and performance metrics in Cs and Rb vapor cell sensors are achieved using, among other things, EIT-based multiphoton Rydberg spectroscopy, low-light detection and single-photon counting, and heterodyne techniques. To arrive at this disclosure, the key improvements in RF sensitivity in state-of-the-art Rydberg potential measurements include four new aspects to the detection approach: (1) multidimensional Doppler matching for true Doppler-free Rydberg spectroscopy in vapors with homogeneous Rydberg linewidths; (2) increasing the optical beam size or the number of atom-light interactions to reduce transition time broadening; (3) dedicated vapor cell geometries and chemically treated vapor cells to reduce surface perturbations; and (4) laser beam power stabilization, frequency comb-based laser frequency stabilization at the kHz level, and heterodyne optical and RF detection techniques.

[0259]

[0320] The interaction of Rydberg atoms with RF electric fields can be classified into the Autler-Townes (AT) regime, the AC shift regime, and the Floquet regime in increasing order of field strength. Here, the AT regime is used to reach the lowest detectable field at the RF frequency of the atomic field resonance. These resonance frequencies follow the well-known Rydberg-Ritz formula. The field sensitivity is given by the RF Rabi frequency Ω RF is the fraction of the AT splitting divided by the transition dipole moment,

number

[0260]

[0321] The most intense transitions in cesium are nD-(n+1)P because the fractional parts of the quantum defects in these states differ by approximately 0.1. For these transitions, the frequency range of the system and method (100 GHz to 10 GHz) corresponds to a range of principal quantum numbers n from 21 to 42 and a range of radiation matrix elements d from 500 to 2200ea0. These d values ​​are 2n* 2 (n* is the effective principal quantum number). In rubidium, the level structure between the S, P, and D states is more evenly spaced. As a result, for the nD-(n+1)P transition of Rb, the frequency range of the system and method corresponds to an n range of 30 to 60 and a radiation matrix element range of 1000 to 4500 eaO. For this class of transition, at a given approximate frequency, Rb has a higher n value than Cs, resulting in a larger dipole moment. Therefore, Rb is generally better in terms of dipole moment and field sensitivity.

[0261]

[0322] Unwanted perturbations that may favor cesium can be considered. The vapor cell has a weak stray DC electric field, a blackbody thermal field (BBR), and the interaction of Rydberg atoms with the ground state and other Rydberg atoms. The DC polarizability is n 7 and the BBR and dipole interactions in atomic gases are scaled as n 3 and the van der Waals shift is n 11 These aspects favor low n over high n. The optical Rydberg excitation intensity scales as n -3 , again favoring lower n. The radiative and BBR lifetimes of low angular momentum states scale as n3 Scaled as , preferring high n.

[0262]

[0323] Another important consideration concerns the vapor cell size. Increasing the signal intensity and interaction time requires a significantly larger beam diameter and therefore a larger cell size. Here, cell sizes of the order of 1 cm can be targeted. Therefore, material surface effects are at a lower range relative to the magnitude of perturbations that affect sensitivity.

[0263]

[0324] Rabi frequency Ω of couplers and probes C and Omega P and the intermediate state decay rate Γ2, we obtain the Doppler-free uniform Rydberg EIT linewidth (Ω C 2 +Ω P 2 To arrive at Γ / Γ, it is necessary to perform a Doppler match in the entire three-dimensional velocity space. This can be done in planar geometry for a wide range of cases for Cs and Rb transitions. For example, a sample case of Cs with three photons is shown in Figure 14. Note that the second step is 1 GHz off-resonance to shift the k resonance in velocity space out of the Doppler profile. The two-photon (k2k3) Rabi frequency is on the order of 200 kHz, and the probe Rabi frequency is 500 kHz. To obtain this and similar results for other cases, the Lindblad equation can be solved to arrive at the EIT absorption coefficient, photon scattering rate, and other observables that can be used in RF field sensing and integrated over multidimensional velocity space.

[0264]

[0325] In some embodiments, as shown in Figure 14, the EIT AT spectrum 1410 for the cesium sample case can be calculated for a three-photon Rydberg EIT case with three beams in plane 1420. Angles can be chosen to eliminate Doppler shift in all dimensions. The data show velocity-averaged absorption coefficients at vapor densities near room temperature. For Cs, there is at least one chance solution with all collinear beam paths. However, this solution has unfavorable wavelengths in the deep IR. Here, a theory in multidimensional velocity space is used that encompasses both the general and exceptional collinear cases.

[0265]

[0326] FIG. 14 shows a plot 1400 of the AT-split Rydberg line 1410 as a function of coupler frequency detuning (x-axis) 1414 and RF Rabi frequency (y-axis) 1412. The usual pair of AT-split EIT lines is seen. Highest sensitivity to RF signals is achieved by using an RF reference or local oscillator (LO) offset in frequency, for example, by a few kHz from the RF signal being measured. It must be emphasized that in RF detection via AT-splitting, the purpose of the LO is not to induce heterodyne gain (because the linear response of the field would cancel out the LO gain). Rather, the purpose of the LO is (1) to enable RF detection at the beat frequency where the noise falls, and (2) to move the operating point away from the x-axis 1414 to maximize s=dα / [dΩ]. RF The goal is to shift the LO frequency to a region with a y-slope of 1418b (i.e., the y-slope of the plot). The two red arrows 1418a, 1418b in Figure 14 indicate usable operating points. The signal is then extracted by detecting the heterodyne beat amplitude of the signal with the LO using a lock-in amplifier or spectrum analyzer. The beat amplitude in the absorption, Δα 1416, is then calculated using the dipole moment d and the slope value s to find E RF = hΔα / (sd) provides the signal RF field strength via

[0266]

[0327] In some embodiments, the lifetimes 1502 of several types of Rydberg states 1504 of Rb at room temperature can be calculated, as shown in Figure 15. The calculation includes all blackbody effects. The downward "bow" in the lifetime at higher n is due to BBR-driven decay, excitation, and photoionization. In Figure 15, s is approximately 0.6 cm -1 / MHz, and RF Rabi frequencies are in Hz.

[0267]

[0328] The measured signal is modeled using this atomic physics input and taking into account technical noise and shot noise in the detection. The noise floor ΔE RF is obtained from the smallest detectable Δα. In some embodiments, lock-in detection allows Δα / α ∼ 10 -5 For the sake of estimation, we assume that Δα / α~2×10 -5 , d=1000ea0 (including angle matrix elements), and ΔE RF In some embodiments, the systems and methods of the present disclosure achieve a noise floor ΔE of about 10 nV / cm for a detection bandwidth of 10 GHz and 1 Hz. RF In some embodiments, when the difference in dipole moments of the resonant transitions is about 10×, the systems and methods of the present disclosure can have a noise floor ΔE of about 100 nV / cm for a detection bandwidth of 100 GHz and 1 Hz. RF (e.g., sensitivity).

[0268]

[0329] Before discussing various improvements, some other important conditions must be mentioned. Because sensitivity, apart from effective Doppler matching, requires the narrowest possible EIT line, the interaction time spread must be reduced to within the 10 kHz range, which means that the beam diameter of interest is in the 1 cm range. Therefore, cells with custom walls and diameters on the order of 1 cm can be implemented. As shown in Figures 15 and 16, the target linewidth value of 10 kHz is obtained from the 300 K atomic lifetime due to spontaneous decay and blackbody radiation at n values ​​near and above 30 (see, for example, Figures 15 and 16, where the linewidth is obtained as 1 / lifetime / (2π). Note the useful factor of 2π). In some embodiments, the integrals of all upward and downward electric dipole transitions and BBR-induced photoionization can be summed for the lifetime calculation.

[0269]

[0330] Large cell sizes comparable to the RF wavelength require RF simulation or characterization to address standing wave effects. Also, the placement of the LO field source is carefully considered. The probe laser power may be very low to reach a uniform EIT linewidth, requiring APD and SPCM detector modules to approach the optical shot noise floor. Large beam sizes may require an optical build-up cavity for the Rydberg excitation optical field. In some embodiments, as an alternative to direct probe field detection, the second excitation level, ρ 33 can be probed via fluorescence detection. For example, this can be done with a four-photon scheme. Good candidates for this are fluorescence monitoring of blue decay light and / or monitoring D1 decay while exciting with the D2 line, or vice versa. Either of these methods may require SPCMs and interference filters.

[0270]

[0331] In some embodiments, as shown in FIG. 16, the four-photon Doppler-corrected Rydberg EIT1600 for Rb is calculated using the background ρ 33 1602 vs. ρ divided by RF Rabi frequency 1604 33The derivative of can be plotted. For example, the highest heterodyne sensitivity may correspond to the LO RF Rabi frequency where this slope is large. In some embodiments, the data may include velocity averages in all dimensions at vapor densities near room temperature.

[0271]

[0332] In some embodiments, the systems and methods of the present disclosure may have a detection bandwidth of 1 Hz. Higher bandwidths are useful for achieving high sensitivity, expressed in units of field per √Hz. In some embodiments, various four-photon cases can be simulated, such as the case of Rb with fluorescence detection. For example, all valid two-photon Rabi frequencies in the simulation of FIG. 16 are in the 100 kHz range, resulting in sub-10 kHz EIT linewidths. 2π×10 4 S -1 The Rydberg decay rate is estimated to be about 10 -4 ρ of the Noko simulation 33 , 10 in the venue 10 atoms, approximately 10 7 s -1 10, including the single atom scattering rate, and angular collection losses -4 With an SPCM efficiency of , the photon count rate is 10 9 / s, for which an analog APD would be appropriate. Then, with a detection bandwidth of 1 second, Δρ 33 / ρ 33 In 10 -4 Using Figure 16 and a target RF Rydberg transition of d = 2000 ea, this is approximately 1 nV / cm (in a 1 Hz bandwidth), ΔE RF =(dρ 33 / [ρ 33 dΩ RF ]) -1 x10 -4 ×h / d. In some embodiments, the systems and methods of the present disclosure may provide, for example, a 10× improvement -4 From 10 -2Signal-to-noise improvements, including improved light collection efficiency up to 0.1 nV / cm / Hz at 10 GHz, as well as reduced laser intensity noise. 0.5 , and 1nV / cm / Hz for 100GHz 0.5 In some embodiments, a wider range of combinations of possible four-photon transitions, optical Rabi frequencies, AC shift cancellation (implemented but not described), intermediate state detuning, etc. may be used.

[0272]

[0333] In some embodiments, RF frequency resolution is achieved automatically via LO and heterodyne detection. The EIT rate (the timescale over which the Rydberg population can reach a quasi-steady state) is limited by the intermediate state decay rate and the pre-photoexcited Rabi frequency. Here, a beat RF frequency of about 1 kHz at highest sensitivity seems reasonable, with a fractional instantaneous bandwidth Δf / f ∼ 10 -7 This results in 10 -6 (10 kHz at 10 GHz and 100 kHz at 100 GHz) is an order of magnitude larger than the target fractional instantaneous RF bandwidth. In some embodiments, the bandwidth estimate may reflect an overall reduction in the EIT linewidth towards a homogeneous Rydberg level width.

[0273] Appendices A-N: Exemplary atom-based closed-loop control

[0334] Appendices A-N attached hereto and described below set forth atom-based closed-loop control devices, systems, and methods according to various exemplary embodiments, which are incorporated herein by reference in their entirety.

[0274]

[0335] Appendix A: “A self-calibrating SI-traceable broadband Rydberg atom-based radio-frequency electric field probe and measurement instrument,” David A. Anderson et al., arXiv:1910.07107v2, published October 18, 2019, pages 1-12, is incorporated herein by reference in its entirety.

[0275]

[0336] Appendix B: “Room-temperature Rydberg THz master,” David A. Anderson and Georg Raithel, Internal Document, November 26, 2019, pages 1-6, is incorporated herein by reference in its entirety.

[0276]

[0337] Appendix C: “Rydberg-based quantum RF phase detector and receiver,” David A. Anderson and Georg Raithel, internal document, pages 1-4, is incorporated herein by reference in its entirety.

[0277]

[0338] Appendix D: “Optical RF phase sensing and measurement with Rydberg atom vapors,” internal document, pages 1-2, is incorporated herein by reference in its entirety.

[0278]

[0339] Appendix E: "Rydberg atoms for radio-frequency communications and sensing: atomic receivers for pulsed RF field and phase detection," David A. Anderson et al., arXiv:1910.07970v1, published October 17, 2019, pages 1-10, is incorporated herein by reference in its entirety.

[0279]

[0340] Appendix F: “Time dependence of Rydberg EIT in pulsed optical and RF fields,” Rachel E. Sapiro et al., J. Phys. B: At. Mol. Opt. Phys. 53, 094003, published April 3, 2020, pages 1-10, is incorporated herein by reference in its entirety.

[0280]

[0341] Appendix G: “Rydberg high-speed, high resolution MMW 2D near-field imager,” David A. Anderson, Internal Document, October 2019, 1 page, is incorporated herein by reference in its entirety.

[0281]

[0342] Appendix H: “Rydberg high-speed, high resolution MMW 2D near-field imager,” Internal Document, February 6, 2020, 1 page, is incorporated herein by reference in its entirety.

[0282]

[0343] Appendix I: “Rydberg Radio Receiver,” David A. Anderson, Internal Document, November 21, 2019, page 1, is incorporated herein by reference in its entirety.

[0283]

[0344] Appendix J: “Atom-based magnetic field monitor,” Internal Document, June 2019, pages 1-12, is incorporated herein by reference in its entirety.

[0284]

[0345] Appendix K: "Atom-based optical RF-power / voltage transducer and sensor," Rachel E. Sapiro et al., American Physical Society (APS): Atomic, Molecular, and Optical Physics, Vol. 64, No. 4, Poster Abstract (L01.00031), May 29, 2019, page 1, is incorporated herein by reference in its entirety.

[0285]

[0346] Appendix L: “An atomic receiver for AM and FM radio communication,” David A. Anderson et al., arXiv:1808.08589v1, published August 26, 2018, pages 1-6, is incorporated herein by reference in its entirety.

[0286]

[0347] Appendix M: “Widely wavelength-tunable narrow-linewidth laser using position-scanned cavity filter,” Internal Document, May 1, 2019, 1 page, is incorporated herein by reference in its entirety.

[0287]

[0348] Appendix N: “Diagram of atomic radio-frequency interferometer for optical RF phase and amplitude sensing: implementation in a Cesium Rydberg vapor,” Internal Document, April 1, 2019, 1 page, is incorporated herein by reference in its entirety.

[0288] Appendix A: An exemplary self-calibrating, SI-traceable, broadband Rydberg atom-based radio frequency electric field probe and measurement instrument

[0349] Appendix A: “A self-calibrating SI-traceable broadband Rydberg atom-based radio-frequency electric field probe and measurement instrument,” David A. Anderson et al., arXiv:1910.07107v2, published October 18, 2019, pages 1-12, is incorporated herein by reference in its entirety.

