Atomic-based electromagnetic field sensing elements and measurement systems

Abstract

Providing atomic-based electromagnetic field sensing elements and measurement systems. [Solution] A method and apparatus for sensing or measuring an electromagnetic field. The method involves an electromagnetic field and excitation of atoms in a gas occupying a test volume in Rydberg states. Transmission along a path of at least one probe beam of electromagnetic radiation across the test volume is measured at one or more frequencies overlapping with certain spectral features, and the physical properties of the electromagnetic field are derived based on variations in the spectral features. In various embodiments, the electromagnetic fields may be set up in an interfering relationship with another electromagnetic field. Time-varying electric field amplitude, frequency, phase, and noise spectral distribution, and thus AM and FM modulated fields as well as a magnetic field of about 1 Tesla, can be measured. The apparatus for measuring the electromagnetic field may be unilaterally coupled to the probe field and a detector or an array of detectors.

Description

Technical Field

[0001] This invention was made, in part, under Government support awarded by the Defense Advanced Research Projects Agency (DARPA) and the United States Army under Contract No. W911NF-17-C-0007. The Government may have certain rights in some aspects of this invention.

[0002] This application claims priority to U.S. Provisional Application No. 62 / 607,034, filed on December 18, 2017, and U.S. Provisional Application No. 62 / 727,764, filed on September 6, 2018. Both of the foregoing applications are hereby incorporated herein by reference.

[0003] The present invention relates to atomic-based field sensing elements and measurement systems and methods, and more specifically, to elements, systems, and methods that employ Rydberg atoms to measure, receive, or image RF field amplitude, polarization, or phase, modulated RF signals, incoherent RF or RF noise, and perform continuous frequency RF field detection.

Background Art

[0004] Atoms with quasi-free electrons in high Rydberg states (characterized by high principal quantum numbers, typically n > 20) each exhibit a large polarizability and an electric dipole moment corresponding to a principal quantum number n of approximately n 7 and approximately n 2 and are extremely sensitive to electric fields. According to the convention of this document, the state of an atom that is not in a Rydberg state may be referred to herein as a "ground state."

[0005] The concept of applying the spectroscopic response of Rydberg states in atomic vapor to the measurement of electric fields has been described, at least, in Mohapatra et al.'s "Rydberg States using Electromagnetically Induced Transparency" Phys. Rev. Lett.It has been publicly known since vol.98,113003 (2007) (incorporated herein by reference). Previous research relating to atom-based field sensing (all found in the prior art) is the subject of U.S. Patent No. 9,970,973 by Anderson et al. (hereinafter, "Anderson's 973 Patent") (incorporated herein by reference and cited herein by reference). More specifically, the Floquet method is, for example, in Anderson et al.'s "Two-photon microwave transitions and strong-field effects in a room-temperature Rydberg-atom gas". Phys.Rev.A As shown in vol.90, 043419 (2014) (incorporated herein by reference), this has been previously established as a preferred means for modeling Rydberg atomic microwave spectra in vapor cell experiments.

[0006] Electromagnetic wave-induced clearing (EIT) is a quantum interference process in which two excitation pathways within a three-level atomic system destructively interfere with a probe laser beam, producing an increase in its transmission. For example, in the Rydberg-EIT cascade scheme depicted in Figure 8B, clearing is formed by the coherent superposition of the ground and Rydberg states. Rydberg-EIT is implemented in both cooled atomic gas and room-temperature vapor cells. It is widely used as a non-destructive optical detection technique for Rydberg spectra, quantum information processing, and measurements of both weak and strong microwave electric fields. AC Stark shifts at Rydberg levels using electrodes in a vapor cell are described in "Enhanced electric field sensitivity of rf-dressed Rydberg dark states" by Bason et al. New Journal of Physics. This is discussed in vol.12, 065015 (2010) (which is incorporated herein by reference).

[0007] As used herein, the term “sensor” refers to any device that detects or measures a physical quantity, and may exclude wiring or waveguides that couple electrical or electromagnetic energy to or from a controller or processor used in conjunction with the sensor. The term “monolithic sensor” refers to a sensor whose entirety can be embodied on a single substrate, or whose components are permanently connected to form a single physical device, as the term is used herein. Embodiments of connection include microfabrication, fusion, anode bonding, and gluing. To the best of the knowledge of the inventors herein, no monolithic Rydberg sensor has been proposed to date.

[0008] Although the Rydberg spectroscopy method has not been previously proposed, it has been suitable for measuring the phase of an electromagnetic field (relative to a phase reference point). To fill this gap, the embodiments of the present invention described below address this issue in particular.

[0009] Suitable sensing elements are required to realize practical atom-based RF sensing, measurement, or imaging devices. All prior art sensing elements described or proposed in previous studies have limitations imposed by physical principles, which are overcome by the insights described below according to the present invention. Prior art sensing elements are taught, for example, by Anderson et al., “Optical measurements of strong microwave fields with Rydberg atoms in a vapor cell” https: / / arxiv.org / pdf / 1601.02535.pdf (January 11, 2016) (incorporated herein by reference).

[0010] Other teachings on atom-based electromagnetic field sensing can be found in Gordon et al.'s "Millimeter Wave Detection via Autler-Townes Splitting in Rubidium Rydberg Atoms" (https: / / arxiv.org / pdf / 1406.2936.pdf, June 11, 2014) and Simons et al.'s "Using frequency detuning to improve the sensitivity of electric field measurements via electromagnetically induced transparency and Autler-Townes splitting in Rydberg atoms". Appl.Phys.Lett. This can be found in vol. 108, 174101 (2016) (both publications are also incorporated herein by reference).

[0011] The performance limitations of existing Rydberg electromagnetic wave-induced transparency (EIT) techniques include the following:

[0012] (1) Low sensitivity; the highest field sensitivity demonstrated to date at the 1 mV / m level is mainly limited by the EIT linewidth. Furthermore, this sensitivity level has only been achieved by monitoring small changes in the EIT peak shape. Unlike directly measuring the Rydberg energy level splitting, where the field is traceable to fundamental constants and invariant atomic parameters, extracting the RF electric field from detailed EIT lineform analysis requires a relatively complex model that depends on experimental parameters such as laser beam power and vapor pressure, thereby making absolute field measurement impossible and unreliable in daily operation. To date, the most sensitive measurement sensitivity in prior art is approximately 3 μV / cm / Hz. 1 / 2The shot noise limiting sensitivity is as described in Kμmar et al.'s "Rydberg-atom based radio-frequency electrometry using frequency modulation spectroscopy in room temperature vapor cells". Opt.Express This was demonstrated in the study vol.25,284263 (January 21, 2017), and an improvement of approximately half the magnitude of its sensitivity has been achieved so far in Fan et al.'s "Effect of Vapor Cell Geometry on Rydberg-Atom-Based Measurements of Radio-Frequency Electric Fields". Phys.Rev.Appl. This was reported in 044015 (2015) (both papers are incorporated herein by reference). The latter study employs subtle RF-induced EIT enhancement of the Rydberg-EIT line by a weakly resonant RF field, a method that is expected to be somewhat unreliable in daily field measurement operations because subtle changes depend on many details such as laser power and cell pressure. A more robust means of enhancing sensitivity is desired.

[0013] (2) It is not possible to measure the RF field over a continuous frequency range. In weak RF fields, this method is limited to measuring RF fields that resonate at dipole-allowed transitions between Rydberg states. Weak RF fields that are off and far-resonant from any transition cannot be easily measured, if not at all.

[0014] (3) RF polarization measurements currently require complex analysis of atomic spectra.

[0015] (4) All prior art Rydberg-EIT measurements are necessarily field amplitude measurements, while information regarding the phase of the RF field is not partially obtainable due to the physical constraints discussed herein.

[0016] (5) The shape factors of the measuring instruments currently used for Rydberg-EIT measurements inevitably require large, non-portable assemblies, i.e., those with a large dielectric footprint, thereby making it impossible to perform measurements in many practical applications or to integrate them into existing RF measurement and transmission systems.

[0017] (6) Prior to the inventions described below in this specification, the Rydberg-EIT technique has served only as a means of measuring coherent fields. Previous methods were incapable of measuring either incoherent fields or noise.

[0018] RF measurement methods employing Rydberg-EIT within a vapor cell typically involve counter-propagation of a laser beam through atomic vapor and account for the Doppler shift of the spectral laser beam within a thermal atomic sample. This aspect has historically presented challenges to the practical application of Rydberg-EIT in vapor cells in sensor design for applications, as it requires the laser beam to enter the cell and exit from both sides either via free-space propagation or through optical fibers on both sides of the cell. This can lead to sensor heads with large dielectric occupancy and size, which are undesirable for measurement applications. Furthermore, to extend to multi-pixel sensor arrays, the entry of optical beams from both sides of the cell can limit the pixel occupancy density and resolution achievable within the array.

[0019] One-sided optical coupling into a vapor cell is discussed, for example, in the context of atomic magnetometers, as in George et al.'s "Pulsed high magnetic field measurement via a Rubidium Vapor Sensor" (https: / / arxiv.org / pdf / 1704.00004.pdf, March 31, 2017) (incorporated herein by reference), where separate fibers are employed for the input and output beams as well as beams of the same or similar wavelengths. Furthermore, in the prior art, the probe beam always enters one side of the vapor cell and exits from the other side.

[0020] While the majority of problems in the observable universe exist in plasma states, measuring or estimating the properties of electric fields within the plasma region presents specific challenges to science unless the collective motion of the plasma can be observed or physical probes can be inserted into the plasma. An example of the former technique is the estimation of the radial electric field within a tokamak, which is derived from poloidal rotational velocity. In the absence of either of these probing modalities, certain assumptions must be made, for example, in Paris et al.'s "Intensity ratio of spectral bands of nitrogen as a measure of electric field in plasmas." J.Phys.D As discussed in vol.38, pp.3894-99 (2005) (incorporated herein by reference), when the intensity ratio of the spectral bands of nitrogen is used, the calculation requires that the nitrogen molecule is excited from the ground state primarily by direct electron collisions.

[0021] To date, optical diagnostic techniques for measuring plasma fields have primarily involved measuring Stark shifts within plasma molecules using emission and absorption spectroscopy, laser-induced fluorescence, and Raman spectroscopy. While existing methods result in passive, non-penetrating measurements, they may also require prior knowledge of the optical absorption or emission spectra of plasma components. This can make it difficult to distinguish a collective plasma phenomenon of interest from a small number of many-body processes involving component plasma particles in diagnostic readings. Furthermore, it necessitates the customization of diagnostic tools specific to the plasma type being studied, preventing the development of generalized techniques that allow diagnostics to be performed on different plasma systems. Thus, some plasmas are expected to have emission profiles at frequencies and emission intensities that are difficult to detect using conventional detectors and spectrometers. Weak IR emissions from vibrational transitions within plasma components may, for example, provide useful information in some cases, but the detectors required to measure these low IR intensity levels are not readily available. Due to these limitations, applications may require the plasma to be engineered with certain atomic / ionic particles to implement well-characterized optical diagnostics. This presents a significant disadvantage to basic plasma research, as the properties of the plasma itself become the subject of study.

[0022] Unless the aforementioned types of prior articulation are always available, science will have to wait for a more general modality for telemetry of electric fields in plasma. Such a modality is described in detail below according to one embodiment of the present invention.

[0023] Probes for high-resolution sensing, measurement, and calibration of strong magnetic fields in the 1-100 Tesla range are becoming increasingly important in the research and development, production, and maintenance of strong magnet systems in various industries. However, atomic vapor or Rydberg-EIT systems for measuring such fields have not been provided and are for the first time made possible using the present invention described below. The maximum magnetic field strength, which can be measured based on a Rydberg atomic model using ultrafine-level Zeeman splitting by Rydberg-EIT analysis as previously practiced, is up to about 10 3 It is Gaussian. Measuring stronger magnetic fields requires new strategies, as described herein in accordance with the present invention. [Overview of the project] [Means for solving the problem]

[0024] According to one embodiment of the present invention, a method for sensing or measuring a first electromagnetic field is provided. This method is The steps include: exciting atoms of a gas occupying a test volume corresponding to the first electromagnetic field, at least partially, within the distribution of the Rydberg state; The steps include structuring the first electromagnetic field by placing it in an interfering relationship with at least one other electromagnetic field, The steps include measuring the transmission along a path traversing a test volume of at least one probe beam of electromagnetic radiation at one or more frequencies that overlap with the spectral characteristics of the atomic gas, At a minimum, the steps include deriving the physical properties of the first electromagnetic field based on changes in spectral characteristics, It holds.

[0025] According to other embodiments of the present invention, the gas may be an atomic vapor, and the atoms of the atomic vapor may be selected from a group of atoms including rubidium, cesium, and other alkalis. The step of exciting the atoms into a distribution of Rydberg states may include the step of optically exciting the atoms into a distribution of Rydberg states, as well as at least one of electromagnetic wave-induced clearing and electromagnetic wave-induced absorption.

[0026] According to further embodiments of the present invention, the change in spectral characteristics may include Autler-Townes splitting, and the physical properties of the first electromagnetic field may be field amplitude.

[0027] The first electromagnetic field may be monochromatic, and the physical properties of the first electromagnetic field may be its phase relative to a reference phase.

[0028] According to another embodiment of the present invention, the step of structuring the first electromagnetic field may include modulation of the electromagnetic field prior to the measurement step. The modulation may be at least one of frequency, amplitude, and step modulation.

[0029] According to yet another embodiment of the present invention, the distribution of Rydberg states may include at least one pair of states with a non-zero dipole moment for interaction between atoms and radio frequency fields.

[0030] According to further embodiments of the present invention, A step of calculating a predetermined Rydberg atomic energy level or Rydberg-EIT spectrum in the presence of an incoherent RF noise field that exists within or constitutes a first electromagnetic field, The steps include propagating light into the atomic vapor cell, The steps include measuring spectral features accompanied by light propagating through an atomic vapor cell, Steps include identifying the matched spectrum, A step to derive the attributes of the incoherent RF noise field, Additional steps may exist.

[0031] According to another embodiment of the present invention, A step of calculating a predetermined atomic energy level or spectrum for an atom in the same first electromagnetic field as a strongly static or low-frequency magnetic field, The steps include propagating at least one other electromagnetic field into the atomic vapor cell as an optical probe, The steps include measuring the spectral characteristics of light propagating through an atomic vapor cell, Steps include identifying the matched spectrum, Steps to derive the physical properties of a strong magnetic field, Additional steps may exist.

[0032] The light may be amplitude- or frequency-modulated in conjunction with a modulation frequency or lock-in detection at multiple such frequencies, and a predetermined atomic energy level or spectrum may be for lower atomic states.

[0033] According to another aspect of the present invention, a monolithic sensor is provided for detecting and / or measuring parameters for characterizing an electromagnetic field. The sensor comprises an atomic vapor contained within an enclosure, an excitation source for exciting atoms of the atomic vapor into a Rydberg state distribution, and at least one waveguide for coupling a probe beam or more beams into the atomic vapor and collecting the probe beam after interaction between the probe beam and the atomic vapor.

[0034] According to another embodiment of the present invention, at least one waveguide may be an optical fiber. At least one of the at least one waveguide may couple radiation from both the excitation source and the probe beam into the atomic vapor. The enclosure may include a dielectric material or a glass vapor cell. The enclosure may be compartmentalized, more specifically, linearly or by area.

[0035] In further embodiments, distinctly different probe beams may be coupled into each of the compartment arrays via an array of optical elements, etc., collected after interaction with atomic vapor, and coupled to a detector element via an array of optical elements. The enclosure may include an absorption surface and may also have a temperature controller.

[0036] A further aspect of the present invention provides a unidirectionally coupled monolithic sensor for detecting and / or measuring parameters for characterizing an electromagnetic field. The unidirectionally coupled monolithic sensor comprises an atomic vapor contained within a dielectric enclosure and an excitation source for generating an excitation beam to excite the atoms of the atomic vapor into a Rydberg state distribution. In addition, the unidirectionally coupled monolithic sensor comprises a first prism for coupling the excitation beam into the atomic vapor and a probe beam out of the atomic vapor, and a second prism for coupling the probe beam into the atomic vapor. The excitation beam and the probe beam may be incident on the separate first and second prisms in substantially parallel directions.

[0037] In a further aspect of the present invention, a sensor is provided for detecting and / or measuring parameters for characterizing an electromagnetic field. The sensor comprises at least one of a material or structure for tuning an electromagnetic field, and atomic vapor contained within an enclosure placed within the tuning material or structure. The sensor also comprises an excitation source for exciting atoms of the atomic vapor into a Rydberg state distribution, a detector for detecting a probe beam after crossing the atomic vapor and generating a detector signal, and at least a processor for deriving parameters for characterizing the electromagnetic field based on the detector signal.

[0038] In other embodiments, the material or structure for tuning the electromagnetic field may be an RF resonator or a waveguide. It may also be a metamaterial.

[0039] The material or structure for tuning the electromagnetic field may include an antenna or one or more electrodes. The material or structure may be conductive, and the electromagnetic field may be tuned by converting a current or voltage signal into an electromagnetic field within an atomic vapor cell. The attributes of the current or voltage signal may be derived from a detector signal.

[0040] In other embodiments of the present invention, the excitation source for exciting the atoms of the atomic vapor into a Rydberg state may have one or more light beams to establish electromagnetic wave-induced transparency or electromagnetic wave-induced absorption within the atomic vapor. The enclosure containing the atomic vapor may be a glass vapor cell.

[0041] In yet another embodiment of the present invention, the material or structure for regulating the electromagnetic field may include a filter or reflector for the electromagnetic field that enters or exits the atomic vapor enclosure. A detector may be used to detect the electromagnetic field generated by the excitation and emission of atomic vapor. The electromagnetic field may be associated with at least one of standing electromagnetic waves and traveling electromagnetic waves.

[0042] According to another aspect of the present invention, a sensor is provided for detecting and / or measuring parameters for characterizing an electromagnetic field. The sensor has an atomic vapor contained within an enclosure, which in turn has a light-absorbing surface. The sensor also has a heating beam source incident on the light-absorbing surface and an excitation source for exciting atoms of the atomic vapor into a Rydberg state distribution. The sensor also has a detector for detecting the probe beam after it has crossed the atomic vapor and for generating a detector signal, and a processor for applying the heating beam to the light-absorbing surface in such a manner as to adjust the temperature for characterizing the atomic vapor.

[0043] In further embodiments of the present invention, the light-absorbing surface may be a film, a polymer, or glass.

[0044] According to another aspect of the present invention, a method is provided for measuring the electric field within a region of plasma contained within an enclosure. This method is The steps include incorporating tracer particles of a specified species into the plasma, The steps include: exciting the tracer particle into a defined Rydberg state, The steps include applying at least a probe beam and a coupler beam and deriving the EIT transmission spectrum of the plasma, The steps include comparing the plasma's EIT transmission spectrum with a spectral model and estimating the electric field associated with the plasma region based on at least one of the field-induced spectral shape change and the field-induced spectral shift, It holds.