[0289]

[0350] 11A-11F and 17A-26 illustrate self-calibrating, SI-traceable, broadband Rydberg atom-based RF E-field probes and measurement instruments according to various exemplary embodiments. Fig. 17A is a schematic diagram of an atomic energy level diagram 1700A of two-photon Rydberg EIT optical readout for cesium vapor. Fig. 17B is a plot 1700B of optical readout from an atomic vapor of the Rydberg EIT resonance 1702 as a function of laser frequency offset 1704.

[0290]

[0351] Figure 18 is a schematic diagram of a Rydberg field measurement system (RFMS) 1800 having a Rydberg field probe (RFP) 1100 and a mainframe control unit 1160. Figure 19 is a plot 1900 of spectroscopic and optical signals 1902 as a function of laser frequency detuning 1904 collected simultaneously by the RFMS 1800 shown in Figure 18. Figure 20A is a plot 2000A of an optical atomic spectrum 2002 as a function of laser frequency detuning 2004 for the RFP 1100 shown in Figures 11A, 11B, and 18. Figure 20B is a plot 2000B of a non-resonant AC Stark shift 2002 as a function of laser frequency detuning 2004 for the RFP 1100 shown in Figures 11A, 11B, and 18.

[0291]

[0352] Figures 21A-21C are plots 2100A, 2100B, and 2100C of the E-field pattern 2102 for single axis rotation angles 2104A, 2104B, and 2104C of the RFP 1100 shown in Figures 11A, 11B, and 18. Figures 22A-22C are plots 2200A, 2200B, and 2200C of the polarization pattern 2202 using peak height ratios R for single axis rotation angles 2204A, 2204B, and 2204C of the RFP 1100 shown in Figures 11A, 11B, and 18. 23A-23C are plots 2300A, 2300B, and 2300C of the atomic spectral output 2302 for single axis rotation angles 2304A, 2304B, and 2304C of the RFP 1100 shown in FIGS. 11A, 11B, and 18. FIG.

[0292]

[0353] Figures 24A and 24B are plots 2400A, 2400B of the E-field pattern 2402 for a single axis rotation angle 2404 for the RFP 1100 shown in Figures 11A, 11B, and 18. Figures 25A-25C are plots 2500A, 2500B, and 2500C of the total RF E-field in three planes for the RFP 1100 shown in Figures 11A, 11B, and 18. Figure 26 is a plot 2600 of the RF E-field probability distribution 2602 in the RFP 1100 atomic vapor along the optical beam path 2606.

[0293]

[0354] A self-calibrating, SI-traceable, broadband Rydberg atom-based radio frequency (RF) electric (E) field probe (Rydberg Field Probe or RFP1100) and measurement instrument (Rydberg Field Measurement System or RFMS1800) are presented. The RFMS1800 comprises the atomic RF field probe (RFP) 1100, which is connected by a ruggedized fiber optic patch cord to a portable mainframe control unit 1160 with a computer software interface for probe RF measurements and analysis, including real-time field and measurement uncertainty readout, and spectral RF waveform visualization. The instrument uses all-optical electromagnetically induced transparency (EIT) readout of spectral signatures from RF-sensitive Rydberg states of atomic vapors for self-calibrating broadband measurements of continuous, pulsed, and modulated RF fields.

[0294]

[0355] The RFP1100 utilizes resonant and non-resonant Rydberg field interactions to achieve broadband RF E-field measurements at frequencies ranging from approximately 10 MHz to sub-THz with a single vapor cell sensing element over a wide electric field dynamic range. The RFMS1800 incorporates an RF-field-free atomic reference and laser frequency tracking unit to ensure RFMS reliability and RF E-field measurement accuracy. Atomic RF field measurement uncertainties reaching less than 1% are demonstrated.

[0295]

[0356] The RFP1100 is characterized, and the measured polar field pattern along the RFP1100's major axis at 12.6 GHz RF is measured, obtained by single-axis rotation of the RFP1100 in the far field of a standard gain horn antenna. Field pattern measurements at 2.5 GHz are also presented. The measured field pattern is in good agreement with finite element simulations of the RFP1100. The data confirm that the atom-based RF E-field probe is well suited for wideband isotropic RF measurement and reception.

[0296]

[0357] A calibration procedure and uncertainty analysis are presented that accounts for deviations from a perfectly isotropic response across 4π solid angles resulting from asymmetric dielectric structures external to the active atomic measurement volume. The procedure includes contributions from both the fundamental atomic spectroscopy measurement methods and their associated analyses, as well as uncertainty contributions due to materials, geometry, and hardware design choices. The calibration procedure and uncertainty analysis result in calibration (C) factors that are used to establish an absolute standard SI-traceable calibration of the RFP1100.

[0297]

[0358] Polarization pattern measurements will also be performed, demonstrating the RF polarization detection capabilities of the instrument, which can be optionally implemented simultaneously with E-field measurements. The RFP1100 measurement capabilities for pulsed and modulated RF fields, as well as direct time-domain RF pulse waveform imaging, will be demonstrated. The practical use of Rydberg atom-based RF E-field probe instruments in RF metrology toward establishing new absolute (atomic) RF E-field measurement standards, areas of application in RF measurement and engineering, and a discussion of their value as a new quantum technology platform easily adaptable for dedicated uses of Rydberg-based devices will be discussed.

[0298] I. Introduction

[0359] Sensors and measurement devices for radio frequency (RF) radiation at radio, microwave, sub-THz, and THz frequencies enable capabilities essential to modern society with far-reaching impacts on industries ranging from government and defense, telecommunications, electromagnetic compliance and safety, security, and healthcare. To date, RF field sensing and measurement has primarily relied on antenna technology to measure or receive RF electric (E) fields. Advances in antenna technology continue to provide improved RF capabilities. Despite continued advances, the very nature of traditional antenna technology, which is based on the driven oscillation of charge in a conductor induced by an incident RF electric field, imposes fundamental limitations on the achievable accuracy, precision, and performance of probes and detectors for RF electric field measurement and sensing applications.

[0299]

[0360] Atom-based quantum sensor technology holds great promise for achieving capabilities beyond those achievable with conventional sensor technologies. Bacterial advances in harnessing the properties of individual atoms in highly excited Rydberg states using optical electromagnetically induced transparency (EIT) in atomic vapors have provided new capabilities in RF sensing, measurement, and imaging. Rydberg atom-based RF electric field (E-field) sensing offers a combination of performance capabilities beyond those possible with conventional antennas and other solid-state RF detectors. This includes single-sensor ultra-wideband RF detection from HF to sub-THz and a dynamic field range of over 120 dB, from a field detection threshold of less than 10 mV / m up to high-intensity RF fields of approximately 10 kV / m, with atomic ionization limits at the MV / m level.

[0300]

[0361] Over a wide range of RF field amplitudes and frequencies, the Rydberg-based measurement method is rooted in a physical model of atomic-field interactions that relies only on invariant atomic parameters and fundamental constants. This enables self-calibrating electric field measurements directly traceable to the Planck constant with atomic RF E-field measurement uncertainties reaching less than 1%, a nearly order of magnitude improvement over existing antenna standards, and holds the promise of becoming the new international atomic RF measurement standard in national metrology institutes worldwide.

[0301]

[0362] In this disclosure, the first Rydberg RF E-field probe (Rydberg Field Probe or RFP1100) and measurement instrument (Rydberg Field Measurement System or RFMS1800) are presented that employ atom-based detection using electromagnetically induced transparency (EIT) readout of spectral signatures from RF-sensitive Rydberg states in atomic vapors. The RFMS1800 is a commercially available instrument that comprises an atomic RF Field Probe (RFP)1100, housing a miniature atomic vapor cell sensing element connected to a portable rack-mounted control unit via a ruggedized fiber optic patch cable for remote probe operation and RF E-field measurements.

[0302]

[0363] The RFMS1800 is operated from a software user interface 1160 that provides real-time RF field measurement and uncertainty readout from the RFP1100 and RF analysis features including spectrum and RF waveform visualization. The RFMS1800 measures the RF field by utilizing resonant and non-resonant Rydberg RF field interactions in the RFP1100, along with an RF field-free atomic reference and active laser frequency tracking to ensure high reliability and accuracy in atomic RF E field measurements.

[0303]

[0364] This disclosure is organized into the following sections: Section II provides a brief overview of Rydberg EIT readout and RF E-field measurements in atomic vapors.

[0304]

[0365] Section III presents and describes the RFP instrument 1100 and its operating principles, including the implementation of RF field-free referencing and optical frequency tracking to achieve high reliability in high-precision RF E-field measurements and field determination methods for both linear and nonlinear regimes of atomic response, with built-in compensation for RF field perturbations caused by the RFP probe material surrounding the atomic vapor detection volume.

[0305]

[0366] Section IV characterizes the RFP probe 1100 by performing polar field pattern measurements along the three major axes of the RFP 1100 at an RF of 12.6 GHz, obtained by single-axis rotation of the RFP 1100 in the far field of a standard gain horn antenna, and field pattern measurements at an RF of 2.5 GHz. The measured RFP field patterns provide atomic E-field measurement uncertainties of less than 1%. RF polarization detection and measurement with the RFP is also demonstrated.

[0306]

[0367] In Section V, finite element simulations of the RF fields in the RFP1100 are performed to quantify the effects of RFP materials and design on the RF fields measured by the atoms, from which calibration (C) coefficients are determined. Using these C coefficients, the RFMS1800 provides absolute RF E-field measurements that are SI traceable to Planck's constant and invariant atomic parameters.

[0307]

[0368] Section VI presents the atomic RF field measurement uncertainty budget and analysis of RFP1100 related to the SI traceability of atomic RF probes and measurement tools in RF metrology.

[0308]

[0369] Section VII demonstrates RFP pulsed RF field and modulated RF field measurements and direct time-domain RF waveform detection and imaging.

[0309]

[0370] Section VIII concludes with a description of the RFP instrument's applications in RF metrology and standards, RF engineering and measurement applications, and its use as a platform technology for other application-specific RF sensing, receiving, and measurement needs.

[0310] II. Rydberg atom-based RF field sensing and measurement by EIT in atomic vapors

[0371] Rydberg atom-based RF field sensing and measurement utilizes optical electromagnetically induced transparency (EIT) readout of the spectral changes from the Rydberg state of an atomic vapor to sense the electric field over a wide range of RF field frequencies, amplitudes, and polarizations. Figure 17A shows the atomic energy level diagram of a two-photon Rydberg EIT optical readout for cesium vapor. The atomic (cesium) vapor is typically contained within a hermetically sealed compartment with a port for optical access to the vapor. See, for example, the miniature glass vapor cell sensing element in front of a standard horn antenna shown in the inset of the figure. In the basic readout scheme, two optical laser fields couple the atomic state to a higher-lying Rydberg state (30D in Figure 17A) with a weak optical probe beam resonant with the first atomic transition between the ground state and the intermediate state, and a relatively strong optical coupler beam tuned to resonate with the second atomic transition between the intermediate state and the Rydberg state.

[0311]

[0372] When the coupler laser frequency is resonant with the Rydberg state, an electromagnetically induced transparency (EIT) window opens, allowing the probe beam to pass through the vapor. Due to the sensitivity of the atomic Rydberg level to RF fields, the field-induced shift and splitting of the Rydberg EIT signal allows for optical measurement of the RF field. An example of a Rydberg EIT resonance is shown in Figure 17B (black curve). In the presence of a weak RF field at a frequency nearly resonant with the allowed transition between the atom's optically excited Rydberg level and its second Rydberg level, the EIT-detected atomic Rydberg line splits into a pair of Autler-Townes (AT) lines that split proportionally to the RF field amplitude (Figure 17B (Magnetor curve)). In this linear AC Stark effect regime, the E field is given by:

number

number

[0312]

[0373] From Equation 1, we can obtain absolute SI-traceable RF E-field measurements that rely only on invariant atomic parameters and fundamental constants. Furthermore, by varying the frequency of the coupler laser, we can optically access different Rydberg levels, which offer different RF field sensitivities and dynamic field ranges. While the AT regime presented here provides an illustrative example of SI-traceable RF measurements with Rydberg EIT in vapors, RFP implements a more generalized method that allows RF field measurements at any frequency over a wide dynamic range, from low RF fields (less than 1 V / m) to high RF fields (approximately 10 kV / m). The physical principles of this RF measurement method have been described in previous work.

[0313]

[0374] Figure 17A: Atomic energy level diagram showing two-photon Rydberg EIT optical readout of cesium vapor. A miniature glass atomic vapor cell sensing element (inset) in front of a standard horn antenna.

[0314]

[0375] Figure 17B: Optical readout of the Rydberg EIT resonance from an atomic vapor in the absence of RF (black curve) and in the presence of an RF field at a frequency nearly resonant with the allowed transition between the optically excited Rydberg level and the second Rydberg level (magenta curve). The Autler-Townes (AT) splitting of the line yields the RF field strength. In RF fields too weak to AT split the line, the field-induced change in the linear shape can provide a measure of the RF field strength (cyan curve).

[0315] III. Rydberg RF Field Probe (RFP) and Measurement System (RFMS)

[0376] A diagram of the RFMS1800, including the RFP1100 and mainframe unit 1160, is shown in Figure 18. The RFP1100 houses an atomic cesium vapor cell detector element with a cylindrical geometry and 10 mm diameter and length. The cell is unidirectionally fiber-coupled to inject overlapping, counter-propagating 852 nm and 510 nm narrow-line laser beams through the vapor, returning the retroreflected 852 nm light to the instrument mainframe for optical readout of the Rydberg resonance. The RFP1100 vapor cell detector element is attached to the probe rod and connected to the portable mainframe 1160 by a ruggedized fiber link patch cable several meters long for remote operation. The mainframe contains all lasers and hardware automated via control software and a computer user interface for RF field measurements, RF signal analysis, and visualization with real-time RF field and uncertainty readouts. The RFP1100 has a removable cap to protect the detector element during daily operational use. The RFP1100 and its fiber link cable are fabricated from a hard dielectric with a low RF permittivity and loss tangent to achieve both a small footprint in RF field environments and mechanical robustness during operation.

[0316] A. Operating Principle for RF E-Field Measurements

[0377] The RFP instrument 1100 achieves traceable measurements of RF E-fields by comparing the spectroscopic EIT signatures of RF-field-sensitive Rydberg states of atoms contained in a vapor cell sensing element (see Section II) with an absolute model of the Rydberg atomic response. This method provides RF field measurement capability over a wide continuous range of RF field frequencies from MHz to sub-THz, and RF electric field amplitudes ranging from weak fields below 10 mV / m through moderate field regimes on the order of tens of V / m to high-intensity RF fields above 10 kV / m.

[0317]

[0378] The disclosed field measurement method considers all nonlinearities in atomic response across the entire RF range, which can be substantial for moderate to strong fields, thereby providing a self-calibrated, linear E-field readout from the RFP1100 across the full frequency and amplitude range of RF radiation. Note also that this method encompasses other limited approaches commonly implemented in laboratory experiments with Rydberg EIT RF field measurements. These include the linear AC Stark effect, where Autler-Townes (AT) splitting leads to the RF electric field according to equation (1). This approach is only valid for RF fields that are nearly resonant with the RF frequency-specific Rydberg-Rydberg transition, and the assumed linear relationship between the field and AT splitting is only accurate over a limited dynamic field range, which may be as low as 10 dB or less.