[0045] According to further embodiments of the present invention, the method may further include the step of applying a magnetic field or RF field to the plasma. The tracer particles may more specifically be atoms, including rubidium atoms. The method may also include the step of generating the tracer particles from a cooling atomic source. For example, this application provides the following items. (Item 1) A method for sensing or measuring a first electromagnetic field, wherein the method is a. A step of exciting, at least partially, atoms of a gas occupying the same test volume as the first electromagnetic field within the distribution of the Rydberg state, b. The step of structuring the first electromagnetic field by placing it in an interfering relationship with at least one other electromagnetic field, c. A step of measuring the transmission along a path traversing a test volume of at least one probe beam of electromagnetic radiation at one or more frequencies that overlap with the spectral characteristics of the atomic gas, d. A step of deriving the physical properties of the first electromagnetic field based on the changes in the spectral characteristics. Methods that include... (Item 2) The method according to item 1, wherein the gas is atomic vapor. (Item 3) The method according to item 2, wherein the atoms of the atomic vapor are selected from the group of atoms including rubidium, cesium, alkali, and alkaline earth atoms. (Item 4) The method according to item 1, wherein the step of exciting the atom into a distribution of Rydberg states includes the step of optically exciting the atom into a distribution of Rydberg states. (Item 5) The method according to item 1, wherein the step of exciting the atom into a distribution of Rydberg states includes at least one of electromagnetic wave-induced transparency and electromagnetic wave-induced absorption. (Item 6) The changes in spectral characteristics are as described in item 1, including Autler-Townes splitting. (Item 7) The physical characteristic of the first electromagnetic field is the field amplitude, as described in item 1. (Item 8) The method according to item 1, wherein the first electromagnetic field is monochromatic, and the physical property of the first electromagnetic field is its phase relative to a reference phase. (Item 9) The method according to item 1, wherein the physical property of the first monochromatic electromagnetic field is its phase relative to the reference point phase of the RF field that modulates one of the other electromagnetic fields using a nonlinear optical element. (Item 10) The method according to item 1, wherein the step of structuring the first electromagnetic field includes superimposing an additional static or radio frequency field to place the first electromagnetic field in resonance with atomic transitions. (Item 11) The method according to item 1, wherein the step of structuring the first electromagnetic field includes a first electromagnetic field that has been modulated prior to the step of measurement. (Item 12) The method according to item 11, wherein the modulation is at least one of frequency, amplitude, and step modulation. (Item 13) The method according to item 1, wherein the distribution of the Rydberg states includes at least one pair of states with a non-zero dipole moment for the interaction between the atom and the radio frequency field. (Item 14) a. A step of calculating a predetermined Rydberg atomic energy level or Rydberg-EIT spectrum in the presence of an incoherent RF noise field that exists in or constitutes the first electromagnetic field, b. The step of propagating light into the atomic vapor cell, c. A step of measuring spectral characteristics accompanied by light propagating through the atomic vapor cell, d. A step of identifying the matched spectrum, e. A step of deriving the attributes of the incoherent RF noise field. The method described in item 1, further including the method described in item 1. (Item 15) a. A step of calculating a predetermined Rydberg atomic energy level or spectrum for an atom in the same first electromagnetic field as a strongly static or low-frequency magnetic field, b. The step of propagating at least one other electromagnetic field into the atomic vapor cell as an optical probe, c. A step of measuring the spectral characteristics of light propagating through the atomic vapor cell, d. A step of identifying the matched spectrum, e. A step of deriving the physical properties of the strong magnetic field. The method described in item 1, further including the method described in item 1. (Item 16) The light is amplitude-modulated or frequency-modulated according to the method of item 15. (Item 17) The method according to item 15, wherein the specified atomic energy level or spectrum relates to a Rydberg atomic state or a lower atomic state. (Item 18) The variation of a strong magnetic field into a small magnetic field is derived using one or more atomic isotopes or species, as described in item 15. (Item 19) A monolithic sensor for detecting and / or measuring parameters for characterizing an electromagnetic field, wherein the sensor is a. Atomic vapor contained within the enclosure, b. An excitation source for exciting the atoms of the atomic vapor into a Rydberg state distribution, c. At least one waveguide for coupling a probe beam or more beams into the atomic vapor, and the same or different waveguides for collecting the probe beam after interaction between the probe beam and the atomic vapor. A sensor equipped with the following features. (Item 20) The monolithic sensor according to item 19, wherein at least one waveguide is an optical fiber. (Item 21) The monolithic sensor according to item 19, wherein at least one waveguide couples the radiation from both the excitation source and the probe beam into the atomic vapor. (Item 22) The enclosure comprises a dielectric material or a glass vapor cell, as described in item 19, for the monolithic sensor. (Item 23) The enclosure is a compartment for the monolithic sensor described in item 19. (Item 24) The enclosure is a monolithic sensor as described in item 19, which is linearly compartmentalized. (Item 25) The enclosure is a monolithic sensor as described in item 19, which is compartmentalized by area. (Item 26) A monolithic sensor as described in item 19, in which distinctly different probe beams are coupled within each of the compartment arrays. (Item 27) The monolithic sensor described in item 26, wherein the distinctly different probe beams are coupled into each of the compartment arrays via an array of optical elements. (Item 28) The monolithic sensor according to item 27, wherein the distinctly different probe beams are collected after interaction with the atomic vapor and coupled to a detector element via the array of optical elements. (Item 29) The monolithic sensor according to item 19, wherein the enclosure includes a light-absorbing surface and further comprises a temperature controller. (Item 30) A unidirectionally coupled monolithic sensor for detecting and / or measuring parameters for characterizing an electromagnetic field, wherein the unidirectionally coupled monolithic sensor is Atomic vapor contained within the enclosure, An excitation source for generating an excitation beam to excite the atoms of the atomic vapor into a Rydberg state distribution, At least one optical component that redirects the propagation direction of at least one of the excitation beam and probe beam into or from the atomic vapor, A monolithic sensor that is unilaterally coupled and equipped with [a specific feature / feature]. (Item 31) The excitation beam and the probe beam are incident on the at least one optical component in substantially parallel directions, in the unidirectionally coupled monolithic sensor as described in item 30. (Item 32) The at least one optical component is a prism, as described in item 30, for a unidirectionally coupled monolithic sensor. (Item 33) A unidirectionally coupled monolithic sensor as described in item 32, wherein a first prism redirects the excitation beam into the atomic vapor and the probe beam out of the atomic vapor, and a second prism couples the probe beam into the atomic vapor. (Item 34) A sensor for detecting and / or measuring parameters for characterizing an electromagnetic field, wherein the sensor is a. At least one of the materials and structures for adjusting the electromagnetic field, b. Atomic vapor contained within an enclosure placed within the aforementioned conditioning material or structure, c. An excitation source for exciting the atoms of the atomic vapor into a Rydberg state distribution, d. A detector for detecting the probe beam after the atomic vapor has crossed and for generating a detector signal, e. A processor for deriving parameters for characterizing the electromagnetic field based on the detector signal, A sensor equipped with the following features. (Item 35) The sensor according to item 34, wherein at least one of the materials and structures for adjusting the electromagnetic field is an RF resonator. (Item 36) The sensor according to item 34, wherein at least one of the materials and structures for adjusting the electromagnetic field is a waveguide. (Item 37) A sensor according to item 34, comprising at least one of the materials and structures for adjusting the electromagnetic field, and a metamaterial. (Item 38) The sensor according to item 34, wherein at least one of the materials and structures for adjusting the electromagnetic field includes an antenna. (Item 39) The sensor according to item 34, wherein at least one of the materials and structures for adjusting the electromagnetic field is one or more electrodes. (Item 40) The sensor according to item 34, wherein at least one of the materials and structures is conductive and modulates an electromagnetic field by converting an electric current or voltage into an electromagnetic field in an atomic vapor, and the associated power through the electric current or voltage or resistance is derived from the detector signal. (Item 41) The sensor according to item 34, wherein the excitation source for exciting the atoms of the atomic vapor into a Rydberg state comprises one or more light beams, and establishes electromagnetic wave-induced transparency or electromagnetic wave-induced absorption within the atomic vapor. (Item 42) The enclosure containing the atomic vapor is a glass vapor cell, as described in item 34. (Item 43) The sensor according to item 34, wherein the material or structure for adjusting the electromagnetic field includes a frequency-selective filter or reflector for the electromagnetic field entering or exiting the atomic vapor enclosure. (Item 44) The detector is a sensor according to item 34, used to detect the electromagnetic field generated by the excitation and emission of the atomic vapor. (Item 45) The sensor according to item 34, wherein the electromagnetic field is associated with at least one of standing electromagnetic waves and traveling electromagnetic waves. (Item 46) A sensor for detecting and / or measuring parameters for characterizing an electromagnetic field using Rydberg atoms, wherein the sensor is a. Atomic vapor contained within an enclosure containing a dielectric light-absorbing material, b. A heating beam source incident on the dielectric light absorbing material, c. An excitation source for exciting the atoms of the atomic vapor into a Rydberg state distribution, d. A detector for detecting the probe beam after the atomic vapor has crossed and for generating a detector signal, e. A processor for applying the heating beam to the dielectric light absorbing material in a manner that adjusts the temperature for characterizing the atomic vapor, A sensor equipped with the following features. (Item 47) The dielectric light absorbing surface is a film, as described in item 46. (Item 48) The dielectric light absorbing surface is a polymer, as described in item 46. (Item 49) The dielectric light absorbing surface is glass, as described in item 40. (Item 50) A method for measuring the electric field within a region of plasma contained within an enclosure, wherein the method is: a. The step of incorporating tracer particles of a specified species into the plasma, b. The step of exciting the tracer particle into a defined Rydberg state, c. Applying at least a probe beam and a coupler beam to derive the EIT transmission spectrum of the tracer particles in the plasma, d. A step of comparing the EIT transmission spectrum of the plasma with a spectral model and estimating the electric field associated with the region of the plasma based on at least one of the field-induced spectral shape change and the field-induced spectral shift. Methods that include... (Item 51) The method according to item 50, further comprising the step of applying a magnetic field or an RF field to the plasma. (Item 52) The tracer particle is an atom, as described in item 50. (Item 53) The method according to item 50, wherein the tracer particle is a rubidium atom. (Item 54) The method according to item 50, further comprising the step of generating the tracer particles from a cooling atomic source. (Item 55) The estimated electric field is the distribution of the electric field, as described in item 50. (Item 56) The estimated electric field is obtained in one, two, or three dimensions, as described in item 50. [Brief explanation of the drawing]

[0046] The aforementioned features of the present invention will be more readily understood by referring to the following embodiments for carrying out the invention, which will be examined with reference to the accompanying drawings.

[0047] [Figure 1]Figure 1 schematically illustrates an RF sensing element with one side optically coupled, according to one embodiment of the present invention.

[0048] [Figure 2A] Figure 2A shows the EIT spectrum of the 30D Rydberg state of 87Rb, obtained using a pen-shaped recurrent EIT configuration according to one embodiment of the present invention.

[0049] [Figure 2B] Figure 2B shows a one-sided atomic vapor sensor according to one embodiment of the present invention, in which the excitation and probe beams are coupled to a vapor cell via a prism.

[0050] [Figure 3] Figure 3 shows a microwave imaging array according to one embodiment of the present invention, consisting of individual vapor cell sensor elements with single-sided couplings.

[0051] [Figure 4A] Figure 4A shows the calculation of the RF field enhancement coefficient along the axis of a 125 μm diameter tip for several frequencies according to one embodiment of the present invention. Figure 4B shows the skin depth associated with the conductive tip. [Figure 4B] Figure 4A shows the calculation of the RF field enhancement coefficient along the axis of a 125 μm diameter tip for several frequencies according to one embodiment of the present invention. Figure 4B shows the skin depth associated with the conductive tip.

[0052] [Figure 5] Figures 5A and 5B show a type of hybrid atomic cavity structure according to one embodiment of the present invention.

[0053] [Figure 6] Figure 6 shows the calculation of the electric field within the hybrid atomic cavity structure shown in Figures 5A-5B for a near-resonant 4 GHz incident RF field of 1 V / m.

[0054] [Figure 7] Figures 7A-7D show a hybrid atomic resonator device according to one embodiment of the present invention. Figure 7A is a top view of the resonator showing the resonator electrode / cavity inside a spectroscopic cell, Figure 7B is a top view of the resonator showing ceramic pins for electrode matching and stabilization, Figure 7C is a side view of the resonator showing glass spacers and gaps, and Figure 7D shows the resonator electrode / cavity structure inside a rubidium vapor cell with wire conductors connected for external voltage / current control or for grounding / short-circuiting the electrodes.

[0055] [Figure 8] Figure 8A shows an experimental setup for measuring field characteristics according to one embodiment of the present invention, while Figure 8B shows a schematic diagram of the related Rydberg-EIT energy levels.

[0056] [Figure 9] Figures 9A–9D demonstrate hybrid atomic cavity field enhancement according to one embodiment of the present invention. Figure 9A plots the 31S Rydberg-EIT spectrum measured as a function of RF / microwave frequency at a fixed -10 dBm injection power. Figure 9B plots the Stark map calculated centered on the 31S1 / 2 Rydberg state with respect to the applied root mean square electric field (ERMS). Figure 9C plots the frequencies obtained using microwave ERMS versus Figures 9A and 9B, while Figure 9D plots the EIT lines measured for 2.5 and 4.35 GHz microwaves, respectively.

[0057] [Figure 10] Figures 10A and 10B show side and end views of a field measurement system with an atomic vapor cell inside a waveguide according to one embodiment of the present invention.

[0058] [Figure 11]Figure 11A shows the experimental 31S Rydberg AC-Stark shift as a function of the microwave frequency applied with a fixed injection power for different angular positions Θ with respect to the vertical axis. Figure 11B plots the microwave electric field at 4.35 GHz as a function of Θ for the data shown in Figure 11A.

[0059] [Figure 12] Figure 12A shows the results of the calculation of the electric field amplitude according to one embodiment of the present invention, and Figures 12B-12D show the electric field vector directions within the hybrid atomic cavity structure of Figures 7A-7D.

[0060] [Figure 13] Figures 13A and 13B show experimental and calculated DC Stark maps of the 30D Rydberg state with respect to the applied DC electric field, respectively.

[0061] [Figure 14] Figure 14 illustrates the Floquet calculation of the AC-Stark shift of rubidium 47S and 47P levels in a 100 MHz RF field.

[0062] [Figure 15] Figure 15 plots the RF intensity and electric field calibration for the rubidium-47S state.

[0063] [Figure 16] Figure 16 plots the measured EIT spectrum of the 47S state at a fixed -14 dBi microwave intensity (separate calibration) for four different injected RF powers versus the microwave frequency detuning from 37.51663492 GHz.

[0064] [Figure 17] Figure 17 plots the measured pseudo-crossing center as a function of the applied RF electric field for a series of values ​​up to approximately 200 V / cm.

[0065] [Figure 18A] Figure 18A shows the simulated electric fields generated inside four different split-ring cavity structures for a 1 V / m incident field, as a function of the applied frequency. [Figure 18B] Figure 18B illustrates a measurement channel within the gap of a split ring cavity structure according to one embodiment of the present invention. [Figure 18C] Figures 18C and 18D show simulated resonance curves for a split-ring resonator with a geometric shape that leads to resonance near 100 GHz. [Figure 18D] Figures 18C and 18D show simulated resonance curves for a split-ring resonator with a geometric shape that leads to resonance near 100 GHz.

[0066] [Figure 19] Figures 19A and 19B show an IR-glass capsule 1901 surrounding a 4 mm diameter atomic vapor cell 1903. Figure 19C shows an all-light heating test platform.

[0067] [Figure 20] Figure 20A schematically illustrates the rear end of a sensing element and the operating principle for phase-sensitive measurement of an RF electric field according to one embodiment of the present invention. Figure 20B illustrates the quantum mechanical level scheme and optical / RF excitation path used in phase-sensitive RF electric field measurement.

[0068] [Figure 21] Figure 21 is a flowchart illustrating the steps in a Rydberg-EIT measurement of magnetic field attributes, made possible for the first time by one embodiment of the present invention.

[0069] [Figure 22] Figure 22 is a flowchart illustrating the steps in a Rydberg-EIT measurement of RF noise attributes over a defined spectral range, made possible for the first time by one embodiment of the present invention.

[0070] [Figure 23] Figures 23A-23C schematically illustrate the probing electromagnetic field in a plasma employing an EIT of a Rydberg atomic tracer according to one embodiment of the present invention.

[0071] [Figure 24] Figures 24A-24C schematically illustrate a measurement of a strong magnetic field using saturation absorption spectroscopy of a two-level Rydberg quantum system according to one embodiment of the present invention.

[0072] [Figure 25] Figures 25A–25C schematically illustrate a measurement of a strong magnetic field using saturation absorption spectroscopy of a three-level Rydberg quantum system according to one embodiment of the present invention.

[0073] [Figure 26] Figure 26A schematically depicts a hybrid atomic-based optical RF power / voltage converter and sensor according to one embodiment of the present invention, and Figure 26B shows plots of signals acquired at various levels of voltage applied across the electrodes of the converter and sensor.

[0074] [Figure 27] Figure 27A schematically depicts an atomic vapor cell compartment with opposing windows for wavelength-selective transmission of electromagnetic waves according to one embodiment of the present invention. Figure 27B shows an image of the atomic vapor cell compartment in Figure 27A. [Modes for carrying out the invention]

[0075] Definitions: The following terms shall have the meanings indicated unless otherwise determined by context.

[0076] One embodiment of the present invention relates to an atomic-based field sensing element, which may also be synonymously referred to herein as “sensing element,” “field sensing element,” and “sensor.”

[0077] "Adjustment" in this specification and any appended claims means confinement, induction, manipulation, or filtering of an electromagnetic field or its physical attributes, including its modes, electric field amplitude, polarization, frequency, phase, and spectral components.

[0078] The term "enhancement," when referring to an electromagnetic wave, shall be defined as the modification of that electromagnetic wave in a manner that increases the value of any physical attribute of the electromagnetic wave.

[0079] A "minor key field" refers to either a static or electromagnetic field characterized by a frequency range of 1% or less of the central frequency.

[0080] An electromagnetic field is considered "structured" only if it is a monochromatic field and is in an interfering relationship with at least one other electromagnetic field. Therefore, "structuring" an electromagnetic field means placing it in an interfering relationship with one or more other electromagnetic fields.

[0081] Atomic-based field sensing element is referred to herein as “integrated” only if it contains at least one material or structure that acts to modulate an RF field, and the term “modulated” is as defined above. The RF field being modified may be referred herein as the “RF field of interest.”

[0082] As used herein, the word “distribution” refers to a set, whether continuous or discrete, and includes the case of a single element. Thus, the distribution of atomic sets among Rydberg states also includes, for example, a single state.

[0083] As used herein, the term “spectral feature” refers to the behavior of the function over a defined continuous frequency subdomain, where the values ​​of the function at the boundaries of the subdomains constitute local minimums or maximums of the function.

[0084] The "splitting" of a spectral feature refers to a decrease in the function's maximum value due to a functional physical effect, resulting in the appearance of two new maximum values: one at a frequency above the original maximum and another at a frequency below the original maximum. The term "splitting" can also refer to the frequency difference between the trajectories of the new maximum values ​​that appear in place of the original maximum, where appropriate in context.

[0085] The term "electromagnetic field" encompasses both DC and AC fields.

[0086] In this specification, "RF" may be synonymous with "microwave," "millimeter-wave," "terahertz," or any electromagnetic radiation with a frequency greater than DC ~ THz.

[0087] The magnetic field is approximately 10 -3 When the magnetic field exceeds Tesla (10G), it is designated as "strong," and at that point, several atomic hyperfine-level m-degeneracy, which are decomposed by the magnetic field, begin to transition from the weak-field (linear Zeeman) region to the Paschen-Back region.

[0088] Electromagnetically induced transparency (EIT) refers to a physical phenomenology in which a coherent optical field, tuned to interact with (at least) three states of an optical system, causes transparency at wavelengths corresponding to otherwise absorptive quantum transitions in a medium. The physics and terminology of EIT can be found in Marangos's "Topical review: Electromagnetically induced transparency". J.Mod.Opt. This is discussed in vol.45, pp.471-503 (1998) (which is incorporated herein by reference).

[0089] "Dielectric" is defined as a material or substance that transmits electrical force without conduction, i.e., an insulator, as the term is used herein. Atomic-based electromagnetic field sensing elements and measurement systems

[0090] According to one embodiment of the present invention, an RF sensing element (also referred to herein as “sensor” and “pen configuration”) optically coupled on one end is provided, generally designated by the number 100, and described with reference to Figure 1. The pen-shaped linear sensor design depicted in Figure 1 results in the use of a single inlet port 102 for optically coupling the required laser beams 103, 104 into and out of a vapor cell volume 108 contained within an enclosure 106, also referred herein as “vapor cell” or “atomic vapor cell”. The vapor cell volume 108 contains atomic or molecular gas. The region of gas within the vapor cell volume 108 probed by beams 103 and 104 may be referred herein and in any appended claims as “test volume”.

[0091] By using a sensor 100 that enters the activity measurement volume 110 from one side, the configuration in Figure 1 ensures that the activity measurement volume 110 is not obstructed by the incident RF / microwave field 112 from all but one side. In the implementation depicted in Figure 1, linearly polarized probe 103 and coupler 104 beams are transmitted 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 vapor cell 106. The probe and coupler beams 103 and 104 copropagate through the atomic vapor cell 106, with the probe beam 103 being selectively retroreflected by a short-pass dichroic mirror coating 130 to return through the cell, while the coupler beam passes through it and is blocked by a thin dielectric absorber beamblock 132. The retroreflective probe beam 134 retraces its path, overlaps with the exit coupler beam, and is recombined by lens 122 to return into fiber 120. A quarter-wave plate 140, positioned before the retroreflection (between the lens and the vapor cell in Figure 1), ensures that the linearly polarized incident probe beam is rotated 90 degrees over the retroreflective exit beam so that it can be selectively split using a polarization-selective element (not shown) for reading after the polarization-maintaining (PM) fiber.

[0092] The sensor 100, as depicted in Figure 1, may offer several advantages compared to other implementations of vapor cell EITs prior to the present invention. Firstly, the linear one-sided design enables a small, thin probe tip and sensor element with a small dielectric footprint. This design also eliminates the need for any optical elements to redirect the optical beam out of the fiber and into the cell. Compared to typical implementations of vapor cell EITs, utilizing a single lens for input and output coupling of larger beam diameters can improve measurement accuracy and sensitivity by resulting in less interaction time spread and, consequently, higher achievable spectral resolution, as well as improved operational stability by reducing device sensitivity to mismatches by reverse coupling the reading probe beam into the same fiber.

[0093] Figure 2A generally uses the pen-shaped recursive EIT configuration 100 of Figure 1, designated by the number 200. 87 The EIT spectrum of the 30D Rydberg state of Rb is shown. The one-sided EIT configuration may be referred to herein as the “recurrent EIT configuration”. The splitting of the fine structure feature 204 is evident. Internal reflection of the coupler beam 104 from the inner cell wall leads to the replicated EIT spectrum 202. The spectrum is obtained without signal lock-in detection of the Si photodiode.

[0094] The replicated spectrum 202 is shifted blue from the primary EIT line 200 by an amount equal to the frequency detuning of the probe beam 103 for a velocity v=0 atom at the center of the Doppler profile. Replication spectra due to internal reflections within the vapor cell are generally observed in vapor cell EIT experiments. These can be avoided by positioning the cell at an angle from the perpendicular incidence of the EIT beam, or by having the cell window at an angle to the incident optical beam.

[0095] Figure 2B generally shows an embodiment of a sensing element, designated by the number 230, which is coupled to a fiber at one end through a rubidium vapor capsule 232. An implementation of the sensing element according to another embodiment of the present invention involves a first prism 212 and a second prism 214 that redirect an excitation beam 216, coupled to a fiber at one end, and a probe beam 218, coupled to a fiber at the other end, into the vapor capsule 232. The prisms 212 and 214 are coupled to the separate fiber-guided beams 216 and 218 by a lens 235.

[0096] According to other embodiments of the present invention, the one-sided optically coupled vapor cell RF / microwave sensing element may be extended to a multisensor array, where the one-sided coupling of the cell array is achieved using a large single beam for the coupler and probe, which collectively collide on the array lens of the micro. One such embodiment is described here with reference to Figure 3. Again, the one-sided inlets of the coupler 104 and probe 103 beams allow for high-density filling of the single element in the array, leaving the active measurement volume / surface unobstructed by the incident RF / microwave radiation to be measured or imaged. With respect to arrays of lower density, grids of individual one-sided elements, such as those shown in Figures 1 and 3, may be employed within the scope of the present invention.

[0097] Figure 3 generally shows a microwave imaging array, designated by the number 300. The microwave imaging array 300 consists of one-sided couplings of individual vapor cell sensor elements 302 arranged in a linear or area (two-dimensional) array. The optical coupler 304 and probe 306EIT beam are split from each other using a dichroic mirror 308. The laser-beam array 310 is derived from a large-diameter laser beam 312, which passes through an array of microlens (ML array) 314. Microlens arrays are commercially available. The laser beam array is matched to a planar array of subcells 316 containing atomic vapor (layer thickness of a certain proportion of the RF wavelength of interest, with subcell periods of less than 1 mm). A dielectric coating 318 on the vapor cell array reflects the 780-nm probe laser beam and transmits the 480-nm coupler and microwave field. The probe beam image reflected by the polarizing beam splitter contains microwave information. This is recorded using a CCD camera 320 and analyzed using an image processor 322. A polarizing beam splitter (PBS) 324 is also shown. Cavity enhancement field sensitivity

[0098] A concept for a hybrid atomic detector for RF detection is presented here, in which an atomic Rydberg vapor, as defined above, is integrated with a different resonant material or structure to tune the RF field of interest. The hybrid atomic detector according to the present invention can advantageously achieve detection capability.

[0099] Near-field effects are well known to generate regions of enhanced electric fields. The aforementioned concept of a hybrid atomic detector, as first described in accordance with the present invention, may be advantageously used, for example, in plasmon resonance in nanoparticles. One embodiment of a hybrid atomic detector according to the present invention employs a split-ring resonator. The simple near-field enhancement device is a sub-wavelength metal tip. The tip enhances the RF electric field, much like a lightning rod that enhances the electric field near the rod during a thunderstorm. Figure 4A shows calculations of the RF field enhancement coefficient along the axis of a 125 μm diameter tip 401 for several frequencies. The illustrations and plots show that a simple structure such as a metal tip integrated into an atomic vapor cell can enhance the field by about 3 times, corresponding to an intensity of 9.5 dB. For enhancement, it is important that the tip diameter exceeds the skin depth depicted in Figure 4B, which is about 1 μm in the 10-100 GHz range (and 1 / frequency) for the example of interest (Cr, beryllium copper, etc.). 0.5 (It is scaled as follows). Hybrid devices such as metal tips embedded in atomic vapor cells enhance field sensitivity through local near-field enhancement.

[0100] A cavity structure that resonates with the RF field provides another means for local enhancement of the field. The cavity structure can easily provide additional control over RF field parameters such as RF field polarization and frequency. Within the scope of the present invention, the cavity may be engineered to reduce field heterogeneity within the atomic RF field interaction volume, which may be desirable in applications and difficult to achieve when utilizing near-field effects with tip-like structures.

[0101] A novel concept of a hybrid atomic cavity structure employed for Rydberg-EIT sensing is described here with reference to Figures 5A and 5B, generally illustrating an exemplary type of hybrid atomic cavity structure, designated by the number 500, and its operating principle for RF field enhancement. Structure 500 consists of two solid metal frames 502, which may also be referred to herein as “electrodes,” separated by a gap 504 in front of a rubidium vapor cell 506. Referring to Figure 5B, the gap 504 between the two metal frames 502 forms a cavity 510 that resonantly couples to a colliding RF field 508, locally compressing the corresponding RF electric field 512 within the cavity volume. The word “cavity” is used herein in a general sense to refer to any structure that imposes any kind of boundary conditions on the solution to Maxwell’s equations over a defined spatial volume. “Cavity” may also be synonymously referred to herein as “resonator” or “resonant structure.”