[0318]

[0379] The RFMS1800 also covers a measurement approach based on the second-order AC Stark shift, which is suitable for measuring continuously tunable RF fields non-resonant with any Rydberg-Rydberg transition. The AC shift approach is applicable over a dynamic range from approximately 1 V / m to greater than 10 kV / m (greater than 80 dB strength range), which is of considerable practical relevance and is wider than the dynamic range covered by the AT splitting approach. For simplicity and proof-of-principle experiments, in this disclosure, the RFP1100 RF field measurements, RFP1100 field pattern characterization, instrument field determination methods, and measurement uncertainty analysis are primarily performed in the AT and AC Stark shift regimes.

[0319]

[0380] Figure 18: Rydberg field probe (RFP) 1100 and mainframe control unit 1160 together comprise the Rydberg field measurement system (RFMS) 1800. The RFP 1100 is shown in the inset next to two conventional horn antennas.

[0320] B. Frequency Referencing and Optical Frequency Tracking in RFMS

[0381] The accuracy of RF E-field measurements by Rydberg EIT spectroscopy depends on the precision with which the optical frequencies between RF-induced atomic spectral features can be determined. This relies on laser scanning frequency calibration, which is not a standard feature in available laser devices. The nature of the RF-induced spectral features also depends in part on the choice of atomic Rydberg state used for a given RF field measurement. For example, the Rydberg S-state and D-state produce different spectral responses to similar RF field frequencies or amplitudes due to their magnetic substructure and other differences. As a general solution, RFMS uses an RF-field-free atomic reference and a scanning laser frequency tracker in real time during RFP operation, which provides maximum versatility and ensures high reliability and accuracy in RF E-field measurements.

[0321]

[0382] Figure 19 shows an example of three optical readout signals collected simultaneously by the RFP instrument 1100 during an RF E-field measurement. In the measurement, a coupler laser (510 nm laser, see Figure 17A) is scanned, and the recorded signals are displayed as a function of laser detuning. The signals are (1) a spectroscopic Rydberg EIT readout from the RFP 1100 in the RF field of interest, (2) an RF-field-free atomic reference spectrum, and (3) a periodic optical frequency marker for the laser scan derived from an uncalibrated optical frequency tracker (OFT, model OFT-NIR-19 from Rydberg Technologies).

[0322]

[0383] The latter two signals are generated by internal devices within the instrument mainframe and ensure high reliability and spectroscopic accuracy of atomic RF E-field measurements, reaching absolute RF E-field measurement uncertainties at the 1% level or lower. For illustrative purposes, in Figure 19, the RF field frequency and amplitude measured by the RFP1100 are selected so that the atomic response is a resonant AT splitting whose value is approximately linear in the RF field, enabling simple and accurate determination of the RF E-field with low measurement uncertainty. The OFT within the RFMS mainframe 1160 provides a frequency ruler for the scanned 510 nm laser with a calibrated fringe spacing (38.30 0.02 MHz in this disclosure). The OFT signal tracks the laser frequency in real time during coupler (510 nm) laser scanning, providing absolute, high-precision laser frequency axis calibration. The calibrated laser frequency axis is a key element that enables the RFMS1800 operating software to process the Rydberg EIT spectrum measured within the RF field and report RF field amplitude readings to the RFMS user.

[0323]

[0384] Figure 19: Spectral and optical signals simultaneously collected by the RFMS during a 12.6 GHz RF E-field measurement with an RFP in the far field of the horn antenna emitter. Shown are EIT readouts from the RFP with the RF field on (red, solid line) and off (red, dashed line), EIT readouts from the RF-field-free Rydberg reference unit housed within the RFMS mainframe (black), and readouts from the Optical Frequency Tracker (OFT) within the RFMS mainframe (blue). The OFT signal provides a "frequency ruler" with a calibration period of (38.30 + / - 0.02) MHz.

[0324] C.RF field determination method

[0385] The RFP instrument 1100 measures RF E-fields by converting optical readouts of the field-modified atomic response from the vapor cell probe into E-field values. Spectroscopic signatures (observed as probe beam transmission changes) match pre-calculated signatures of the atomic response linked to invariant atomic properties and fundamental constants. These signatures are unique and can be mapped to E-field values ​​through this comparison. To perform SI-traceable, self-calibrating broadband RF measurements over a wide dynamic range, the RFP1100 implements the Floquet RF E-field determination method across all atom-field interaction regimes, including the AT and AC Stark shifts. The RFMS1800 implements dedicated spectral analysis for field determination that accounts for both the varying atomic response in different atom-field interaction regimes and the broadening and shifts of atomic spectral features in the readout due to RF field inhomogeneities that may exist within the atomic detection volume as a result of field perturbations by the RFP material.

[0325]

[0386] 20A and 20B show examples of RFP spectral readouts of RF E-field measurements performed in the AT and AC Starkle regimes for RF E-fields of 12.6 GHz (FIG. 20A) and 2.5 GHz (FIG. 20B), respectively. The method for determining the E-field is similar in the AT and AC Starkle regimes. In both cases, a signal averaging approach is used so that the routine automatically locates peaks in the EIT signal and accounts for linear substructure. Here, the spectral EIT signal S(Δv) is integrated over the field variation peaks. From this integral, the average frequency shift (Δv) of the RF variation peaks is determined with respect to the field-free EIT spectrum.

number

[0326]

[0387] In the AT regime, the average RF field in RFP1100 is given by the equation 〈E〉 = 2h〈Δv〉 / (d rad d ang ) from the peaks on either side, where h is Planck's constant and d radis the radial matrix element of the Rydberg transition, and dang is the angular matrix element. Here, E is the amplitude of the RF electric field amplitude, the average 〈E〉, over positions in the RFP field probe volume and over the magnetic substates of the atom, as appropriate. The representative measurement example in Figure 20A is in the low E field regime, where the AT splitting lines are located at the non-splitting magnetic quantum number m j It contains known substructures of spectral components belonging to different values ​​of m j = 1 / 2 angle matrix element d ang and m j = 3 / 2 ang Since the two components differ by 20%, selecting one component and ignoring the other for determining the E field will give erroneous results. To take this into account, the RFMS1800 uses m j (In the case of Figure 20A, m j = 1 / 2 and m j =3 / 2) to approximate the angle matrix elements.

[0327]

[0388] In AC Starklesiem, 2 〉=4×〈Δv〉 / α j where αj is the AC polarizability, which is the Rydberg level, |m j | state, and RF frequency. The AC Stark-induced line shifts are similarly given by 〈E 2 >, providing the RMS value of the RF electric field amplitude averaged over the RFP1100 field probe volume, and a measure of the intensity of the RF radiation. The RFMS1800 field determination method in the AC Starkle regime is implemented similarly to the AT regime. The automatic location and peak integration routines applied to AC-shifted and AC-split spectra also take into account line shape substructure and line overlaps that occur over a dynamic field range of approximately 1 V / m to greater than 10 kV / m with widths of greater than 80 dB.

[0328]

[0389] In the illustrative example shown in FIG. 20B, the field determination routine j |m separated from the line |=5 / 2 jnD of cesium with lines |=1 / 2 and 3 / 2 5 / 2 applied to the AC-shifted and AC-split spectra of the Rydberg state, where the field determination routine is j Use the higher field sensitivity of the lines with |=1 / 2, 3 / 2. These have large line shifts and at low fields |m j shows a larger line shift compared to the field sensitivity of the line with |=5 / 2. j The |=5 / 2 line instead shows a stronger EIT signal, line variations and shifts at higher fields for RF field measurements over the wide dynamic range given by the AC Starkle regime.

[0329]

[0390] The RFMS1800 peak integration approach described in this section can be generalized to any other field detection method that involves comparing observed and calculated spectral features, including the most general case of Floquet arithmetic. Throughout this discussion, the average peak position 〈Δv〉 is found and used to determine the mean field 〈E〉 or 〈E²〉 (proportional to the average RF intensity). Another possible field determination approach would be to identify the Δv values ​​at which the signal S(Δv) peaks and use those Δv values ​​to calculate the RF electric field. In this method, the Δv values ​​corresponding to the peak position would be obtained by identifying the actual maximum of the signal S(Δv), or by performing local fits over the peak region of the signal and identifying the maximum of these local fits.

[0330]

[0391] However, these most common peak locations can be misleading. If field inhomogeneities exist within the RFP due to its material and geometry, the most common magnetic field may be a node or antinode of an internal standing wave rather than a true measure of the RF field incident on the RFP. Such inhomogeneities can occur even in measurement devices much smaller than the RF wavelength due to dielectric boundary conditions. The average field over the entire detection region more faithfully represents the incident field. The average field and the most common field can differ by as much as 15–20%. Also, even in the absence of field inhomogeneities, the presence of multiple transitions with different RF field shift values ​​of Δv due to atomic magnetic substructure can distort the shape of the spectroscopic peak in S(Δv). At low RF field levels, separate |m j |The peaks cannot be resolved, but the shape of the unresolved composite peak depends on the detailed widths and intensities of its unresolved subcomponents, which may in turn depend on the RF polarization.

[0331]

[0392] Such effects would artificially skew the peak-finding or fitting method toward one of the unresolved subcomponents contributing to the composite peak. However, using the integration method described above to find the average peak location and then determining the E field based on the weighted contributions from the different |mj| components significantly ameliorate this distortion. Furthermore, the averaging method is robust to RF standing wave effects and intra-cell inhomogeneities.

[0332]

[0393] Figure 20A: Cs39D 5 / 2 →40P 3 / 2 Rydberg field probe (RFP) optical atomic spectrum S(Δv) versus laser frequency detuning Δv, showing the Autler-Townes (AT) splitting for measurements of a 12.6 GHz RF electric field resonant with the transition. The region over which the AT splitting lines are integrated to obtain Δv is shaded blue.

[0333]

[0394] Figure 20B: Cs48D for measurement of RF electric fields at 2.5 GHz 5 / 2The two blue-shifted lines are due to the magnetic substate m j = 1 / 2 and 3 / 2 lines and are shaded in blue, while m j The =5 / 2 line is shaded red.

[0334] IV. RFP field pattern measurement

[0395] The usefulness of an RF probe or sensor in measurement and receiving applications depends on the calibration and verification of the directional dependence of the detector's sensitivity to incident RF waves. In this regard, the RFP1100's atom-based RF sensing offers fundamental differences and performance advantages compared to antennas. First, the RFP1100's atom-based RF sensing method offers a rare case of a truly isotropic receiver. Unlike antennas, which cannot be constructed to radiate or receive in all directions due to electromagnetic boundary conditions, atoms sense RF incident from any direction. This is due to the fact that the quantum structure of the atomic state constantly changes in the presence of an incident RF field, and the RF-sensitive state can be accessed by optical (or electronic) readout.

[0335]

[0396] Second, the atom-based method 1800 optionally provides the capability of RF polarization detection simultaneous with, but independent of, electric field measurement. This is due to the fact that the shift or splitting of the field-modified spectral lines depends on the amplitude of the RF field, while the relative intensity of the spectral lines depends on the orientation of the incident RF field polarization relative to the orientation of the optical polarization. Independent (and simultaneous) RF polarization and field detection is not possible with antennas whose sensitivity to the field is inherently linked to the orientation of the RF field polarization relative to the conductive antenna structure.

[0336]

[0397] The directional dependence of the RFP1100 atom-based RF field probe was characterized by performing field and polarization pattern measurements on the RFP1100. To accomplish this, we adapted the method described in Section III and used the AT splittings (Sections IV and VI) and AC shifts (Sections IV and VII) to determine the RF electric fields and their uncertainties for a range of conditions.

[0337]

[0398] Figure 11B shows a diagram of the measurement setup. The RFP1100 is placed at an initial position (X,Y,Z) = (0,0,0) mm, with an uncertainty of ±1 mm in each component, defined as the center of a 10 mm cylindrical vapor cell and optical detection volume. The orientation shown in Figure 11B corresponds to (α,θ,φ) = (0,0,0). Under this condition, the cylindrical axis of the vapor cell is

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[0338]

[0399] Figure 11B: RFP field pattern measurement setup (top) and main axis

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[0339]

[0400] Figures 21A through 23C show field and polarization pattern measurements of the RFP1100 performed at 12.6 GHz RF for a single-axis rotation of the RFP1100 about its major axis at rotation angles α, θ, and φ (see the inset in Figure 11B). Figures 23A through 23C show the spectral output S(Δv,*) of the RFP1100 for * = α, θ, or φ. In the measurements, the range 180° < θ < 360° is omitted from the characterization due to the presence of the RFP handle. The RFP electric field reception pattern is obtained by implementing the <E> field determination method described in Section III-C. The corresponding RF polarization pattern is represented by the line intensity ratio of the peaks of S(Δv,*). The results are shown in Figures 21A through 21C and Figures 22A through 22C, respectively.

[0340]

[0401] Figures 21A to 23C: 12.6 GHz RF for each axis

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[0341]

[0402] In all RFP rotation planes, field patterns with deviations from 4π isotropy are observed due to mild RF perturbations by the RFP material structure surrounding the active atomic vapor. Detailed simulations of RFP field perturbations, their impact on measurement uncertainty, and RFP self-calibration of SI traceability using field pattern measurements and simulation results are presented in subsequent sections.

[0342]

[0403] The RFP polarization pattern is quantified by the ratio R between the average area of ​​the two AT-shifted peaks (blue peaks in Figure 20A) and the area of ​​the central peak (white peak in Figure 20A). The underlying physics is briefly explained below. The central peak in the AT spectrum in Figure 20A is located in the magnetic substate m of the Rydberg level 42D5 / 2. j = 5 / 2, where the direction of polarization of the RF field corresponds to m j Defines the axis along which the value is measured. j The Θ = 5 / 2 level is not RF-shifted due to the RF transition selection rule used in Figure 20A. The Θ shifted peak (blue peak in Figure 20A) is due to the magnetic sublevel m j = 1 / 2, 3 / 2 components, m j =1 / 2 AT shift is m j In FIG. 20A, the m j = 1 / 2 and m j =3 / 2 component is not resolved. The center (m j =5 / 2) component and AT shifted (m j The line intensities of the (=1 / 2, 3 / 2) components are a function of the angle between the RF polarization and the polarization of the optical field inside the vapor cell of the RFP. Therefore, the line intensity ratio between the central peak and the AT-shifted peak shown in Figures 22A to 22C is a function of the angle between the central peak and the AT-shifted peak in the (body frame) of the cell.

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[0343]

[0404] For broadband atom-based RF measurements, the frequency dependence of the RFP response to the incident RF field must also be considered. Figures 24A and 24B show RFP field pattern measurements at α for a 2.5 GHz RF (Figure 24A) alongside the corresponding 12.6 GHz RF pattern (Figure 24B). It can be seen that higher frequencies have a stronger dependence on α, as expected from the fact that shorter wavelength RF fields have a greater tendency to form standing wave patterns in the RFP vapor cell. Nevertheless, even at 12.6 GHz, the observed dependence is smooth and suitable for calibration.

[0344]

[0405] Figures 24A and 24B: at 2.5 GHz (Figure 24A) and 12.6 GHz (Figure 24B)

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[0345] V. SI-traceable self-calibration of finite element simulation and RFP

[0406] One expected benefit of replacing antenna RF standards with Rydberg atom-based RF measurements is that greater accuracy and reliability can be achieved by eliminating the unavoidable perturbation of the target RF field by the metal antenna probe used to measure the field. Rydberg atom-based RF sensing methods offer a clear advantage in this regard, since the atoms represent perfectly frequency-matched quantum receivers for the incident RF field, while there is negligible back-effect of the atoms on the incident RF field. However, the practical realization of SI-traceable, self-calibrated Rydberg atom-based RF primary standards and Rydberg-based RF measurement instruments requires atomic RF probes with material structures to contain alkali vapors, guide and condition optical beams, and provide structural robustness and a practical form factor for reliable use of the probe in test environments. Therefore, field perturbations by the atom probe and non-uniform line broadening of atomic spectral signatures in optical readouts are unavoidable to some degree across the ultra-wideband of RF frequencies accessible by the wide variety of Rydberg atomic states that can be used. As a result, to ensure accurate and traceable RF field measurements, the RFP must be pre-calibrated to account for RF E-field perturbations due to RFP geometry and material design choices, as well as the effects of these perturbations on the Rydberg atomic spectrum readout when performing atomic RF E-field measurements.

[0346]

[0407] The RFP1100 presented here is designed with a geometry and low dielectric constant material that provides both a small RF footprint and mechanical robustness for everyday use. To characterize the effect of the dielectric material structure surrounding the photodetection region through atomic vapor within the RFP1100, a finite element simulation of the RFP1100 can be performed for the test points used in the field pattern measurements in Section IV. Simulation results for a 12.6 GHz RF plane incident on the RFP are shown in Figures 25A-25C. The simulations show:

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[0347]

[0408] Figures 25A-25C show a simulation of the incident 12.6 GHz RF field inside the RFP1100. Field non-uniformity in the optically interrogated atomic vapor detection region is due to the vapor cell compartment being close to the size of the 12.6 GHz RF wavelength, while asymmetries in the vapor cell geometry, such as the vapor cell stem, have minimal effect. To experimentally verify the simulation results, Figure 26 shows the field through the RFP1100 vapor cell.

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[0348]

[0409] Figures 25A-25C: Simulated RF E-fields inside the RFP1100 for the 12.6 GHz incident source shown in Figure 11B. From left to right: total RF E-field in the YZ plane (Figure 25A), XZ plane (Figure 25B), and XY plane (Figure 25C) through the RFP1100. Field amplitudes are displayed in units of incident plane wave field amplitude on a linear color scale ranging from 0.5 (blue) to 1.2 (red). The "ghost shapes" visible in the images outline the glass walls of the vapor cell used.

[0349]

[0410] Figure 26: RF E-field probability distribution 2600 in RFP1100 atomic vapor along the optical beam path of a 12.6 GHz incident source. Plotted are the measured distribution (dashed black line) and the simulated distribution (solid black line), as well as

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[0350]

[0411] To quantify the effect of enclosure-induced RF perturbations on atom-based field measurements using the RFP1100, the enclosure calibration factor C = 〈E〉 / E incident is defined, where 〈E〉 is the average internal field measured by the atom, and E incident is the external incident RF electric field. A simulation at 12.6 GHz with α = 0° yields a C coefficient of 0.71. Using the C coefficients and field patterns of Figures 22A-22C and 23A-23C, the RFP1100 is fully characterized to provide self-calibrated E field measurements that are directly SI-traceable to Planck's constant. Following this methodology, the RFP for self-calibrated SI-traceable broadband operation implements angle-dependent C coefficient tables and frequency-dependent C coefficient tables that are specific to the RFP model. The first-time characterization process performed on the RFP model presented here for SI traceability and self-calibrated operation in RF field measurements is generally applicable to other atom-based RF probes and detector types.

[0351]

[0412] Due to the need for a compartment to hold the atomic vapor in RFP, some level of non-uniform line broadening of the atomic spectral signature in the readout is unavoidable across the ultra-broad band of RF frequencies accessible to Rydberg atoms. In addition to designing a given RFP probe to ensure minimal RF field perturbation across the desired RF field frequency and amplitude operating range, RFP characterization and operation requires a means to account for changing RF field conditions and non-uniformities within the detection volume during normal use of the instrument. This is made possible by using the spectral analysis method presented in Section III and used in Section V for determination of the RF E field in the detection region. RF measurement uncertainties associated with using this and other approaches in atom-based devices and probes such as RFP are presented in the following sections.

[0352] VI. Uncertainties in Rydberg atom-based RF electric field measurements

[0413] For the application of the RFP instrument 1100 in RF metrology and the realization of self-calibrated, SI-traceable RF standard devices, a measurement uncertainty analysis and budget are required when using Rydberg-based measurement instruments. A preliminary analysis of RF measurement uncertainty considering EIT linewidth and spectral features in the Autler-Townes regime has been discussed previously, and characterization of RF perturbations in the atomic detection volume due to the presence of dielectric vapor cell materials and geometry has been investigated. Furthermore, an overview of the fundamental factors contributing to RF sensitivity limitations using Rydberg EIT in atomic vapors for weak RF field detection in the sub-Autler-Townes regime is reviewed. These provide useful general insights into the limiting factors contributing to uncertainty in low RF E-field measurements using Rydberg EIT and Autler-Townes splitting.

[0353]

[0414] However, they are insufficient for the realization of robust and practical Rydberg atom-based probes and instruments as SI-traceable RF standards and measurement tools suitable for use in real-world environments. Therefore, it is necessary to establish a general framework for a comprehensive uncertainty budget for atomic RF E-field measurements using real devices that considers uncertainty contributions from both atomic measurements and implemented analyses of atomic spectral signatures for RF E-field determination, as well as systematics due to physical probe device design attributes and back-end instrument hardware performance, such as the C coefficients introduced above.

[0354]

[0415] A comprehensive uncertainty budget and an overview of the factors contributing to uncertainty due to the RFP instrument 1100 are presented. A detailed proposal and discussion of the uncertainty budget is provided and is intended to be generally applicable to atomic-RF probes and devices employing Rydberg atom-based RF E-field measurements that encompass linear Autler-Townes splitting, AC Stark shifts, and other nonlinear regimes of atom-RF interactions for SI-traceable (self-calibrating) RF E-field measurements. Table I presents uncertainty budgets for several cases. The uncertainty budgets are divided into two general classes of uncertainties: 1. atomic measurement uncertainty, and 2. probe device uncertainty arising from external material and geometry design choices, as well as laser hardware stability during the measurement.

[0355]

[0416] The first two data columns in Table I are for two different field determination analyses in the AT splitting regime, as in Figure 20A. The first data column is based on the field expectation value 〈E〉 in the atomic detection region, and the second data column is based on finding the major AT-shifted peak in the spectrum S(Δv) and the E field E of that peak. P The uncertainty analysis shows that the first method, described in some detail in Section III and used for measurements performed in Section IV, is more robust. The third column shows the RMS electric field using the second-order AC Stark effect, as in Figure 20B.

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[0356]

[0417] Although there are operational uncertainties that ultimately contribute to the final E-field measurement, they are under the direct control of the operator and can, in principle, be eliminated. For example, there are field measurement uncertainties that arise from probe-to-source positioning uncertainties in the setup. These types of systematic uncertainties affect E-field measurements performed with any class of probe device and are not specific to atom probe performance. Therefore, such operational uncertainties are not included in the uncertainty budget in Table I. However, they are mentioned and explained in the RFP field patterns presented in Section IV.

[0357] [Table 1]

[0358] VII. Pulse Detection and Time-Domain RF Waveform Imaging

[0418] Many RF field detection and measurement applications require measurement of pulsed or modulated fields in addition to the continuous wave (cw) fields presented thus far in this disclosure. To meet these needs, the RFMS1800 provides time-dependent field detection and RF waveform imaging capabilities. In this mode of operation, the RFMS1800 tracks the time dependence of the atomic response received by the RFP1100. The time-dependent signal record S(Δv,t) reveals how the RF field depends on time t.

[0359]

[0419] Time-dependent field detection using the RFMS1800 and RF waveform imaging is demonstrated in Figures 11C-11F. The principle of operation is to use spectral data recorded as a function of time to implement a field determination method similar to that used in the cw case described above. A 2.5 GHz carrier wave is incident on the RFP1100 and its intensity varies over time. 42D 5 / 2The time-dependent AC Stark shift of the state is recorded and displayed in real time with a time resolution of 1 μs. FIG. 11C shows, from left to right, recordings of rectangular RF pulses with pulse lengths of 10 μs, 100 μs, and 200 μs, with a pulse frequency of 1 kHz in all cases shown. The rectangular profile of the pulse is resolved within the 1 μs time resolution used in this disclosure. The RFMS1800 can also resolve substructures within the RF pulse; for example, FIG. 11D shows a recording of an RF rectangular pulse with superimposed sinusoidal amplitude modulation (10% modulation depth, 5 kHz baseband frequency). FIG. 11E shows a recording of an amplitude-modulated cw RF signal (2.5 GHz carrier, 100% modulation depth, 5 kHz baseband frequency). FIG. 11F shows a recording of an FM-modulated cw signal (12.6 GHz carrier, 5 kHz FM baseband frequency, 160 MHz peak deviation). The FM signal resonates with the carrier. 5 / 2 40P 3 / 2 It is probed using resonance.

[0360]

[0420] Figures 11C to 11F: Recordings of time-dependent RF fields. Recordings show RFP optical transmission displayed on a linear grayscale (arbitrary units) measured versus time and laser detuning. Figure 11C: EIT AC Stark shift response to square pulses of a 2.5 GHz RF signal with pulse lengths varying from 10 μs, 100 μs, and 200 μs from left to right at a repetition rate of 1 kHz. The RF intensity is constant throughout the pulse. Figure 11D: EIT AC Stark shift response to a pulsed signal, also amplitude demodulated within the pulse. Figure 11E: Recording of a continuous amplitude-modulated RF signal. The carrier frequency is 2.5 GHz, and the AM baseband frequency is 5 kHz. Figure 11F: Recording of a continuous frequency-modulated RF field near the AT resonance. The carrier frequency is 12.6 GHz, 5 kHz, and the FM deviation is 160 MHz.

[0361] VIII. Conclusion

[0421] In this disclosure, the first self-calibrating, SI-traceable, broadband Rydberg atom-based radio frequency electric field probe (RFP) 1100 and measurement instrument (RFMS) 1800 is presented. The RFMS 1800 is a commercially available device comprising an atomic RF field probe (RFP) 1100, which is connected by a ruggedized fiber optic patch cord to a portable mainframe control unit 1160 with a computer software interface for probe RF measurements and analysis, including real-time field and measurement uncertainty readout, and spectral RF waveform visualization. The RFP 1100 uses atom-based detection using electromagnetically induced transparency (EIT) readout of spectral signatures from RF-sensitive Rydberg states of atoms in an atomic vapor.

[0362]

[0422] The RFMS1800 measures RF E-fields from resonant and non-resonant Rydberg RF-field interactions detected by the RFP1100 probe head, and uses an RF-field-free atomic reference and optical laser frequency tracker (OFT) integrated into the RFMS mainframe 1160 to ensure high reliability and accuracy in RF E-field measurements using Rydberg EIT spectroscopy in atomic vapors. An overview of Rydberg EIT readout in atomic vapors for RF E-field measurements is provided, and the operating principles of the RFP1100 and RFMS1800 are explained. An approach for determining the average RF E-field from the spectral signature in the RFP1100 atom probe head is introduced and implemented in demonstrative RFP measurements of both near-resonant and far-resonant RF E-fields from atomic Rydberg transitions.

[0363]

[0423] Full characterization of the RFP probe 1100 was performed by measuring the RF polar field pattern at 12.6 GHz, obtained by single-axis rotation of the RFP1100 along its major axis in the far field of a standard gain horn antenna. Field pattern measurements at 2.5 GHz were also performed to verify RF polarization sensitivity. Detailed finite element simulations of the fields inside the RFP1100 at 12.5 GHz (FIGS. 25A-25C) and 2.5 GHz (not shown) were performed to quantify the effects of the probe's component materials and geometry on RF E-field measurements with optically interrogated Rydberg atoms. Simulation results were found to be in good agreement with the RFP field pattern measurements, revealing deviations of the RFP1100 from a perfectly isotropic RF receiver due to its specific materials and geometry.

[0364]

[0424] The measurement and simulation results were then used to calibrate the probe 1100 relative to SI-traceable atomic RF E-field measurements. A Rydberg atom-based RF E-field measurement uncertainty budget and analysis was introduced and implemented in RFP operations for SI-traceability of Rydberg atom-based RF probes and measurement tools in RF metrology. Modulated and pulsed RF field measurement and detection capabilities using the RFP 1100 were also demonstrated and explained. In some embodiments, wideband RF measurements from 3 MHz (HF band) to greater than 100 GHz and sub-THz RF fields have also been performed.

[0365]

[0425] The RFP instrument 1100 is a standalone device and a new quantum technology platform with broad applicability. In metrology, the RFP1100 provides the first instrument suitable for use by metrology institutes worldwide for the establishment of new atomic primary RF E-field standards by enabling the management of round-robin tests requiring standardized metrology and measurement. As a portable broadband atomic RF E-field probe, the RFP1100 is a single, self-calibrating device that provides RF E-field measurement capabilities across RF frequency ranges that are otherwise accessible only using multiple receiver antennas. This can simultaneously reduce operational complexity, improve reliability, and lower calibration costs in RF test and measurement applications. As a new platform technology, the RFP1100 can be easily adapted to other application-specific RF sensing, receiving, and measurement needs, as well as for communications, surveillance, and the implementation of novel Rydberg atom-based RF capabilities in the THz range.

[0366] Appendix B: An exemplary room-temperature Rydberg THz maser

[0426] Appendix B: “Room-temperature Rydberg THz master,” David A. Anderson and Georg Raithel, Internal Document, November 26, 2019, pages 1-6, is incorporated herein by reference in its entirety.

[0367]

[0427] Figures 27-30 illustrate a room-temperature Rydberg THz maser 2700 and a room-temperature Rydberg THz transceiver 3000 according to various exemplary embodiments. Figure 27 is a schematic diagram of a Rydberg atomic radio frequency (THz) maser 2700. Figures 28A and 28B are plots 2800A and 2800B of the Rydberg versus potential 2802 as a function of the internuclear axis 2804. Figures 29A and 29B are plots 2900A and 2900B of the absorption coefficients 2902 and 2906 as a function of the laser frequency detuning 2904. Figure 30 is a schematic diagram of a Rydberg atomic radio frequency (THz) transceiver 3000.