[0102] The Rydberg atomic vapor inner cavity 510 is optically invoked for field 512 measurement. Figure 6 shows the calculation of field enhancement provided by a hybrid atomic cavity structure 500, with conventionally machined electrodes inside a rubidium vapor cell, illustrated and described with reference to Figure 5A and 5-band Figures 7A-7D. Structure 500 has a gap size of 460 μm, which locally enhances the electric field 512 of 4 GHz microwaves linearly polarized along Y (vertical direction in Figure 5B) by approximately 10 times, corresponding to an intensity of 20 dB, within the gap 504. Using an EIT laser beam waist in the range of 50-100 microns, the enhanced electric field remains highly homogeneous within the active measurement volume inside the measurement channel, which has dimensions of approximately 0.46 × 0.5 × 9 mm. The 9 mm long "cavity channel" (a term used herein synonymously with both "gap" and "cavity") provides a sufficiently long interaction volume for higher optical absorption during the measurement, and also advantageously provides an improved signal-to-noise ratio in the EIT spectrum.

[0103] Generally, a hybrid atomic resonator device according to an embodiment of the present invention, designated by numeral 700, will now be described with reference to FIGS. 7A-7D. The perspective view shown in FIG. 7A highlights a spectroscopic cell 702 (alternatively referred to as an "atomic vapor capsule" of a "vapor capsule"), with an internal structure corresponding to a Stark tuner / compressor 704. FIG. 7B is a top view of the hybrid atomic resonator device 700. The side view in FIG. 7C shows a top electrode 706 and a bottom electrode 707, separated by a spacer 708 and forming a gap 710, also referred to as a "cavity". The perspective view of the hybrid atomic resonator device 700 depicted in FIG. 7D shows electrode wire leads 712 coupled into the vapor capsule 702 via electrode connections 714.

[0104] To demonstrate field enhancement using a hybrid atomic cavity device for highly sensitive atom-based RF field measurements, the hybrid atomic resonator device 700 of FIGS. 7A-7D can be deployed in the experimental setup shown in FIG. 8A. The RF field within cavity 7,10 is measured using Rydberg-EIT as a highly efficient non-destructive optical probe of the field-induced level shift of the high-lying Rydberg states of Rb atoms within cavity 710. A related rubidium Rydberg-EIT energy level schematic is shown in the inset of FIG. 8B. Two laser beams, with λ = 780 nm (720) and 480 nm (722), are counter-propagating and overlap through the center of cavity 710 as illustrated in FIGS. 5B and 8A. In an exemplary embodiment of the present invention, the 780 nm beam 720 is focused to a 70-micron half-width at the center of cell 702 and has a power of 8 μW, while the 480 nm beam 722 is focused to a 70-micron half-width and has a power of 40 mW. Rydberg-EIT spectroscopy is performed while the frequency of the 480 nm laser is linearly scanned across selected Rydberg levels at a repetition rate of a few Hz. 85 Rb5S 85 Rb5S 1 / 2 (F = 3) ~ 5P 3 / 2This is performed by monitoring the 780nm transmission through vapor using a laser frequency stabilized to the (F=4) transition. The optical frequency reference is derived from a 480nm laser beam 720 to calibrate the Rydberg-EIT spectrum.

[0105] For an improved signal-to-noise ratio in the EIT spectrum, according to one embodiment of the present invention, modulation spectroscopy may be implemented. As used herein, modulation includes either frequency, amplitude, and step modulation, or a combination thereof. For example, the 480 nm beam 720 may be amplitude-modulated with approximately 20 kHz square pulses in a 50 / 50 duty cycle, and the 780 nm signal 730, derived by detection of the 780 nm beam using a photodetector 732, may be demodulated, for example, using a lock-in amplifier (not shown). The hybrid atomic cavity structure 700 is maintained at an ambient temperature of approximately 45°C for increased rubidium vapor density and 780 nm absorption. Two electrodes 706 and 707 forming the cavity 710 are both electrically coupled to ground outside the cell 702. In one embodiment, an RF field is generated using a signal generator and amplified by a 20 dB supply into a WR229 open-end waveguide (2.577–5.154 GHz) 735 (alternatively referred to herein as the “guide”). A measurement channel / cavity 710, through which Rydberg-EIT laser beams 720, 722 pass, is positioned approximately 1 cm in front of the guide 735. In the embodiment shown, the RF and optical beams are linearly polarized, and the polarization is directed parallel to the minor axis (Y) of the cavity 710.

[0106] Figure 9A shows the relative 31S Rydberg-EIT spectral line shift as a function of RF / microwave frequency with respect to a fixed injected microwave power of -10 dBm. The Rydberg level is selected such that, for the 2.5–5.2 GHz microwave frequency range covered in the experiment, the applied microwave is far-resonant from any Rydberg transition, and the 31S state exhibits an AC-Stark shift proportional to the microwave electric field amplitude. At the far left of the plot shown in Figure 9A, the laser frequency axis is centered on the 31S line for the applied 2.5-GHz microwave field. As the microwave frequency increases, the 31S level begins to substantially shift from approximately 3.5 GHz to the large microwave cavity-induced field resonance at 4.35 GHz (4.37 + / - 0.01 GHz for higher resolution scanning not shown here). Other features, including a prominent resonance at 4.85 GHz, are also evident in the spectrum. Multiple resonances are unexpected from this device due to the complexity of the bulk cavity structure (e.g., three holes 740 (shown in Figure 7B)) which includes alumina rods for electrode / cavity matching and long electrode wires 712 on the back of each electrode 706, 707.

[0107] Figure 9B shows the applied root-mean-square (RMS) electric field E RMS Regarding 31S 1 / 2 Figure 9C plots the calculated Stark map centered on the Rydberg state. Figure 9C shows the microwave E obtained using Figures 9A and 9B. RMS While Figure 9D plots the EIT lines against frequency, it plots the measured EIT lines for 2.5 GHz (trace 902) and 4.35 GHz (trace 904), respectively.

[0108] The embodiments discussed herein illustrate the suitability of hybrid device geometry as a matter of design options by those skilled in the art for high electric field measurement sensitivity at desired application-specific RF / microwave frequencies. In these embodiments, the microwave electric field amplitude is obtained by fitting a spectroscopically measured microwave-induced AC-Stark shift line to a Gaussian function and converting the peak frequency shift to an electric field value using the calculated Stark shift of the rubidium 31S Rydberg state. Figure 9B shows the unfielded 31S with respect to the applied electric field. 1 / 2 The calculated Stark map, centered on the Rydberg state, is shown. Figure 9C shows the resulting microwave electric field, measured inside the cavity as a function of microwave frequency. At 4.35+ / -0.05 GHz resonance, the cavity-enhanced microwave field E RMS A value of >=13.5V / cm was measured with a relative uncertainty of <0.3V / cm, given by the <0.1MHz fitting uncertainty of the peak position.

[0109] In Figure 9A, the EIT linewidth increases from 21.7 MHz at 2.5 GHz to 84.0 MHz at 4.35 GHz (see also Figure 9D). This increase is due to field heterogeneity within the measurement volume, which occurs because the EIT beams 720, 722 and cavity channel 710 are comparable in size, and near-field effects at the cavity edges are sampled by the optical beam. The edges and corners at the end of the 9 mm long cavity channel 710, where the EIT beam enters and exits the cavity in the atomic vapor, may also contribute. For measurement applications requiring narrower spectral linewidths, the spread of heterogeneous fields can be mitigated by implementing cavity structures with larger cavity volumes and / or by using smaller beam sizes for more spatially localized measurements.

[0110] To estimate the cavity enhancement coefficient for the electric field, the cavity-enhanced 4.35 GHz field measurements described above with reference to Figures 9A-9D can be compared to the field measured outside cavity 710. For this purpose, the EIT beams 720, 722 are moved Δz = -0.9 mm from the center of cavity 710 toward the front of the vapor cell 702 and waveguide 735. To obtain the measurable line deviation at this position outside the cavity, the injected microwave power is increased from -10 to -5 dBm. This is 3.16 times higher power (and 1.78 times higher field) compared to that used in the discussion in Figures 9A-9D. Under these conditions, E RMS A 4.35 GHz microwave field-induced AC-Stark shift of -3.80 MHz, corresponding to 1.47 V / cm, is measured. Using this value for the RF field outside the cavity, and considering the increased injection power, neglecting the field changes emitted from the waveguide over small Δz (|Δz| / d=0.03<<1 (where |Δz|=0.9 mm is the beam position relative to the cavity and d=29.1 mm is the short axis of the waveguide)), this is equivalent to a 24 dB increase in sensitivity. [ka] The cavity field enhancement coefficient is obtained.

[0111] A simulation simulating the field inside a hybrid atomic cavity structure with an incident 4.37 GHz microwave field with an amplitude of 1 V / m and linearly polarized along y is discussed below with reference to Figure 12. This simulation yields an enhancement factor of 18.6, which is about 14% higher than the value measured for a 4.35 GHz field. The difference can be explained by a 0.02 GHz difference in frequency between the measured and simulated fields. The simulation does not consider microwave losses attributable to dielectric cell 702, which depend on the exact cell geometry, including wall dimensions and material dielectric constants, with respect to the microwave frequency of interest.

[0112] In complementary implementations of hybrid devices, instead of inserting the resonant structure 510 into a cell containing atomic vapor, the atomic vapor may also be incorporated into the resonant structure, within the scope of the present invention. This may be desirable in applications where atomic measurements need to be incorporated into an existing RF system (horn receiver, waveguide, etc.) for absolute leveling of RF power and field. As an example, in the sensing element 100 discussed with reference to Figure 1, a similar narrow dielectric capsule 232 containing atomic vapor may be incorporated into the measurement channel 710 of the resonant structure 510, as shown in Figures 5A-5B or 7A-7D. Within the scope of the present invention, the resonant structure 510 may be any type of RF resonator or component.

[0113] Another implementation within the scope of the present invention, having a vapor cell 1002 inside a waveguide 1004, is described here with reference to Figures 10A and 10B, which show side and end views of a field measurement system, generally designated by the number 1000, respectively. A hole 1006 in the waveguide 1004 provides a passage for the EIT coupler 1008 and probe 1010 beam. This system is used for high-intensity field measurements inside a waveguide. Such a hybrid system can be advantageously inserted into an existing RF circuit for absolute power leveling through the circuit. As an embodiment, hybrid devices incorporating atomic vapor within a horn, diode, waveguide structure, or coaxial cable provide a versatile, compact internal module for measurement, calibration, or power leveling in microwave sources, transmission systems, and other instruments in terrestrial, sea, air, and space-based applications.

[0114] The absolute sensitivity achievable using the hybrid atomic resonator device 700 as described herein is all within the design capabilities of those skilled in the art and can be tailored and further increased by implementing Rydberg states resonantly coupled to a cavity-enhanced RF field, as well as Rydberg levels with higher principal and / or orbital quantum numbers. All such enhancements are within the scope of the present invention. Field enhancements and sensitivity may be further customized by engineering the hybrid device, for example, using resonant structures other than those conventionally described and using modules, metamaterials, known or to be discovered in the art. Similarly, complementary implementations in which atomic vapor is incorporated into the resonant structure, also within the scope of the present invention, may be a particular advantage when integrating atomic measurement capabilities into existing RF systems (horn receivers, waveguides, etc.) and DC circuits / components. Polarization selectivity in hybrid systems

[0115] Another feature of a hybrid device, such as one described above, is its ability to distinguish between different RF / microwave polarizations and achieve polarization-sensitive, atom-based field measurements. With respect to the cavity structure shown in Figure 5A-5 band 7A-7D, cavity 710 acts as an RF polarization filter, where only RF fields with linear polarization components along the cavity axis Y are coupled into the cavity and field-enhanced within the active measurement volume.