[0368] Introduction

[0428] Advances in communications technology, THz imaging (especially wide-field THz imaging), security, and other applications require advances in high-power, low-SWaP, and low-cost THz sources and detectors. In communications, cellular devices and WLANs occupy bands up to approximately 2 GHz and 5.8 GHz, respectively. General pressure on wireless bandwidth is becoming an increasing problem, with data traffic on mobile devices, as just one example, estimated to be growing by over 50% annually. These applications require efficient THz "flashlights" for THz illumination and focal-plane, pixelated, room-temperature, yet highly sensitive THz receivers.

[0369]

[0429] The current underutilization of the sub-THz and THz ranges of the electromagnetic spectrum in these fields stems primarily from a lack of technology in THz sources and detectors / receivers. At frequencies above 30 GHz, current technologies include difference frequency generation using RF circuits, solid-state devices, vacuum electronics, lasers, and nonlinear optical elements, as well as frequency doubling using molecular FIR / THz lasers.

[0370]

[0430] Despite the availability of these sources, THz technology has not yet found its way into mainstream communications. This is, in part, due to the inherent power inefficiency, cost, weight, and size limitations of existing THz sources, detectors, and receivers. For example, frequency doubling of high-quality microwave signals is highly inefficient and price-prohibitive at higher frequencies. Quantum cascade lasers (QCLs) typically operate at higher frequencies (10–100 THz), and QCLs approaching 1 THz typically require cryogenic operation. Conversion of laser light to THz via difference frequency generation is inherently inefficient. On the receiver / detector side, standard bolometer-based sensors lack baseband bandwidth, while highly sensitive superconducting transition edge sensors require cryogenic temperatures, and pixelated devices with thousands of pixels are mostly still in development.

[0371]

[0431] This disclosure investigates and develops atom-based THz sources and detectors. The proposed Rydberg atomic THz laser / maser 2700, 3000 has the potential to generate coherent, narrowband, tunable radiation in the range between 0.1 THz and several THz. This source disclosure is divided into several stages, progressing from the fundamental demonstration of THz emission from Rydberg atomic vapor toward the realization of efficient THz generation at substantial powers (over 1 mW). On the receiver side, atom-based field sensors are used to detect and demodulate the THz signal emitted from the frequency-matched atom-based source. Both the Rydberg maser transmitter 3010 and receiver 3020 are scalable to pixelated arrays. The matched Rydberg atom-based transmitter and receiver unit 3000 is suitable for general imaging applications and, when combined with atom-based modulation and demodulation methods, for applications in communications technology.

[0372] Rydberg atomic THz maser operating principle

[0432] Figure 27: Concept of the high frequency (THz) Maser 2700 for cesium implementation.

[0373]

[0433] A dense sample of Rydberg atoms provides, to a certain extent, an ideal laser gain medium. Herein, a radio frequency (THz) maser 2700 is disclosed having a bound-bound masing transition between a pair of Rydberg states. Figure 27 shows the proposed concept of a Rydberg THz source or transmitter (Tx) 2700. The Rydberg gain medium is contained within a cesium or rubidium thermal vapor cell 2702 and is pumped from ground to the Rydberg state by a laser 2701 via a suitable one-photon or multi-photon excitation process. To achieve reasonable conversion efficiency of laser energy to THz radiation, a large fraction of the laser light needs to be absorbed.

[0374]

[0434] In the most general case of two-photon excitation, the lower transition can be on the D2 line, in which case the Behr absorption coefficient can be reduced to a few cm -1 This is large enough to ensure efficient absorption. However, the upper (Rydberg) transition is always 1% cm -1 The THz maser will have an absorption coefficient in the range of 1 / 2 or less. This problem can be addressed by injecting up-excited pump light 2701 using optical cavities 2704a, 2704b. The cavities serve two purposes: first, to increase the effective absorption length in the medium, and second, to increase the up-excited Rabi frequency while maintaining a small device size. The optical pumping beam 2701 propagates transversely to an elongated cell containing or embedded within tunable THz cavities 2706, 2708 with moderate Q factors. THz maser radiation occurs in the longitudinal Gaussian modes of the resonator. Maser radiation 2710 is extracted into free space through an impedance-matched coupling hole 2708 by selecting the appropriate hole diameter and length (coupling loss = other cavity losses). The geometry and detailed shape of the coupling hole also determine the diffraction-limited output mode of the THz maser.

[0375]

[0435] A Rydberg THz receiver (Rx) can be implemented by inverting Figure 27 in many respects. The THz field is then detected by Rydberg electromagnetically induced transparency (Rydberg EIT) on the lower (852 nm) transition. In Rx mode, the 852 nm beam acts as the EIT probe, while the upper transition acts as the EIT coupler. The symmetry of atomic physics methods and RF engineering between the proposed Tx and Rx Rydberg maser and receiver units ensures considerable efficiency of the proposed research and development effort, both in terms of the basic concept of matched Tx and Rx devices and in the use of budget and resources to realize and fabricate them. Selected details are provided below.

[0376] Rydberg maser threshold

[0436] For example, THz and emission from Rydberg samples cascading through lower levels have been observed by C. Adam's group, by T. Pfau's group, and at CQT (National University of Singapore). Achieving Rydberg superfluorescence and maging, which leads to coherence of the emitted field, presents somewhat unexpected challenges. To illustrate this point, superfluorescence in an elongated pump medium, whose length is much larger than the wavelength and whose cross-section is larger than one square wavelength, is considered.

[0377]

[0437] In this case, superfluorescence occurs when the Rydberg density is greater than the dipolar relaxation rate g dipole and the spontaneous decay rate of the maging transition g maser This occurs when the ratio (item b) between the inverted cube wavelength (item a) and the 300 GHz field is 1 mm 3 This corresponds to one Rydberg atom per second (i.e., almost none), which may seem very favorable, but it is not. Item b makes Rydberg superfluorescence and imaging difficult. As an example, the 25D level of rubidium in a 300 K radiation field has a fluence of g per second at 300 K. all= 90,000, which includes all spontaneous decays, all upward and downward blackbody bound-bound transitions, and blackbody ionization. The most favorable 25D to 25P transition has a spontaneous decay rate g of 59 per second. maser (This is calculated at 0 K.) The resonant field is 150 GHz, with about 42 thermal photons at 300 K. A first guess is g dipole ~g all This means that (at 150 GHz) 3 10 per 5 corresponds to a critical Rydberg atom density of approximately g dipole / g maser =90,000 / 60~10 3 This would suggest a ratio (item b).

[0378]

[0438] However, the Rydberg transition can also be broadened by interaction time broadening, the Rydberg interaction, and stray electric and magnetic fields. These additional broadening mechanisms are typically dipole ~10 6 From 10 7 s -1 This causes a dipolar relaxation rate of about g dipole / g maser ~10 5 This gives the ratio (item b) of 1 cm (at 150 GHz). 3 A corresponding critical Rydberg atom density of 10 to 10 per 10 s should be achievable (see below), which is not a trivial task. The fact that the medium is embedded in a medium-Q cavity reduces the critical Rydberg atom density by a small factor.

[0379]

[0439] Inhomogeneous broadening can be largely eliminated by providing a very low density, collisionless, and cryogenic environment, and a very high Q superconducting microwave cavity resonant with the maser transition. These systems ensure maximum cooperativity and minimum maser field energy (typically measured in number of microwave photons). These systems with cold atoms have been used in high-profile efforts in cavity QED, quantum state control, and quantum engineering.

[0380] Rydberg atomic interactions

[0440] It is well known that Rydberg atoms interact via long-range multipolar interactions, resulting in attractive and repulsive molecular potentials. From the perspective of building masers, these result in undesirable level shifts of optical Rydberg atomic excitations and maser transitions. In a recent publication [X. Han et al., J. Phys. B 52, 135102 (2019)], it was found that the equilibrium distance of long-range Rydberg molecules scales as the 2.5th power of the effective quantum number, in good agreement with other previous studies. This scaling appears to hold across several species and quantum states, giving a predicted size of a Rb25D Rydberg pair of molecules of approximately 0.3 microns.

[0381]

[0441] Figures 30A and 30B show the interaction potential of the pair state (Rb25D5 / 2)2 for one case of total angular momentum M along the internuclear axis. We find that bound molecular states can exist around an internuclear separation of R = 0.3 μm, and that the van der Waals shift drops to less than 2 MHz at R = 1.5 μm, which is a low 10 11 cm- 3 corresponds to the Rydberg atom density in the range. Noting that the magnitude of the interaction does not depend much on M, the calculations indicate that the van der Waals shift should not severely limit maser operation in Rb25D. Similar results are expected for the Cs system.

[0382]

[0442] Figure 28A and Figure 28B: (Rb25D 5 / 2)2 Rydberg pair potential 2802 and total angular momentum M=2 along the internuclear axis 2804, for both of which p is a two-body molecular state. The symbol domain is 5P 3 / 2 is proportional to the excitation rate from the circularly polarized excitation laser, averaged over all alignment angles between the polarization of the circularly polarized excitation laser direction and the internuclear axis. The enlarged view in Figure 28B shows the long-range van der Waals interactions.

[0383] Rydberg atomic excitation

[0443] For given Rabi frequencies on the down- and up-excitations, the Lindblad equation can be solved to find the Rydberg atomic population averaged over the Maxwellian velocity distribution in the cell. Figures 29A and 29B show an example for Rb at a cell temperature of 350 K. The absorption on the down-excitation (780 nm) is approximately 1 cm. -1 , which is on the order of the path length of each beam through the vapor cell. The upper transition is only 0.3 m -1 The Rydberg-pumped medium has an absorption coefficient of about 5×10. To ensure reasonable optical-to-THz energy conversion, this disclosure specifies an optical cavity for the upper transition light with a finesse on the order of 30. The cavity increases the effective path length of the beam in the medium to nearly 1 meter, resulting in improved deposition of the upper transition laser energy into the Rydberg pump medium. Finally, estimates indicate that roughly 1% of the atoms of all velocity classes in the cell can be promoted to the Rydberg state. Approximately 5×10 11 cm -3 At 350 K, the atomic density of Rb-85 is 5×10 9 cm -3 This estimates a Rydberg atom density of about 1000, which is more than an order of magnitude higher than the estimated critical density for superfluorescence in the Rb25D to 26P transition, and more than an order of magnitude lower than the density at which the van der Waals shift becomes important.

[0384]

[0444] Figure 29A: Upshift of the indicated Rabi frequencies (solid line, Ω) versus detuning from the downshifting laser resonance 2904. C ) and downward transition (dashed line, Ω P) absorption coefficients 2902, 2906. The up-transition laser is resonant and frequency-locked. The plot shows the EIT (dip in the dashed curve) as well as the typical absorption level at the transition. Figure 29B: Up-transition absorption coefficient 2902 and Rydberg state population 2908 versus down-transition detuning 2904.

[0385]

[0445] FIG. 30: THz source and matched receiver 3000.

[0386] THz source

[0446] Rydberg Technologies Inc. can manufacture miniaturized Rb and Cs vapor cells with inner diameters ranging from 3 mm to several centimeters and lengths of 5 mm or more. The THz source cell used in this disclosure contains a Pyrex cylinder with an anodically bonded float-zone (FZ) silicon instead of a conventional optical window. While Pyrex glass absorbs THz radiation, FZ silicon has low absorption and a high dielectric constant in the THz range, allowing a low-finesse THz cavity to be formed within the cell. Cell fabrication can include anodic bonding for monolithic construction, including fabrication of FZ glass vapor cells for other applications.

[0387]

[0447] In this disclosure, the THz cavity 2700, 3010 has a fixed-position exit disk 2708, 3014a of FZ silicon with an aperture shape optimized for directional emission of THz from the cavity. The rear THz cavity mirror 2706, 3014b is a solid disk without an embedded THz exit structure. The outer surfaces of both FZ silicon reflectors 3014a, 3014b are coated with a metal surface to ensure minimal radiation losses and a high Q factor of the THz cavity. For frequency tuning of the THz cavity, the rear THz reflector 2708, 3014b may be an adjustable component embedded within the cell and translated back and forth by an external actuation device. It is part of this disclosure to (a) calculate the best possible shape and material selection for the exit port that will provide good output coupling, diffraction-limited beam, impedance matching (cavity absorption loss = coupling loss), and mechanical stability against external atmospheric pressure, and (b) determine the best solution that will provide frequency tunability of the THz cavity 2700, 3010.

[0388]

[0448] As can be seen in Figures 27 and 30, the atomic sample is pumped laterally. Pumping is performed by counter-aligned down-excitation laser beam 3016a and up-excitation laser beam 3016b. In Figure 29B, the Rydberg population ρ 33 reaches a value of about 2% of all atoms (i.e., resonant atoms with the correct velocity in the pump beam direction have a ρ of about 50% 33 Therefore, 5 × 10 11 cm -3 At the atomic density of (Rb-85 at 350 K), the density is about 10, which is low enough to avoid interactions and high enough to significantly exceed the above-estimated maging threshold. 10 cm -3 can be expected to have a Rydberg atom density of

[0389]

[0449] The achievable output power is limited by the quantum conversion efficiency of optical light to THz and the time scale of the Rydberg atomic population. The ionization energy of Rb is 4.2 eV, so the quantum efficiency at 150 GHz is 1.5 × 10 -4 Several tens of mWcm -2 Pump strength and 10cm 2 With a pump cross section of 1 m, tens of microwatts of power can be expected in coherent narrowband THz radiation delivered in a diffraction-limited beam. 2 For a coverage area of ​​1000 m, the THz electric field is on the order of 0.1 V / m, which is well above the sensitivity limit of Rydberg EIT-based field sensing methods. In some embodiments, achievable output power levels can be determined experimentally and optimization measures investigated.

[0390]

[0450] Note that the lower maser levels in a Rydberg maser should be efficiently depleted by spontaneous decay, and spontaneous decay is faster for lower maser states than for higher maser states. It is possible to harvest THz emission from the entire Rydberg cascade, with the topmost being the first collected Rydberg level. This scheme clearly increases the overall optical-to-THz energy conversion efficiency. Finally, if the lower maser levels are found to deplete too slowly to allow cw THz emission, the decay rate of the lower levels of the Rydberg maser transition can be accelerated by quenching. In this way, the lower Rydberg maser levels can be quenched using a quenching laser. 1 / 2 (in Rb) or 6P 1 / 2 (in Cs). The atoms then decay rapidly to the ground state via spontaneous emission on the D1 line. The quenching laser would be an additional auxiliary laser introduced into the source (Tx) cell.

[0391] THz receiver

[0451] Perfect matching of source (Tx) and receiver (Rx) frequencies is an inherent advantage of atom-based THz technology. As shown in Figure 30, the Rydberg level in the Rx cell 3220 is probed by a combination of EIT probe and coupler beams 3002 and 3004, which have frequencies similar to the pump beams 3016a and 3016b in the Tx cell 3010. Absorption of the probe beam exhibits an EIT signal when the coupler resonates with the Rydberg level (cascaded EIT). Field-induced level shifts and AT splitting of the sensor Rydberg state are observed by scanning the coupler laser frequency across the atomic Rydberg resonance and recording the probe transmission. The observed spectrum reflects the radio frequency (RF) electric field. This method of RF field sensing has been investigated and developed for the field sensing devices and products of this disclosure. Here, the THz Rx cell 3020 is used to measure the THz output 3008 from the Tx cell 3010.

[0392]

[0452] Note that the Rydberg Tx and Rx cells 3010, 3020 can be used and tested independently of each other. For example, a standard bolometer broadband THz sensor can be used to verify the basic THz emission functionality of the atom-based Tx cell. Similarly, the functionality of the atom-based Rx cell 3020 can be verified by measuring the THz emission of a commercially available THz source.

[0393] Appendix C: Exemplary Rydberg-Based Quantum RF Phase Detector and Receiver

[0453] Appendix C: “Rydberg-based quantum RF phase detector and receiver,” David A. Anderson and Georg Raithel, internal document, pages 1-4, is incorporated herein by reference in its entirety.

[0394]

[0454] Figures 31 through 33 illustrate a Rydberg atom RF phase detector and receiver 3100 according to various exemplary embodiments. Figure 31 is a schematic diagram of the Rydberg atom RF phase detector and receiver 3100. Figure 32 is a schematic diagram of an atomic energy level diagram 3200 for the Rydberg atom RF phase detector and receiver 3100 shown in Figure 31. Figure 33 is a plot 3300 of the optical phase 3302 as a function of laser frequency detuning 3304 for the Rydberg atom RF phase detector and receiver 3100 shown in Figure 31.

[0395] 2. Relevance

[0455] At the heart of this disclosure is the development of a novel quantum sensor 3100 for RF phase detection and measurement using Rydberg atoms. This disclosure addresses existing limitations of Rydberg-based quantum RF field sensing by employing the new capability of RF phase detection using all-optical superheterodyne technology. The new quantum sensor 3100 offers substantial improvements in achievable RF phase resolution, detection sensitivity, and bandwidth compared to state-of-the-art antenna technology. Using established phase-sensitive technologies such as synthetic aperture radar (SAR), phase-modulated signal transmission and telecommunications, antenna characterization, and the emerging trend in phased array antennas in 5G, the quantum RF phase sensor 3100 enables previously impossible RF applications thanks to the performance advantages exhibited by Rydberg-based RF sensors compared to antennas. This includes ultra-subwavelength RF detection with a single subwavelength atomic detector, wideband frequency, and large dynamic field range capabilities, as well as EMP / EMI immunity for use in harsh EM environments and calibration-free operation for long-term stability and reliability.

[0396]

[0456] In this disclosure, a feasibility study of the quantum RF phase detector 3100 is conducted, demonstrating core capabilities relevant to a wide range of applications, including communications, security, surveillance and reconnaissance, electronic support countermeasures, navigation, RF power, and antenna engineering. This disclosure includes the design, development, and laboratory demonstration of the quantum RF phase detector 3100. Detector characterization is performed to establish feasibility and baseline performance metrics in sensitivity, spatiotemporal resolution, and dynamic range. Demonstrations of super-resolution wideband detection, isotropic reception, and enhanced phase-modulated signaling are also performed. The quantum RF phase detector 3100 has substantial size, weight, power (SWaP), and long-term cost savings compared to existing long-wavelength antenna receiver and detector systems used across these application areas.

[0397] Basic principles of Rydberg-based RF field and phase detection

[0457] Rydberg atomic RF field sensing uses electromagnetically induced transparency (EIT) as a quantum optical readout of Rydberg states in atomic vapors. Parameters of the incident RF field are obtained by passing an optical EIT beam through a vapor cell, which spectroscopically interrogates the electric-field-sensitive Rydberg states of atoms exposed to the incident RF field. Detected changes in the transmission of the optical probing beam through the atomic vapor provide direct atom-mediated RF optical readout and information about the incident RF signal field. Broadband sensing of the RF electric field is given by the large electric dipole moment d of the RF resonant transition between Rydberg states, which, in a single atom, spans a wide range of RF frequencies from MHz to sub-THz, with a minimum field detection level of less than 1 V / m. The electric field amplitude of the RF wave is proportional to the atom-field coupling strength Ω. RF where, in the small field limit, the field amplitude is

number

number

[0398]

[0458] Rydberg-based RF phase sensitivity is achieved using a fundamentally new heterodyne detection scheme 3100 based on electro-optic encoding of the RF phase of a local RF oscillator within the optical field used for quantum optical readout (EIT). In this quantum superheterodyne (quantum superheterodyne) detection scheme 3100, an optical reference RF modulation is injected into an optical coupler laser to imprint an RF reference onto the Rydberg atoms that is phase coherent with the incident RF field being measured. Here, the coupler beam is driven at a signal frequency Ω tuned to near the frequency of the incident RF field. RF The resulting effective EIT coupling Rabi frequency Ω c ~cos(φ RF +φ OPT ) is the phase of the incident RF field, φ RF , optical phase φ OPT , and the common factor. Therefore, changes in the incident RF phase can be detected from changes in the optical absorption of the EIT probe beam passing through the atomic vapor. Detailed examples are shown in Figures 31 to 33.

[0399] 3. Technical purposes 3.1. Detailed analysis of the physical principles underlying quantum RF phase reception and measurement.

[0459] The parameter space of relevant tuning parameters of Rydberg-based detectors, including optical Rabi frequency and optical modulation parameters, is explored for optimal performance in superheterodyne RF detection, ultra-narrowband intermediate frequency (IF) amplification, and RF signal channel selectivity.

[0400] 3.2. Development of Rydberg RF phase sensor for laboratory demonstration.

[0460] In the second component, a laboratory prototype 3100 was designed and built using a miniaturized vapor cell detector 3106 with optical components for optical injection and readout, along with back-end optical beam modulation and conditioning for heterodyne RF phase detection. An RF transmission and antenna characterization platform was designed for testing and practical demonstration.

[0401] 3.3. Characterization, Verification, and Performance Demonstration.

[0461] In the third component of this disclosure, the detector 3100 was validated and characterized by evaluation of performance metrics including achievable phase sensitivity, spatiotemporal resolution, and dynamic range. Proposed practical demonstrations include super-resolution wideband detection, isotropic reception, sub-wavelength near-field antenna field and phase mapping, and extended phase-modulated free-space signal reception and communication. The design of the low-SWAP quantum RF detector and receiver device 3100 was evaluated.

[0402] 4.Technical approach to achieve the objectives

[0462] In this disclosure, the technical design and development of a Rydberg-based quantum RF phase detector has been carried out, and proof-of-principle measurements, detector characterization, and laboratory demonstrations have been performed. Fundamental atomic physics research has been developed and applied for ultra-sensitive RF phase detection using an all-optical RF heterodyne Rydberg EIT readout scheme. Key components of this paper are described in the following sections.

[0403]

[0463] Figures 31 and 32 illustrate the operating principle and basic design of a Rydberg-based quantum RF phase detector 3100. The experimental setup shown in Figure 31 comprises a miniaturized rubidium vapor cell detector 3100 with probe (780 nm) and coupler (480 nm) laser beams 3102, 3104 counterpropagating through the vapor 3106 for a typical scheme in two-photon Rydberg EIT quantum optical readout. (The detector 3100 may also be designed using cesium vapor with a corresponding optical wavelength.) The probe transmission 3108 is detected by a photodetector for electrical readout of the detector 3100 response to RF phase and amplitude when the coupler is tuned to a selected field-sensitive Rydberg level and phase-modulated with the RF frequency to imprint an RF reference phase onto the detector atoms.

[0404]

[0464] In our setup, RF phase modulation of the coupler laser 3104 is generated using an electro-optic (fiber) modulator 3120, and an additional optical phase control 3110 is added in-line to allow optional scanning over the phase of the incident RF field. The corresponding modified Rydberg EIT ladder scheme 3200 implemented here is shown in Figure 32, where two RF phase-modulated coupler frequency components couple the rubidium 5P → nS and 5P → (n + 1)S Rydberg levels. The incident RF field couples these S Rydberg levels to the nearby nP Rydberg level, establishing an atom-mediated interference relationship between the RF-modulated optical signal and the incident RF. The coherent two-photon EIT ladder scheme 3200 converts the relative phase of the incident RF into a probe transmission change.

[0405]

[0465] Figure 33 shows a simulated RF phase measurement of a 5 GHz RF field incident on a Rydberg-based quantum RF phase detector 3100 in a room-temperature vapor cell 3106. The probe signal intensity 3300 from the detector 3100 is shown on a relative color scale 3306 as a function of the optical phase delay 3302 relative to the Rydberg resonance and the probe frequency 3304. Here, direct atom-mediated conversion of the phase of the RF wave from the Rydberg quantum phase detector 3100 to the optical signal output is readily observed, with variations in the optical signal intensity during a linear scan of the optical (RF reference) phase at the detector 3100 revealing the phase of the incident RF wave (the black arrow indicates a π phase shift).

[0406]

[0466] In applications where the RF signal phase is varying relative to the detector 3100, such as spatial field and phase mapping in phase-modulated communications or antenna measurements, the optical signal output 3300 responds in real time to RF carrier phase changes without scanning the optical phase. Conversely, optical phase control enables RF phase detection in applications where the incident signal is not modulated or locked relative to the optical (RF reference) phase in the detector. Embedded optical (RF reference) phase control also enables selectable high-frequency modulation of the RF reference, enabling the detector to achieve all-optical (super)heterodyne RF detection capabilities with improved sensitivity, high spatiotemporal phase resolution, and RF frequency selectivity. Furthermore, this is all done in the analog domain in atom-field interactions, instead of heterodyning and processing on electrical signals as required in antenna-based platforms.

[0407]

[0467] Figure 31: Illustration of quantum RF phase detector sensing element backend and operating principle 3100 for phase-sensitive measurement of RF electric fields. RF / microwave horn (MW) 3140 represents any RF signal source 3130, e.g., an antenna under test, an RF communication signal, or other object wave of interest. Fiber modulator 3120 phase-coherently imprints an RF reference beat onto coupler beam 3104 sent to atoms in vapor cell 3106. The RF reference beat replaces the reference beam typically required in phase-sensitive (holographic or superheterodyne) field detection. The vapor cell 3106 in atom-based RF sensing element 3100 is small (approximately 1 mm) and has 780 nm and 480 nm laser beams 3102, 3104 counter-propagating through the vapor. Fiber modulator 3120 and optical phase control element 3110 are part of the sensing element backend, which includes the laser, signal readout electronics, and a computational unit for analysis.

[0408]

[0468] FIG. 32: Quantum mechanical level diagram and optical / RF excitation pathway 3200 used in phase-sensitive RF electric field detection and measurement 3100.

[0409]

[0469] Figure 33: Optical phase 3302 and frequency detuning (ΔP Calculated optical signal readout 3300 from a Rydberg-based quantum RF receiver of the phase of a 5 GHz RF field incident on the Rydberg base as a function of Δ P The optical phase separation between the maximum (cyan) and minimum (red) of pattern 3306 in the plot along the vertical direction at ≈0 MHz, the shift in the RF field picked up by the quantum RF receiver. P For , the phase of the incident RF carrier signal is mapped directly onto the optical signal.

[0410]

[0470] Unlike antenna receivers, the Rydberg-based quantum RF phase detector / receiver 3100 is essentially free of stray external radiation and interference from a local reference oscillator due to the local oscillator being imprinted on the field-sensitive Rydberg atom via optical modulation. Direct optical injection into the frequency-matched Rydberg resonance also renders the Rydberg-based quantum RF phase receiver 3100 immune to oscillator sideband noise, a key practical and design constraint in antenna systems. Noise immunity arises due to the inherently weak interaction between the atom and the coupling light of the target atomic transition and typically non-resonant higher-order optical sidebands. Finally, the presence of image frequencies, another major drawback of conventional antenna-based superheterodyne receivers (SUPERHETERs), can be completely avoided by taking advantage of the ultra-narrow IF amplification and high frequency / channel selectivity enabled by narrow-line atomic Rydberg transitions and parametric amplification.

[0411]

[0471] In some embodiments, simulation codes for solving the master equations for four-level and five-level systems for Rydberg EIT field and phase detection can be utilized. In some embodiments, numerical simulations can be performed to model EIT readout of RF fields and phases for selected resonant and near-resonant RF fields. In some embodiments, theoretical detector performance metrics can be evaluated, including baseline performance in sensitivity, spatiotemporal resolution, dynamic range, parametric amplification, and RF frequency selectivity.

[0412] Appendix D: Exemplary optical RF phase detection and measurements with Rydberg atomic vapor

[0472] Appendix D: “Optical RF phase sensing and measurement with Rydberg atom vapors,” internal document, pages 1-2, is incorporated herein by reference in its entirety.

[0413]

[0473] Figures 5A-5C illustrate a quantum state space interferometer 500 according to various exemplary embodiments. Figures 5A and 5B are schematic diagrams of the quantum state space interferometer 500. Figure 5C is a plot 550 of the optical readout of the quantum state space interferometer 500 shown in Figures 5A and 5B.

[0414] Optical RF phase detection and measurement with Rydberg atomic vapor.

[0474] Relevance: In recent years, there has been a surge in efforts to harness the unparalleled sensitivity of Rydberg atoms to RF electric fields across the electromagnetic spectrum from DC to THz to enable new capabilities in RF and novel atom-based quantum RF field sensors and devices. To date, progress in Rydberg atom-based RF field sensing remains rooted in the same fundamental method: spectroscopic detection of the atom's field-sensitive Rydberg state, which measures the electric (E) field amplitude of incident RF electromagnetic waves. Initially motivated in part by the need to replace century-old antennas as RF electric field standards with broadband, SI-traceable, absolute (atomic) standards for RF E fields at national metrology institutes, this has more recently been established as a novel quantum technology platform with broad capabilities that will mature into commercial RF detection and measurement instruments.

[0415]

[0475] Beyond RF E-field metrology and measurements, most RF applications require phase-sensitive detection capabilities. Some examples include antenna near-field / far-field mapping, synthetic aperture radar (SAR), communications, phased array antenna characterization, and 5G receivers. To address this, this disclosure has developed and demonstrated a fundamentally new all-optical RF phase detector 500 based on Rydberg atomic vapor. As a new device, the Rydberg quantum-enhanced field sensor 500 addresses these needs.