[0116] Figure 11A shows the experimental 31S Rydberg AC-Stark shift as a function of the applied microwave frequency at a fixed injection power with respect to different angular positions Θ of the microwave field polarization vector relative to the vertical (Y axis). This is 10 0 Step by step, Θ=0 0 (From the short axis of the waveguide along the Y direction) 90 0 This is done by rotating waveguide 735 (shown in Figure 8A) counterclockwise around the Z-axis in the XY-plane by degrees (the minor axis of the waveguide along X). Θ=0 0Then, the microwave polarization is aligned with the cavity axis of cavity 710 for maximum coupling into the cavity, as is evident from curve 1102 shown in Figure 11A. As Θ increases, the signal becomes linear with respect to the microwave field parallel to the cavity axis (Θ=0 0 The ) component decreases, so it decreases. Figure 10B plots the microwave electric field at 4.35 GHz as a function of Θ with respect to the data shown in Figure 10A (obtained from the 31S line shift and the calculated Stark map as described above). As Θ increases, the field decreases as Θ=0 of the microwave field vector. 0 The component (the component coupled in the resonance) decreases due to Θ dependence. The cosine fit to the data, given by the dashed curve 1110 in Figure 10B, confirms this prediction, but the 4.35 GHz field in the cavity decreases due to some electrode mismatch and cavity defects such as surface quality, resulting in Θ = 90. 0 It does not reach zero. The power of the linearly polarized resonant electromagnetic wave coupled inside the resonator and detected by atoms in the resonator gap is cos 2 This means that it has Θ dependence (where Θ is the microwave polarization angle defined above). Therefore, it can be seen that such a cavity resonator mimics the functionality of an integrated microwave polarizer. DC field tuning capability using an electrode-integrated vapor cell

[0117] A major limitation of weak RF field Rydberg-atom-based measurements is that they generally require the RF field to resonate with dipole-allowed Rydberg transitions, which result in large electric dipole moments and strong atomic responses to electric fields. Consequently, weak field measurements can only be performed with respect to a discrete set of RF frequencies that resonate with one of a finite number of discrete transitions within a given atom. To overcome this limitation, it is desirable to use an external field to tune atomic-level energies and transitions to resonate or near-resonate with the RF field of interest, providing sufficient atomic sensitivity for the measurement. The hybrid atomic resonator, first proposed in accordance with the present invention, provides a practical means for this purpose to apply a local field to an atom using the cavity / antenna / electrode structure itself.

[0118] Using the hybrid atomic resonator 700 described above, according to a further embodiment of the present invention, in the context of RF field enhancement, the same electrodes described above are used to Stark tune the Rydberg transition frequency to resonate with the weak RF field, either simultaneously or separately, by applying a DC electric field. Figures 13A and 13B show experimental and calculated DC Stark maps of the 30D Rydberg state with respect to the applied DC electric field, respectively. Note that the Stark maps are symmetrical with respect to the zero field. The experimental spectral map in Figure 13A is acquired using a cavity by grounding one electrode and applying a voltage to the other electrode, thereby generating a DC field within the measurement channel 710 (shown in Figure 5B). The map in Figure 13A shows both the three |mj|=0.5, 1.5, and 2.5 sublevels of the j=2.5 fine structure component and the |mj|=0.5, 1.5 sublevels of the j=1.5 fine structure component. In zero-field and linearly polarized optical beams, the rubidium EIT ladder scheme illustrated in Figure 5B optically excites |mj|=0.5 and 1.5 Rydberg sublevels due to m-mixing by the 5P3 / 2 hyperfine structure. The appearance of a weak j=2.5, i.e., |mj|=2.5 Rydberg level in the experimental spectrum may be due to some optical-beam polarization mismatch or ellipticity.

[0119] Figures 13A and 13B provide a demonstration of tuning Rydberg levels and transitions using a DC electric field in a hybrid atomic cavity or similar structure with electrodes integrated with atomic vapor or gas. As an example, see 30D 5 / 2 and 30D 3 / 2 A 2RF photon transition between mj=1.5 levels can be considered. With an applied electric field of 0 V / cm, this corresponds to a transition that resonates at approximately 540 MHz and is dipole-allowed in the second step, using two approximately 270 MHz RF photons. With an electric field of + / -10 V / cm, the energy difference between states increases to approximately h*700 MHz (where h is Planck's constant in appropriate units), and the transition is dipole-allowed, using two approximately 350 MHz RF photons. The application of a DC field of 0 to + / -10 V / cm allows the transition to be sustainably tuned to resonate with RF photons of approximately 270 to 350 MHz. The range of tunability can be extended within the scope of the invention, for example, by using higher field values, different atomic states with different polarizations and electric dipole moments, and multiphoton excitation processes. AC-Stark tuning using external electrodes

[0120] Continuous frequency measurements of weak Ka-band microwave electric fields can also be performed by AC-Stark tuned Rydberg transitions using low-frequency RF, both applied using internal or external tuning electrodes as described above. In one embodiment of the present invention, an AC-Stark tuned 100 MHz RF field is applied to a vapor cell using external electrodes to Stark tune the transition from a no-RF field transition to an off-resonance state to resonate with the microwave. Figure 14 shows the calculated Floquet spectral maps for both the 47S state (1401) and the 47P state (1403) modulated by the 100 MHz RF field. The 47S and 47P maps are overlaid and referenced to the same zero-field frequency, showing the RF-induced differential shift of the 47S1 / 2 to 47P3 / 2 transition. Thus, with an applied 100 MHz RF of 0-200 V / cm, the resonant microwave transition can be expected to be continuously downtuned by approximately 200 MHz.

[0121] The RF intensity and electric field calibration in the 47S state are shown in Figure 15, mapping the incident RF power to the 47S state shift in different Stark detunings of the excitation beam. The experimental and calculated maps fit well, with dBi=dBm+50.5 dBi / dBm conversion and I=I0*10 dBI / 10 = 1 / 2εcE0 2 (In the formula, I0=1W / m 2 This results in an electric (E0) field calibration using (where ε is the free-space permittivity and c is the speed of light). The calibration in Figure 15 is then performed by K a A band-band microwave is employed to set the RF electric field for the desired differential shift of the 47S to 47P transition (curve 1405 in Figure 14), which is tuned to the resonance.

[0122] Pseudo-crossover is, for example, described in Zhang et al.'s "Stark-induced L-mixing interferences in ultracold cesium Rydbergatoms Phys.Rev.AAs reported in vol.87,033405 (2013), it is used in the interpretation of electric field-induced l-mixed populations in high l states. Figure 16 shows the measured EIT spectrum of the 47S state versus microwave frequency detuning from 37.51663492 GHz (no-RF transition frequency) at a fixed -14 dBi microwave intensity (separate calibration) for four different injected RF power / field intensities in the cell. In the no-RF state (upper plot in Figure 16), the 47S line exhibits expected Autler-Townes behavior as the microwave frequency is scanned across the no-RF field resonant transition. The center of the pseudocrossing is at 0 MHz detuning, and the Autler-Townes splitting peak is split symmetrically. As the RF power / field increases (lower plot in the figure), the pseudocrossing shifts to a larger microwave detuning, tracking the AC-Stark tuning transition frequency. With an applied RF of -38.2 dBm (bottom plot in Figure 16), the microwave resonates with a transition at approximately 60 MHz during detuning.

[0123] In Figure 17, the measured pseudocrossing center is plotted as a function of the applied RF electric field for a range of values ​​up to approximately 200 V / cm. An uncertainty bar is set to an approximate EIT linewidth of + / - 10 MHz. The calculated differential shift shown in Figure 14 is again plotted here by curve 1701 for comparison with the experimental shift. The agreement between experiment and calculation is good almost over the entire range, and the measured AC-Stark shift exhibits the expected quadratic dependence on the applied RF field. At the highest RF fields, the coupling between the modulated sidebands of the 47S and 47P states, along with variations in atomic microwave field coupling strength, under certain experimental conditions (large optical Rabi frequency and EIT linewidth), makes it difficult to determine the pseudocrossing center in the spectrum, leading to a deviation between the plotted measured and calculated values. Continuous AC-Stark tuning beyond the approximately 200 MHz microwave detuning measured here is considered possible, and transitions between the modulated sideband and other Floquet states in the strong field may also be used.

[0124] Within the scope of the present invention, it should be understood that AC-Stark tuning may also use electrodes outside the vapor cell, although they are located within the sensing element, for continuous frequency microwave electric field measurements. Integrated split-ring resonator

[0125] An embodiment of a field tuning structure within the scope of the present invention is provided by a split-ring resonator 1801, which is described with reference to Figures 18A-18D. The split-ring resonator 1801 is a simple resonant structure commonly used for metamaterials in the microwave, mm-wave, and THz regions of the electromagnetic spectrum. The split-ring field amplifier shares conceptual similarities with plasmon resonances of microspheres used in the optical and infrared spectral ranges for spectroscopic and photo-sampling applications. An atomic vapor cell within a quantum RF sensing element having an integrated split-ring structure, engineered to achieve low-noise field amplification, high sensitivity, and polarization selectivity in atomic-based RF electric field sensing applications, constitutes another embodiment of an atomic cavity structure for high sensing capability.

[0126] Figure 18A illustrates the structure of one basic type of split-ring structure, namely a tubular ring with a single slit. At resonance, the electric field of the incident mm-wave field 1803 is compressed at the slit (or "gap") 1805. The gap 1805 also defines a measurement channel 710, where atomic vapor is optically probed for measurement of the amplified field. This operating principle is illustrated in Figure 18b with respect to a slit / gap with dimensions of 1 × 0.2 × 0.2 mm for the split ring shown in the insert, and a perpendicularly polarized microwave field incident on the cavity from the right. In Figure 18a, the simulated electric field values ​​inside the slit of this resonator type are plotted as a function of the incident microwave field frequency (fixed 1 V / m incident field amplitude) for three different gap sizes and geometric shapes. These split rings resonate at 14, 44, and 54 GHz, with field amplification factors of 46.8x, 74.1x, and 27.3x, respectively. The resonant frequencies are engineered using the simple geometric parameters of the split rings. In Figures 18C and 18D, the simulated resonant behavior of other split ring resonator structures, including a square tubular structure, is plotted, providing amplification at 42.5, 125, and 94 GHz, with individual amplification factors of 81.9x, 12.5x, and 9.4x. These amplification factors correspond to intrinsic non-electronic gains ranging from approximately 20 dB to 35 dB. Using 1 mV / m as an upper limit for target field measurement sensitivity without amplification, a hybrid device yielding 81.9x field amplification at 42.5 GHz microwaves can achieve effective sensitivity at the 0.01 mV / m level (with respect to the incident field).

[0127] Other split-ring resonator structures, such as concentric high-Q microwave cavities, and other types of resonators, applied to field enhancement within vapor cells, are also within the scope of the present invention. Non-contact optical heating of a steam cell for temperature stabilization

[0128] Hereinafter described with reference to Figures 19A-19C, non-contact all-optical vapor cell heating can be an essential component as an active vapor pressure control system for Rydberg RF sensors and hybrid devices, where temperature control hardware (electronics, metal wires) must not alter the RF field response of the detector. According to embodiments of the present invention, one or more optically absorbing materials are incorporated into the cell. The optically absorbing material is heated via absorption or inelastic scattering of an incident light beam, which in turn heats the atomic vapor (or solid metal) in the cell for a higher atomic vapor density. The atoms may be indirectly heated by optically absorbing material elements, which are in conductive thermal contact with the optically heated elements or in thermal contact with the vapor enclosure, for example, by using a cell constructed from IR-absorbing glass.

[0129] In addition to heating, stabilizing the cell temperature during operation is crucial. This may be important when measurements are performed in an environment where the external air temperature can significantly alter the cell temperature. This is particularly a concern when using small cells (approximately mm or less), whose atomic temperature and density are more susceptible to ambient temperature fluctuations due to their smaller volume. To address this, active stabilization may be implemented, within the scope of the present invention, by actively monitoring changes in atomic vapor temperature or density via optical absorption through the cell of a second laser beam that resonates with atomic transitions. This absorption signal provides active feedback on the amount of optical heating power required to reach the desired temperature and density. Furthermore, the cell can be insulated from its environment, for example, by incorporating an insulating vacuum layer between the optically heated cell and the environment.