[0416]

[0476] Background: Phase detection and heterodyne methods rely on providing a local oscillator field within the detector for phase referencing and, optionally, parametric amplification. This is common knowledge in many fields, including RF, holography, and nonlinear optics. Ongoing research in Rydberg-based E-field detection has used an external RF reference field generated by a secondary antenna for this purpose. The all-optical RF phase detection method 500 presented here employs an effective RF reference via appropriate electro-optic modulation of a laser beam used to read out the Rydberg atom's response to the measured field. Modulated laser fields have already been employed in Rydberg atom RF detection, providing the atoms with an efficient means of using the same optical field as the RF reference carrier. This optical method 500 eliminates the need for an external RF source, such as an antenna. RF wave phase referencing methods are conceptually the easiest to understand and implement in laboratory tests using an external source, but they require an antenna structure with the atomic detector, and for many applications, they simply cannot deliver a phase-stable, interference-free RF reference wave to the atoms. The optical RF phase referencing method 500 eliminates these drawbacks. Furthermore, optical RF phase referencing is spatially selective at the sub-mm scale, i.e., a dense grid of sensor atoms can be probed with an optical reference beam that varies from one grid point to the next. Optical spatial resolution for broadband RF phase and amplitude sensing offers the potential for massive parallelization and miniaturization.

[0417]

[0477] All-optical RF phase sensing: Briefly, all-optical RF phase sensing 500 uses a closed interference loop within the atom's internal state space. The driving field is a modulated optical field with a known reference phase, and an external RF field of interest whose phase and amplitude are to be detected or measured. The closed interference loop exhibits quantum interference between the two optical excitation paths within the Rydberg state space (see Figure 5B). The atom's EIT response thus senses the signal phase and amplitude, enabling all-optical readout of the RF phase and amplitude. A patent application for this method has been published (Anderson et al., WO 2019 / 126038 A1). Successful laboratory testing of the method is reported here. All-optical readout of RF amplitude and phase will likely supersede more basic approaches. Figure 5C shows the first demonstration results.

[0418]

[0478] Figure 5C: Optical RF phase measurement 550 of a 5 GHz RF field. Plot 550 shows the optical (EIT) response of Cs Rydberg atoms in a vapor cell to an applied external 5 GHz RF field, relative to the EIT laser frequency (vertical axis) 552 and optical RF reference phase 554 applied to the atoms via an electro-optic modulator. It can be seen that the optical EIT signal at a specific fixed frequency 556 of the EIT laser exhibits a strong modulation that reveals the phase of the RF signal field.

[0419] Appendix E: An exemplary Rydberg atom for radio frequency communication and sensing: Atomic receiver for pulsed RF fields and phase detection

[0479] Appendix E: "Rydberg atoms for radio-frequency communications and sensing: atomic receivers for pulsed RF field and phase detection," David A. Anderson et al., arXiv:1910.07970v1, published October 17, 2019, pages 1-10, is incorporated herein by reference in its entirety.

[0420]

[0480] Figures 17A, 17B, 31, 32, 34, 35A, and 35B illustrate Rydberg-based atomic receivers (e.g., 1100, 3100) for pulsed RF field and phase detection according to various embodiments. Figure 17A is a schematic diagram of an atomic energy level diagram 1700A of two-photon Rydberg EIT optical readout for cesium vapor. Figure 17B is a plot 1700B of optical readout from atomic vapor of the Rydberg EIT resonance 1702 as a function of laser frequency offset 1704. Figure 31 is a schematic diagram of a Rydberg atomic RF phase detector and receiver 3100. Figure 32 is a schematic diagram of an atomic energy level diagram 3200 for the Rydberg atomic RF phase detector and receiver 3100 shown in Figure 31. Figure 34 is a plot 3400 of an AM baseband signal 3402 as a function of time 3404 for a Rydberg-based atomic detector. 35A and 35B are plots 3500A, 3500B of transmission over time 3502 as a function of coupler laser frequency 3504 for a Rydberg-based atomic detector.

[0421] I. Introduction

[0481] The emergence of atomic sensor technology is driving a paradigm shift in modern sensing and measurement by harnessing quantum phenomena to achieve fundamentally new detection capabilities unmatched by their classical counterparts. Atomic detection of radio frequency (RF) electric fields using Rydberg electromagnetically induced transparency (EIT) in atomic vapors is a subject of growing scientific interest. Motivated in part by attempts at national metrology institutes to replace century-old antennas as RF electric field standards with absolute (atomic) standards for RF electric fields, it has recently been established as a novel quantum technology platform with widespread capabilities that have matured into commercial RF detection and measurement instruments.

[0422]

[0482] A notable advance in atomic RF devices and measurement tools is the recent realization of the first Rydberg RF Field Probe (RFP) 1100 and Measurement System (RFMS) 1800 for self-calibrating, SI-traceable, wideband RF measurement and imaging of continuous, pulsed, or modulated fields. Related developments include the realization of miniature atomic sensing elements capable of wideband RF electric field measurements from MHz to >100 GHz, fiber-coupled atomic vapor cell RF field probes, demonstration of ultra-wide dynamic field ranges from sub-10 mV / m up to >10 kV / m (dynamic range >120 dB), and all-optical, circuitless RF sensors for EMP / EMI immunity detection and operational integrity in high-intensity RF environments.

[0423]

[0483] Hybrid atom-RF technologies that combine atom-based optical sensing with conventional RF circuits and resonators have also been developed, realizing hybrid sensors with increased performance capabilities, such as resonator-enhanced ultrasensitive polarization-selective RF detectors, waveguide-embedded atomic RF E-field measurements for SI-traceable RF power standards, and atom-mediated optical RF power / voltage transducers and receivers. Recently, Rydberg atom-based field sensing has also been adapted for modulated RF field detection, promising new possibilities in RF communications, with demonstrations including a Rydberg atom transmission system for digital communications, atomic fiber-optic radio, and "atomic radio" using multiband atomic AM and FM radio receivers based on direct atom-mediated RF-to-optic conversion of baseband signals picked up from a modulated RF carrier.

[0424]

[0484] In this disclosure, the fundamental principles of atomic RF sensing methods are explained, and developments in atomic pulsed RF detection and RF phase sensing are presented that establish relevant capabilities for communications and sensing applications. To date, advances in Rydberg atom-based RF field sensors have been rooted in methods where the fundamental physical quantity detected and measured is the electric field amplitude E of an incident RF electromagnetic wave. Sections III and IV focus on using atom-based E field measurements for RF field sensing and communications applications. With established phase-sensing technologies such as synthetic aperture radar (SAR) and the emerging trend in phased array antennas in 5G, methods are desirable that enable robust optical retrieval of RF phase using enhanced atom-based field sensors. Section V focuses on fundamentally new atomic RF sensors and methods for measuring the phase of RF electromagnetic waves that offer all the performance advantages exhibited by atomic sensors. The presented phase-sensing RF field detection capabilities open atomic RF sensor technology to a wide range of applications, including phase-modulated signal communication systems, radar, and field amplitude and phase mapping for near-field / far-field antenna characterization.

[0425] II. Background of Atomic Physics and Field / Phase Sensing

[0485] Atom-based field sensors (e.g., 1100, 3100) use Rydberg atoms as RF receiving media. Classically, a Rydberg state is an atomic state in which the valence electrons reside in orbits far from the atomic core. The weakly bound, quasi-free electrons of a Rydberg atom endow the atom with a unique set of physical properties, including high sensitivity to external electric and magnetic fields. Atomic physics principles for one-electron and two-electron systems have been described by Bethe and Salpeter. Alkali, alkaline earth, and various other Rydberg atoms fall into this class of atomic systems. Some textbooks that focus specifically on the physics of Rydberg atoms include works by Gallagher, Stebbings, and Dunning. For the purposes of this disclosure, a Rydberg atom can be considered a quantum oscillator perfectly frequency-matched to a selection of incident RF frequencies, which is fairly easy to prepare via laser excitation. This is because the orbital frequency of the Rydberg valence electrons can be tuned to resonate with RF radiation. The set of highly responsive frequencies varies for each Rydberg state. Rydberg atoms offer a broadband RF range from the MHz to the THz regime, as there are a variety of different Rydberg states accessible by tuning the Rydberg atom pump laser.

[0426]

[0486] A single Rydberg atom receiver consists of the valence electrons of a single atom laser-excited to a Rydberg state, whose orbital frequency allows for a (near-)resonant RF-driven transition to another Rydberg state. Frequency matching combines very small receiver size with high electric field sensitivity. While single-receiver Rydberg atoms have sizes on the order of microns, atomic ensembles large enough to build technically viable and robust receiver instruments can range in size from hundreds of microns to several centimeters. The response of an atomic ensemble to an incident RF field corresponds to the quantum mechanical energy level splitting and level shift observed by an EIT laser beam, presenting an all-optical, robust tool for measuring atomic responses and thereby determining RF fields. Because measurements are based on known, invariant atomic properties, this method of RF field determination is atom-based and essentially calibration-free. Sections III and IV describe the use of Rydberg atom field sensors (e.g., 1100, 3100) to measure RF field amplitudes and receive modulated RF signals.

[0427]

[0487] To achieve phase sensitivity in an atom-based Rydberg receiver, elements of holographic phase sensing methodology can be employed. The phase of a signal wave Φ is determined by a reference oscillator or reference wave Φ ref is defined with respect to the phase of . To be able to measure the phase of a signal wave, the signal electromagnetic field must be brought into interference relation with a reference field. In practice, the phase reference is often mediated via a reference wave that is physically superimposed with the signal wave on the detector that measures the field amplitude. The principle of superposition, common to all wave phenomena that obey the (linear) wave equation, allows the phase difference Φ-Φ ref -Φ ofs is obtained from the interference measurement. In the most basic implementation, the net signal has amplitude A and is used to adjust the interference pattern from constructive to destructive and thereby Φ-Φ ref The controllable offset phase φ used to determine the value of ofs The sum of two sinusoids of the same frequency, A sin(ωt+Φ)+A ref sin(ωt+Φ ref +Φ ofsThe measurement of the net wave amplitude vs. Φofs is given by the phase difference Φ-Φ between the wave to be tested and the reference wave. ref This usually condenses the task of phase measurement.

[0428]

[0488] The principle of differential phase measurement through superposition of an object wave and a reference wave is widely used in holography, where phase- and amplitude-sensitive recording of the interference pattern of a signal wave and a reference wave on a planar recording medium with subwavelength spatial resolution allows for accurate three-dimensional reconstruction of the signal wave field. This holographic concept can be transferred from the optical domain to the RF domain. Section V describes a recently devised atom-based method for RF phase detection, measurement, and enhanced reception. This method is not limited to signal and reference waves at the same RF frequency. Frequency-offset reference waves enable heterodyne and superheterodyne signal amplitude and phase detection.

[0429] III. Atomic RF Electric Field Sensing

[0489] The atomic RF receiver technique uses EIT as a quantum optical readout of the Rydberg states of atoms in a vapor. Figure 17A shows a photograph of a miniature atomic vapor cell detector element 1710 containing pure cesium gas adjacent to a standard Kα-band horn antenna. To detect and measure parameters of the incident RF field, a light beam passes through the vapor cell to interrogate the field-sensitive Rydberg states of atoms exposed to the RF field. The detected change in the transmission of the optical probing beam through the atomic vapor provides a direct RF optical readout and information about the incident RF signal field. Under typical operating conditions, the atomic vapor has a sufficiently high optical density for the EIT probe laser beam propagating through the cell to obtain a robust EIT signal with a high signal-to-noise ratio, as required for RF field detection. Furthermore, the atomic vapor within the cell is sufficiently dilute that Rydberg atom interactions can be neglected. Therefore, the spectroscopic response of the medium to the field can be modeled based on the quantum mechanical picture of a single, isolated atom.

[0430]

[0490] Figure 17A shows an atomic energy level diagram for two-photon Rydberg EIT readout of cesium vapor. In this basic scheme, two optical laser fields couple the atomic state to a higher-lying Rydberg state (30D in Figure 17A) with a weak optical probe beam resonating with the first atomic transition between the ground and intermediate states, and a relatively strong optical coupler beam is tuned to resonate with the second atomic transition between the intermediate and Rydberg states. When the coupler laser frequency is resonant with the Rydberg state, an EIT window opens and the probe beam passes through the vapor. Due to the sensitivity of the atomic Rydberg levels to RF electric fields, the Rydberg EIT signal provides an optical measure of the RF field. An example of a Rydberg EIT resonance is shown in Figure 17B (black curve). In the presence of a moderate RF field at a frequency nearly resonant with the allowed transition between the optically excited Rydberg level and the second Rydberg level of an atom, the EIT-detected atomic Rydberg line splits into a pair of Autler-Townes (AT) lines that split proportionally to the RF electric field amplitude (Figure 17B (Magnetor curve)). In this linear AC Stark effect regime, the E field is given by

number

number

[0431]

[0491] Figure 17A: Atomic vapor cell RF detector element 1710 in front of a Ka-band horn antenna and atomic energy level diagram 1700A for RF detection and measurement using a two-photon Rydberg EIT scheme in cesium. Figure 17B: Rydberg EIT signal readout 1700B from the Rydberg state without RF (black), with a weak RF field on resonance (turquoise), and with a moderate RF field (magenta) showing Autler-Townes splitting.

[0432]

[0492] Equation 1 provides a direct optical measurement of the electric field amplitude E of the RF wave in absolute (atomic) units traceable to fundamental constants. In general, for low RF field levels, the sensitivity of an atomic receiver is specified by (1) the electric dipole moment d of the Rydberg-Rydberg transition resonant with the incident RF field, and (2) the spectroscopic EIT linewidth in the optical readout, which determines the achievable resolution for measuring Ω. For RF field frequencies in the range of 100 MHz to 500 GHz, the resonant dipole moment of alkali atoms is typically 10 2 From 10 5 The Rydberg EIT linewidth is typically about 1 MHz or greater, while the electron energy ranges from ea0, where e is the elementary charge and a0 is the Bohr radius, and the principal quantum number n ranges from about 10 to 300.

[0433]

[0493] Equation 1 provides a useful approach to RF E-field sensing and measurement using EIT in Rydberg atomic vapors, but it serves largely as a didactic model because it is valid only within a relatively limited E-field range and for a discrete but large set of RF-field frequencies that are nearly resonant with the Rydberg transition, making it impractical for many real-world E-field measurement scenarios. It utilizes EIT and the full quantum response of the Rydberg atom interaction with RF fields, including non-resonant AC Stark shift readout, to measure direct E-fields of continuous-frequency RF-field frequencies spanning tens of GHz with a dynamic range greater than 60 dB. RMS This is addressed by well-developed measurement methods and approaches that allow measurements: fully non-perturbative Floquet processing allows measurements of electric field values ​​and frequencies of even stronger (coherent) RF fields.

[0434] IV. Communication and Modulated RF Field Detection with Atomic Receivers

[0494] For example, as described in U.S. patent application Ser. No. 16 / 222,384, filed December 17, 2018 (now issued as U.S. Patent No. 10,823,775), the adaptation of Rydberg atom-based RF E-field sensing and measurement approaches to the detection of modulated, time-varying RF fields promises to enable new capabilities in RF sensing and communications. This application is incorporated herein by reference in its entirety. Recent laboratory research has demonstrated modulated RF E-field detection and baseband signal reception via Rydberg EIT in atomic vapors. Key findings include Rydberg atom-based transmission systems for digital communications, atomic fiber-radio, and multiband atomic AM and FM receivers for wireless communications recently adapted for dual-channel reception using two atomic species. Atomic receivers for communications are a nascent technology awaiting advanced development and adaptation to real-world systems.