[0130] Referring to Figures 19A-19C, according to an all-light vapor cell heating method integrated into a Rydberg RF sensor, an IR-absorbing glass capsule is illuminated by a bright light source to raise the internal temperature where the atomic vapor cell is located. Figures 19A and 19B show an IR-glass capsule 1901 surrounding a 4 mm inner diameter atomic vapor cell 1903. Figure 19C shows an all-light heating test platform. A light source 1905, such as a 50-watt halogen bulb, is imaged over the capsule, and the temperature of the IR glass capsule 1901 is monitored using a temperature sensor, such as a thermistor (not shown), installed within the volume of the IR glass capsule. A feedback loop between the thermistor and the light source intensity is implemented to regulate the internal temperature of the capsule and provide a stabilized operating temperature for uniform heating of the atomic vapor cell. A steady-state temperature of up to 130°C, uniformly distributed within the capsule, is achieved in one embodiment. Active temperature stabilization of the capsule temperature at 50°C (the typical operating temperature when using a small 4mm inner diameter Rb cell) has also been achieved. RF phase measurement capability using modulated laser field

[0131] A method for extracting the phase of an RF field using a sensing element is described here. According to embodiments of the present invention, phase-sensitive recording of a coherent electromagnetic field on a surface can advantageously enable the reconstruction of the field in all space. The applications of this reconstruction principle are numerous and include holography in optics, radar based on interference schemes such as SAR and InSAR, and far-field characterization of antenna radiation patterns based on near-field measurements of the amplitude and phase of the field emitted by an antenna under test. In the last application listed, the measurements are performed on a surface, and near-field / far-field conversion is applied to compute the field in all space.

[0132] To achieve phase sensitivity in field measurements, holographic methods are typically employed, where a reference wave interferes with the wave emitted by an object. In this case, the object is considered an antenna under test that emits an RF field that needs to be fully characterized. The reference wave, with clearly defined amplitude and phase, is preferably a planar RF field that interferes with an object wave in an atomic vapor cell or hybrid atomic cavity cell structure. Here, the cell is manufactured so that the atomic field interaction volume measures less than one RF wavelength across any given direction. The atomic field interaction volume is given by the overlap between the atomic vapor, the probe laser beam, and the coupler laser beam. The magnitude of the coherent electric field sum of the object and the reference mm-wave or microwave field is then measured using a well-established method.

[0133] The measured magnitude depends on the phase difference between the reference wave and the object wave. In principle, such readings can be obtained on a surface surrounding the object. This can be achieved, for example, by moving the vapor cell sensor unit onto a suitable grid using a spatial resolution much smaller than the RF wavelength. The phase-sensitive electric field values ​​measured on the grid then allow for a complete three-dimensional reconstruction of the object wave. To obtain the far distance of the antenna under test, known algorithms for near-field / far-field conversion can be used. This measurement method can be easily extended to include full polarization sensitivity for electric field vectors utilizing hybrid atomic cavity structures (see above) or other spectroscopic techniques.

[0134] In RF field phase measurements, generating a clearly characterized reference wave presents a significant challenge. For comparison, let's first consider optical holography, where the reference wave is typically an extended, nearly perfect plane-wave laser beam interfering with an object scattered within a layer of photographic emulsion (or equivalent). It is well known that the purity of the reference wave is crucial in optical holography. The system should be free of diffraction rings, primarily caused by dust particles and other defects. Spurious reflections of the reference wave from smooth glass surfaces pose an even greater problem. In the context of RF measurements, this condition is extremely difficult to encounter, even when using state-of-the-art anechoic chambers. For quantitative studies, it will also be important that the reference wave has a fixed amplitude, or at least a well-known, slowly fluctuating amplitude function. Preparing a defect-free RF reference wave with smooth amplitude behavior across a large surface presents a significant challenge and is not always possible.

[0135] Figure 20A schematically illustrates the rear end of a sensing element and the operating principle for phase-sensitive measurement of an RF electric field, generally designated by the number 2000, according to one embodiment of the present invention. The microwave horn 2002 (MW) represents any antenna under the wave of the test or other object of interest. Driven by the RF source 2006, the fiber modulator 2004 phase-coherently transfers an RF reference beat onto a coupler beam 104 transmitted to atoms in the vapor cell 106. The RF reference beat replaces the reference beam, which is typically required in phase-sensitive (holographic) field measurements. The vapor cell 106 in the atom-based RF sensing element is approximately 1 mm in dimensions and is fiber-coupled to 780 nm and 480 nm laser beams. The sensing element 100, fiber-coupled on one end, is mounted on a sensor stick (not shown) with a minimal dielectric profile. The sensing element and stick are the only parts of the detector that are actually in the RF field. The fiber modulator and optical phase control elements are integrated with an external sensor remote control station (not shown) of the sensing element 100, and include a laser, signal reading electronics, and a calculation unit for analysis. Figure 20B depicts the quantum mechanical level scheme and optical / RF excitation path used in phase-sensitive RF electric field measurements.

[0136] To address the need for these practical measurements, a solution is integrated into an atomic-based RF sensing element and measurement. The operating principle is to transfer a phase-coherent RF reference onto an optically coupled laser beam via electro-optic modulation techniques. Using a commercially available fiber optic high-frequency modulator, the coupler beam is set to the same frequency ω as the frequency of the RF field to be measured. RF The frequency or amplitude is modulated in this manner. In one implementation, the field frequency is selected to be the same as half the separation between two neighboring S-type Rydberg levels. The level energy and its separation are known with very high precision. Many options exist regarding such transitions. Furthermore, the carrier frequency of the coupler laser beam 104 is nP between S levels. 3 / 2It is tuned to resonate with the transition to the Rydberg level 2010. The Rydberg nP level is not midway between the two S Rydberg levels, leading to a detuning Δ of the modulation coupler frequency 2012 from the S-state resonance. In rubidium, these detunings are about 100 MHz, which is typically greater than the Rabi frequency of either of the transitions involved. Thus, the two-photon Rabi frequencies that explain the transition from 5P to nP via absorption of one coupled laser photon and absorption (channel B in Figure 20B) or stimulated emission (channel A in Figure 20B) of an RF photon are given by: [ka]

[0137] There, [ka] and [ka] This is the Rabi frequency of the optical coupler laser transition to the S Rydberg level, [ka] From S Rydberg level to nP 3 / 2 The Rabi frequency of the RF transition to Rydberg levels, [ka] This is the phase of the RF field. Also, [ka] and [ka] is the phase of the modulation sideband of the coupled laser. [ka] Note that there is an important difference in the sign before it. Furthermore, the RF field amplitude E RF teeth, [ka] Therefore, [ka] Included within, in the formula, [ka] This is a well-known RF electric dipole transition matrix element for RF Rydberg / Rydberg transitions. Net coupling between 5P states and nP Rydberg states. [ka] However, this is then given by the coherent sum of channels A and B in Figure 20B. [ka] During the ceremony, for convenience, [ka] and [ka] It is assumed that they are identical, and that both RF Rabi frequencies are identical (both are good approximations). These assumptions are not important, but are helpful in explaining the mathematics. Optical phase [ka] and

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[0138] In this description, the RF field phase (and amplitude) measurement capability is achieved by introducing an RF reference wave via optical frequency modulation. The novelty of this approach lies in eliminating the need for an external RF reference wave by replacing the optical modulation of a laser beam directly applied to atoms within a quantum RF sensing element. In practice, the reference wave can also be introduced to the location of the sensing atom within the atom-based RF sensing element using a cell-integrated electrode or cavity structure (hybrid system) as illustrated in Figures 5A and 5B, or by using an external reference wave. Modulated RF detection in atomic vapor cells

[0139] For telecommunication applications, the detection of a modulated RF field is desired. Due to the <100 ns EIT response time, the amplitude and frequency modulation of a high-frequency field can be detected directly, without relying on quantum interference, by using an atom-based sensing element as an RF / optical converter. Similarly, RF phase modulation detection is obtained from the phase detection capabilities described above. A typical scenario is described below.

[0140] AM modulation in acoustic frequencies : Most Rydberg states in the Floquet map at any carrier frequency from about 100 MHz to several 100 GHz exhibit a differential dynamic dipole moment with magnitudes on the order of thousands of Debye. The EIT lines on the map have linewidths given by the coupling and probe Rabi frequencies. For modulation purposes, moderate probe and large coupling Rabi frequencies may be used to maintain a fast EIT response time for AM and broaden the EIT line to up to several tens of MHz. When a carrier RF is applied to the EIT test cell and the operating point of the coupling laser frequency is selected on one of the fluctuation points of the Rydberg-EIT line, the AM of the RF signal will lead to a direct response in the photodiode reading of the EIT sensing element. For the differential dipole moment d, the AM depth dE in the field must be dE < h×dL / d, where dL is the EIT linewidth. Thus, the relative modulation depth is dE / E < h×dL / (Ed). This value can range from several 10% to 1% depending on the exact conditions and sensitivity requirements.

[0141] According to one embodiment of the present invention, a microphone, a linear amplifier, and a voltage-controlled RF attenuator may be used to convert the signal into an acoustic signal and produce an AM modulated RF test field. The EIT test signal is transmitted using an antenna or microwave horn. The EIT cell is used as a receiver. By selecting the operating point as described, the EIT probe photodiode signal is transmitted through bandpass, allowing the acoustic frequency range to be transmitted. The detected signal is amplified and transmitted to a recording device and / or loudspeaker. It should be noted that in this method, demodulation is not required on the receiver side (processing of the EIT cell and EIT probe laser signal). The EIT physics act as the demodulator. The same receiver principle can also be applied when detecting AM modulated transmissions from other locations. Since the EIT sensor cell, incorporated into an antenna receiver, is optically coupled, the AM receiver based thereon is highly EMI and EMP resistant and can withstand high voltage spikes while constituting a sensitive AM radio receiver under normal operating conditions. Modulation of an FM field can be implemented in a similar manner. Incoherent RF field and RF noise measurement capability

[0142] Prior to the present invention, Rydberg-EIT systems were only capable of characterizing coherent RF fields because Autler-Townes splitting requires coherent field interactions. This physical constraint was removed for the first time according to the present invention, as described herein. Steps for quantifying RF noise attributes according to one embodiment of the present invention are described here with reference to Figure 22. In the first step 2201, a given Rydberg atomic energy level or Rydberg-EIT spectrum is calculated in the presence of an incoherent RF noise field. A model of Rydberg-EIT in the presence of noise is presented in the following section. Measurement light is propagated within an atomic vapor cell (2203), and spectral features of the atomic vapor are measured (2205). The measured and calculated spectral features are compared (2207), and matching spectra are identified (2209). This provides a step (2211) for quantifying the presence and attributes of incoherent RF noise, including spectral noise density, spectral power, electric field amplitude, polarization, RF noise field propagation direction, and source characteristics such as the gain of a horn antenna that may emit such RF noise.

[0143] In RF electric field measurements using Rydberg-EIT and Autler-Townes in atomic vapor, the EIT probe beam couples two atomic levels |1> and |2>, the EIT coupled beam couples level |2> to the Rydberg level |3>, and the RF field to be measured couples level |3> to another Rydberg level |4>. The Rabi frequency Ω of the RF-driven transition. RFHowever, this then becomes evident in the Autler-Towns (AT) splitting of the two lines observed in the EIT spectrum, which, in turn, leads to the electric field through fundamental atomic physics calculations. To account for the effects of broadband RF field noise in this type of atomic-based RF electric field measurement, a quantitative explanation of the effects of broadband microwave noise is required. The situation under consideration can be quite common, as microwave amplifiers typically add broadband noise to the amplifier output. That is, the noise will therefore affect the atomic-based electric field measurement.

[0144] To conform to general experimental testing conditions, this process assumes that both the coherent microwave signal and the noise signal, whose amplitudes are to be measured, are transmitted from a common microwave horn located at a distance exceeding the horn's far-field limit. The fundamental theory described herein is sufficient to present the physics of noise-induced effects. The theory can later be extended to cover more general types of field geometric shapes and extended to broader applications (without adding substantially new fundamental physical insights).