[0435]

[0495] The basic operating principle of an atom RF receiver based on Rydberg EIT in a vapor cell exploits the large differential dipole moment of the atom's Rydberg state. When an RF carrier wave is applied to the atomic sensing volume, the coupler laser frequency is set to the operating point of one of the inflection points of the EIT spectral line (see, for example, Figures 17A and 17B). As the incident modulated RF wave impinges on the atoms, they respond synchronously to the time-varying RF electric field, resulting in a change in the probe light transmission through the vapor. This realizes direct Rydberg atom-mediated optical pickup and demodulation of the baseband modulated RF carrier signal, which is performed within the atomic vapor cell without the need for any demodulation or signal processing electronics required by conventional antenna receiver techniques.

[0436]

[0496] For the general case of a differential dipole moment d of the transmitted AM signal and the target Rydberg state at the atomic receiver, the typical range of the AM depth δE / E is given by δE / E ~ h × δΓ / (Ed), where δΓ is the EIT linewidth. Figure 34 shows real-time optical readout from an atomic rubidium vapor cell receiver detecting and demodulating a 1 kHz baseband signal transmitted in free space on an AM-modulated 37.4065 GHz RF carrier. The received signal is shown for three different AM modulation depths of the carrier. The modulation depth can typically range from several tens of percent to less than 1%, depending on the exact operating conditions and receiver sensitivity requirements. In addition to being sensitive to changes in RF field amplitude, the Rydberg state is also sensitive to changes in RF field frequency, enabling receiver pickup and demodulation of FM RF carrier signals using a similar approach. This basic approach has been implemented in the reception of both AM and FM radio communications on RF carriers across a wide range of carrier bands, with wideband operation of the single atom receiver demonstrated for carrier frequencies spanning more than four octaves, from C-band to Q-band.

[0437]

[0497] In addition to wireless and digital communications, pulse-modulated RF field detection and measurement with Rydberg atomic receivers promises to extend atom-based RF technology for enhanced performance capabilities in application areas including high-intensity pulsed RF measurements and electromagnetic testing, pulsed radar, surveillance, and electronic support countermeasures (ESM) systems. To this end, we describe below the direct detection of pulsed RF fields with atomic receivers in the time domain to separate atom-light interactions from atom-RF interactions under typical EIT operating conditions, and investigate the behavior and response time of atomic detectors (e.g., 1100, 3100) for both RF-free pulsed RF field detection and pulsed Rydberg EIT readout.

[0438]

[0498] Figure 35A shows the time-domain detection and measurement of a 1 μs long 36.2 GHz narrowband RF field pulse with a rubidium Rydberg-based atomic detector (e.g., 1100, 3100). The pulse-modulated RF pulse measurement shows that the RF is rubidium 47S. 1 / 2 From 47 pages 1 / 2 This is done in the weak-field regime, resonating with the transition to , resulting in AT splitting of the EIT line according to Equation 1. In the measured data, it is observed that AT splitting is well resolved in time for 1 μs-long RF pulses. The time resolution in the detection of Figure 35A approaches the 10 ns level and is primarily limited by the response time of the photodetector used in the measurement. Extension to shorter RF pulse width detection is readily achievable, corresponding to larger RF detection bandwidths.

[0439]

[0499] In a closely related study of time-dependent effects, this disclosure investigates the time dependence of the underlying EIT readout from atomic vapors for pulsed Rydberg EIT alone, without the application of an external RF field, allowing us to distinguish between atom-light and atom-RF interaction effects that contribute to the detection process and to elucidate the short-time scale response of Rydberg EIT pulses in thermal atomic vapors for typical intermediate optical Rabi frequencies.

[0440]

[0500] Figure 35B shows the field-free Rb5P 3 / 2 From 30D 5 / 2Figure 35B shows the EIT probe transmission (grayscale) of a 5 μs-long coupler optical pulse as a function of time (vertical axis) and coupler laser frequency (horizontal axis) near the Rydberg state resonance to . Here, the coupler pulse is switched on at 11.7 μs and off again at 16.7 μs, with a precision of less than 100 ns. When the coupler pulse is turned on, a sudden decrease in transmission, or equivalently an increase in probe absorption, is observed over a period of approximately 20 ns (white horizontal band in the data, labeled I in Figure 35B). This is followed by an increase in transmission until it reaches a steady-state value over a period of 1 to 2 μs. When the coupler pulse is turned off, a sudden increase (gain) in optical transmission is observed (black horizontal band in the data, labeled II in Figure 35B), also over a period of approximately 20 ns, after which the signal decays to zero over several microseconds.

[0441]

[0501] Figure 34: Cesium-47S 1 / 2 From 47 pages 1 / 2 Real-time optical readout from an atomic receiver of an AM 1 kHz baseband signal transmitted on a 37.406 GHz RF carrier resonantly driving the Rydberg transition to cesium-47S. The received signal with three AM modulation depths of 5% (blue), 25% (purple), and 45% (black) is shown. 1 / 2 The coupler laser frequency operating point is shown set at the Rydberg line.

[0442]

[0502] Figure 35A: Time-domain detection and measurement of a 1 μs long RF field pulse at 36.2 GHz using a rubidium Rydberg-based atomic detector as a function of time and coupler laser frequency. The time evolution is along the y-axis. The coupler laser beam is switched on at 11.7 μs and left on, and the RF pulse incident on the detector element is switched on at 21.7 μs. The RF frequency is rubidium 47S. 1 / 2 From 47 pages 1 / 2 This resonates with the Rydberg transition to β (dipole moment d = 745ea0), producing EIT line splitting (double-sided arrows) proportional to the pulsed RF field amplitude of approximately 5 V / m.

[0443]

[0503] Figure 35B: Time and Rubidium 30D 5 / 2 Relative EIT probe transmission of a 5 μs long coupler laser square pulse (probe laser continuously on) as a function of coupler laser frequency near the Rydberg regime. No RF is applied. The coupler pulse is on at 11.7 μs and off again at 16.7 μs, with an uncertainty of less than 100 ns. The probe transmission is in grayscale; the absorbing background without the coupler is at a level of 0.236, and the transmission increases relative from white to black.

[0444]

[0504] The transient phenomenon measured at both the beginning and end of a Rydberg EIT coupler pulse in an atomic vapor has not been observed before. The observed process appears similar to, but differs from, photon storage and retrieval via EIT-mediated Rydberg polaritons in cold-atom systems: probe photons are stored as collective Rydberg excitations in the medium in the presence of the coupler beam and are released / retrieved when the coupler is turned off. In this study, a certain excess of probe pulse energy (contained in the probe light incident on the medium) is stored and then released. In this interpretation, the "stored" 780 nm light is "retrieved" after an extremely long time (>10 μs pulses in other experiments) exceeding the sub-μs transit time of atoms through the EIT beam used. The concept of collective Rydberg polaritons propagating along the laser beam direction through a medium of atoms frozen in place (a picture commonly used in cold-atom EIT experiments) is not directly applicable. However, during the short, approximately 100 ns-long time interval following the optical switching event, the atoms are nearly frozen in place, even in the proposed case of Rydberg EIT in a room-temperature vapor cell. This allows the frozen-atom model to be used to explain the fast transients observed in Figure 35B.

[0445]

[0505] The transient response of the Rydberg EIT readout discussed here provides sub-10 ns time resolution. Implementation of the transient response in RF field sensing is proposed here to achieve high-bandwidth reception of modulated RF communication signals, short RF pulse detection, and high-frequency RF noise measurement. In this disclosure, the Rydberg EIT system dynamics for the conditions of FIG. 35B are modeled, which provides Rydberg EIT transient dynamics that reproduce the observed transient behavior in great detail. In some embodiments, the Rydberg EIT transient dynamics can be implemented in an ultrafast RF detection method.

[0446]

[0506] Comparing Figures 35A and 35B, we can see that the EIT linewidths are quite different. This is due to the use of different laser beam parameters and Rydberg states, which leads to different Rabi frequencies f...

Claims

1. 1. An atom-based closed-loop control system, comprising: a compartment containing a gas of excited atoms having one or more Rydberg states; a device configured to apply an input signal to the one or more Rydberg states; a detector configured to detect a response of the one or more Rydberg states due to an interaction of the one or more Rydberg states with electromagnetic radiation; a controller configured to adjust a characteristic of the applied input signal based at least in part on the detected response of the one or more Rydberg states to the electromagnetic radiation; and Including, the system.

2. The system of claim 1 , wherein the controller is further configured to adjust the characteristics of the applied input signal based on the characteristics of the electromagnetic radiation.

3. The system of claim 2 , wherein the characteristics of the electromagnetic radiation comprise frequency, amplitude, phase, polarization, power, direction of arrival, angle of arrival, and / or combinations thereof.

4. The system of claim 1 , wherein the controller is further configured to adjust control and / or process signals based on the detected response of the one or more Rydberg states to the electromagnetic radiation.

5. The system of claim 1 , wherein the controller is further configured to adjust the characteristic based on differential feedback between the detected response and a set point.

6. The system of claim 1 , wherein the controller is further configured to adjust the characteristic based on one or more detector sensitivity parameters.

7. 10. The system of claim 1, wherein the detected response of the one or more Rydberg conditions is further based on a temperature of the gas, a pressure of the gas, an electric field applied to the gas, a magnetic field applied to the gas, and / or a supplemental RF waveform applied to the gas.

8. The system of claim 1 , wherein the device comprises a mechanical device, an electrical device, and / or an optical device.

9. the applied input signal comprises an electromagnetic field, an electric field, and / or a magnetic field; The system of claim 1 , wherein the characteristics comprise parameters of the applied electromagnetic, electric, and / or magnetic field.

10. The system of claim 1 , wherein the controller is further configured to automatically adjust the characteristic based on the detected response.

11. The system of claim 1 , wherein the controller comprises hardware or software configured to automatically adjust the characteristic to a set point.

12. the device comprises an RF generator or source; The system of claim 1 , wherein the applied input signal comprises an RF electromagnetic wave, an RF electronic signal, an electric field, and / or a magnetic field.

13. The system of claim 1 , wherein the detected response comprises a light transmission, light absorption, or scattering signal from the excited atoms.

14. The system of claim 1 , wherein the device is further configured to apply a reference RF electromagnetic wave or a reference local oscillator wave.

15. The system of claim 1 , wherein the applied input signal comprises multiple fields for multi-field modulation of the one or more Rydberg states.

16. the applied input signal comprises a laser beam; The system of claim 1 , wherein the characteristics comprise parameters of the laser beam.

17. The system of claim 1 , wherein the characteristic and the detected response comprise phase-encoded signals.

18. The system of claim 1 , wherein the characteristic and the detected response are electronically synchronized, frequency locked, and / or phase locked.

19. The system of claim 1 , wherein the controller is further configured to determine an electromagnetic spectrum.

20. 10. The system of claim 1, wherein the detected response is further based on multidimensional Doppler matching of parameters of multiple laser beams for Doppler-free Rydberg spectroscopy in a gas of excited atoms at or near the homogeneous Rydberg linewidth.

21. 1. A system for detecting radio frequency (RF) signals, comprising: a stripline configured to receive an input RF signal and a reference signal; a device configured to apply the reference signal; a gas of excited atoms having one or more Rydberg states and disposed within said stripline within a vacuum enclosure; a detector configured to detect a response of the one or more Rydberg states due to an interaction of the one or more Rydberg states with electromagnetic radiation inside or adjacent to the stripline based on the input RF signal and / or the applied reference signal; a controller configured to determine parameters of the input RF signal based at least in part on the detected response of the one or more Rydberg states to the electromagnetic radiation, and to adjust characteristics of the applied reference signal based at least in part on the detected response of the one or more Rydberg states to the electromagnetic radiation; A system comprising:

22. 22. The system of claim 21 , wherein the controller is further configured to adjust the characteristic of the applied reference signal based on a second characteristic of the electromagnetic radiation, the input RF signal, and / or the applied reference signal.

23. 23. The system of claim 22, wherein the second characteristic of the electromagnetic radiation, the input RF signal, and / or the applied reference signal comprises frequency, amplitude, phase, polarization, power, direction of arrival, angle of arrival, and / or combinations thereof.

24. 22. The system of claim 21, wherein the controller is further configured to adjust control and / or process signals based on the detected response of the one or more Rydberg states to the electromagnetic radiation.

25. 22. The system of claim 21, wherein the applied reference signal comprises a reference RF signal.

26. 22. The system of claim 21, wherein the input RF signal comprises an electrical signal, an optical signal, and / or an electromagnetic wave.

27. 22. The system of claim 21, wherein the stripline comprises one or more electrodes, waveguides, and / or vapor cell compartments.

28. 22. The system of claim 21, wherein the device comprises a controller configured to vary the parameter of the input RF signal.

29. 22. The system of claim 21, wherein the reference signal comprises a reference RF signal included in modulating a parameter of a laser beam that interacts with the one or more Rydberg states.

30. 22. The system of claim 21, wherein the stripline is further configured to receive one or more modulation RF signals for multi-field modulation of the one or more Rydberg states.

31. 22. The system of claim 21, further comprising a multiplexer configured to parallelize or multiplex one or more combinations of the one or more Rydberg state optical and RF electromagnetic fields, interference paths, and / or interference signals.

32. 32. The system of claim 31, wherein the multiplexer is configured to apply space, time, and / or frequency multiplexing.

33. 32. The system of claim 31, wherein the multiplexer is configured to provide an increased detected RF bandwidth.

34. The stripline includes a pair of electrodes, 22. The system of claim 21, wherein the parameter of the input RF signal is power or field equivalent voltage across the pair of electrodes.

35. 22. The system of claim 21, wherein the parameter of the input RF signal is the characteristic of the applied reference signal.

36. 22. The system of claim 21, wherein the controller is further configured to determine an electromagnetic spectrum.

37. 37. The system of claim 36, wherein the controller is further configured to determine power, voltage, communication signal, direction of arrival, and / or combinations thereof.

38. 22. The system of claim 21, wherein the detected response is further based on multidimensional Doppler matching of parameters of multiple laser beams for Doppler-free Rydberg spectroscopy in a gas of excited atoms at or near the homogeneous Rydberg linewidth.

39. 39. The system of claim 38, wherein the multi-dimensional Doppler matching of parameters of the multiple laser beams comprises at least two laser beams positioned at angles that suppress Doppler shift in one, two, and / or three dimensions.

40. The three laser beams are non-collinear to achieve Doppler matching in two degrees of freedom, or 40. The system of claim 39, wherein the four laser beams are non-collinear to achieve Doppler matching in three degrees of freedom.

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