[0145] The effect of broadband noise on Rydberg atomic systems consists of two main parts. Rydberg levels |3> and |4>, captured by a coherent source (laser, coherent microwave radiation), can transition to other Rydberg levels due to the frequency components of the noise spectrum that resonate with transitions between Rydberg states. This process is analogous to the attenuation driven by blackbody radiation. The usual processing, where the radiation field is quantized and the transition rate is obtained from Fermi's golden rule as well as the possible field polarization and the sum over the available final angular momentum states, needs to be modified to apply to a noise field with a clearly defined polarization and propagation direction (given by the geometry of the microwave horn). Also, the blackbody energy density of the field must be replaced by the context-specific noise characteristics. At atomic locations, the noise is either known or actually subject to study, with respect to its spectral intensity, i.e., W / (m2 has a noise intensity per frequency interval, measured in Hz.

Chemical formula

[0146] To model a hypothetical RF field test scenario where the coherent microwave field and noise to be measured are applied to the atom via the same microwave horn and the atom is located at a distance from that horn, the field is quantized in only one dimension (the propagation direction of the microwave field emerging from the horn), assuming a fixed field polarization. The noise-induced transition rate R from the initial state |i> to the final state |f> fi For, the analysis shows the following.

Chemical formula

[0147] In the assumed measurement scenario, the coherent microwave field to be measured drives the transition between the Rydberg states |3> and |4>. If the noise spectrum covers the transitions |3> and |4>, the noise-induced transitions are at an equal rate R 34 =R 43In the form of two noise-induced bidirectional attenuation terms accompanied by , it must be included in the Master equation. Furthermore, within the coherence attenuation rate of any off-diagonal density matrix element accompanied by level |3> or |4> or both, R 34 and R 43 It is necessary to include this.

[0148] With respect to coherently driven |3>←→|4> transitions and different transitions |3>→|f> and |4>→|f>, the noise is R f3 =R 3f and R f4 =R 4f The transitions are driven at a rate per atom. Note that the noise-introduced level |f> has no coherence with each other or with any of the levels |1>-|4> because noise-induced transitions have random quantum phases. Therefore, all levels |f> that are incorporated from level |3> due to noise can be grouped into the hypothetical level |d>. Similarly, all levels |f> that are incorporated from level |4> can be grouped into the hypothetical level |e>. Due to the electric dipole selection rule, there is no overlap between the levels grouped into the hypothetical level |d> (incorporated by noise from |3>) and the levels grouped into the hypothetical level |e> (incorporated by noise from |4>).

[0149] The net rate to the hypothetical level is as follows: [ka] Also, R d3 =R 3d and R e4 =R 4e The noise also induces AC shifts, which are calculated using quadratic perturbation theory based on the same-field quantization model. The shifts for levels |i>=|3> or |4> are found as follows: [ka]

[0150] Integral limit ν min and ν max It is selected to be broad enough to cover the entire noise spectrum. fi 3 Note that the sign of the transition frequency is important (as expected) due to the term. The AC deviations of levels |3> and |4> will need to be added to the Master equation as noise-induced detuning terms. All other noise-induced AC deviations of Rydberg levels, which are included in the model by combining them into hypothetical levels |d> and |e>, are not important.

[0151] Comparing the three equations above, it becomes clear that AC shift is more difficult to calculate than attenuation. Regarding attenuation, only transitions associated with frequencies within the noise band are affected, and the noise spectral density is required only at these frequencies. Typically, only a few (sometimes none at all) Rydberg-Rydberg transitions with level |3> or |4> are within the noise band. In contrast, all permissible transitions with level |3> or |4>, including transitions associated with frequencies outside the noise band, are, in principle, relevant to the equations above. Furthermore, for each of these transitions, the integral across the entire noise band must be evaluated. Regarding transitions within the noise band, some consideration must be given to polarity.

[0152] To evaluate the above equation, the noise spectral intensity function I ν (ν) is required. In many scenarios, the user will be able to measure the power spectral density function dP / dν of the noise injected into the horn using a spectral analyzer. The propagation equation available in the textbook is then I ν This yields an equation in terms of (ν). [ka] In the equation, dP / dν is inserted into the distance x from the horn in meters, in units of W / Hz. The spectral power dP / dν is normalized (in watts) to integrate with the total noise power injected into the horn. Linear gain g with respect to the horn. L(ν) This is typically provided according to the specifications of the horn manufacturer. ν The result of (ν) is then input into the above equation to determine the noise-induced attenuation rate and the AC level shift.

[0153] Using the results of the above equation, the fourth-order Master equation for this problem can be extended to include the effects of noise up to the second order. The state space of the Master equation is the net collective ρ, which is transmitted by noise from individual levels |3> and |4> (levels whose electric fields are coupled by the coherent microwave signals to be measured). dd and ρ ee The equations are revised by hypothetical "levels" |d> and |e>, which will retain the same properties. The revised Master equations include additional terms relating to the level sets of Rydberg states |3> and |4>. [ka]

[0154] The equations for the decay of coherence with levels |3> and / or |4> are also, they, all R 3d , R 3e , and R 34 It needs to be revised to include the terms. The new equations for the hypothetical levels |d> and |e> are as follows: [ka] The modified Master equation does not include any equations relating to coherence with respect to hypothetical levels (coherence with hypothetical levels is always identity zero). After revising the standard fourth-order Master equation with all these terms, the coherence ρ is solved using the standard method as a function of the coupler laser frequency. 12 This is required, and it is necessary to extract the EIT spectrum.

[0155] The model EIT spectrum is, for example, related to the coupler-laser detuning α(Δ) with respect to the given atomic vapor and cell temperature used. C This can be obtained by calculating the absorption coefficient of Beer in the medium as a function of ). Note that this involves an integral over the Maxwell velocity distribution in the cell, as each velocity class has its own Doppler shift of the coupler and probe beam. The ratio of input to output probe power is then e -αL The formula is given by, where L is the cell length. Calculated atom-specific matrix elements for all experimentally available inputs and all noise-driven transitions.<f|r|i> It should be noted that after using this method, there are no remaining fitting parameters to adjust the model results. This results in an absolute mismatch when comparing the measured and modeled spectra of the Rydberg-EIT-AT spectrum under the influence of broadband noise. Continuous-frequency RF electric field measurement capability using the strong atomic field interaction region

[0156] As used herein, the term “strong atomic field interaction region” refers to a microwave field characterized by an electric field intensity exceeding that of the Autler-Townes region, which is sufficient to explain the spectral line splitting observed in the two-processing. To measure the RF electric field within the strong atomic field interaction region, the Floquet state is considered to exhibit a high-density state, a differential dynamic dipole moment fluctuating throughout, and multiple pseudocrossings. Such processing is first proposed according to a certain embodiment of the present invention. Plasma diagnostics

[0157] One method according to an embodiment of the present invention may be referred to as plasma diagnostics, using electromagnetic wave-induced clearing on plasma-embedded particles or plasma components for the measurement of plasma fields, particle interactions, and parameters. A method for plasma field measurement and diagnostics is described, employing electromagnetic wave-induced clearing (EIT) or electromagnetic wave-induced absorption (EIA) as a high-resolution quantum optical probe for energy level shifts of plasma-embedded Rydberg atoms, acting as a highly sensitive local electric field sensor with a large dynamic range.

[0158] An embodiment of EIT-based plasma diagnostics is described here with reference to Figures 23A-23C. Rubidium or another type of tracer particle suitable for EIT is incorporated into the plasma 2300 during its generation. The tracer atom is optically queried using EIT, and the EIT beam 2303 spatially overlaps with the tracer atom in the plasma, as shown. The relevant atomic-level structure and Rydberg-EIT configuration are illustrated in Figure 23C with respect to the rubidium atom, which consists of a 780 nm probe laser beam 2320 whose frequency resonates with the transition from 5S1 / 2 to 5P3 / 2D2, and a counter-propagating 480 nm coupler beam 2322 whose frequency is scanned around the transition from 5P3 / 2 to the Rydberg state. In this embodiment, the 58S Rydberg state is selected. The EIT beams are overlapped and focused to the beam waist to optimize the EIT signal intensity and desired spatial resolution within the plasma 2300 (typically about 100 micrometers). The probe beam transmission is detected on the photodetector 2306 for reading. As the coupler beam is scanned across the Rydberg state resonance, the coupler frequency matches the resonance from 5P to the Rydberg state, and when a reduction in the probe beam transmission is detected, the tracer atom becomes transparent to the probe light. In this way, Rydberg-EIT spectroscopy is performed on tracer atoms in the plasma that are susceptible to the plasma environment (field, particles). From the EIT spectrum, information about the plasma field and particles is obtained, then from plasma-induced Rydberg line shifts and line shape changes, which can be calculated with high precision.

[0159] The polarization rate of the low angular momentum Rydberg state is approximately n 7 The scaling is performed as n, where n is the principal quantum number. This strong scaling results in a broad range of measurement and sensitivity for diagnostics by tuning the coupler laser frequency and targeting the desired Rydberg level for measurement.

[0160] In plasma science and applications, plasmas can be confined using magnetic fields, which directly affect the plasma's properties. Furthermore, the magnetic field itself, arising from the charge currents within the plasma, is of interest. EIT plasma diagnostics can also be used for measuring plasma magnetic fields, following the same methodology. The calculated spectra of Rydberg atoms in a magnetic field, as well as the combined spectra in magnetic and electric fields, allow, for example, that EIT spectra measured from tracer atoms in a magnetically confined plasma be mapped onto their corresponding electrical and / or magnetic fields.

[0161] In another embodiment of the diagnostic, as described with reference to Figure 23B, a tracer atom group 2330 is collected in a magneto-optical trap and generated from a cooled atom source 2332, such as atoms, which are injected into the plasma of interest using a pulsed pusher beam 2334. Similarly, a pulsed beam of hot atoms or molecules may be used. The atoms are seeded into the plasma, where they can interact with the plasma and its environment. The atoms are then optically queryed using a Rydberg-EIT optical probe 2336 that spatially and temporally overlaps with the atom group in the plasma. The optical probe transmission is also detected on a photodetector 2306 for reading and analysis. In this configuration, a particle collector / detector 2340, such as a microchannel plate (MCP), may also be integrated and used to measure the atom bundle, providing additional information about the plasma density via collision-induced losses from the atom group as it passes through and interacts with the plasma, or similarly, by detecting charges / molecules resulting from interactions between atoms and plasma components. Atomic high magnetic field sensor and measurement method

[0162] According to further embodiments of the present invention, a method is disclosed that forms the basis of a new probe technology for sensing and measuring high magnetic fields.

[0163] The field measurement method described herein is based on atomic spectroscopy of low-density atomic vapor encapsulated in small (approximately 1 cm in diameter or less) glass cells. In the atom-based field measurement method, a laser beam is used to measure the magnetic field-induced atomic energy level shifts caused by the Zeeman effect. In advanced implementations, it is also proposed to utilize the enhanced diamagnetic response of highly excited Rydberg atoms to a magnetic field in order to achieve higher sensitivity in strong fields. Magnetic fields several times greater than 0.1 T for several hours split the hyperfine level of the Rydberg state into multiple Zeeman sublevels, transitioning from a weak field (linear Zeeman) region into the Paschen-Back region. The resulting saturated absorption spectrum exhibits significantly more diffuse, linear characteristics, and cross-resonances disappear due to nuclear separation and electron spin. The absolute line positions and relative separations between them are excellent magnetic field markers.

[0164] As depicted in Figure 25A, saturation spectroscopy is a well-known method for eliminating the broadening of heterogeneous lines caused by the Doppler effect. It has a wide range of applications in science and technology where obtaining accurate spectroscopic information about atomic and molecular transitions and their shifts caused by external fields is required. In saturation spectroscopy of alkali atoms in a weak magnetic field, the hyperfine levels of the excited states, symbolically shown as |2> and |2'> in Figure 25A, are split by less than the Doppler width, leading to multiple saturation peaks and cross-resonances in the probe laser spectrum of the absorption line broadened by a given Doppler. As is known from textbook quantum mechanics, in magnetic fields several times greater than 0.1 T, the hyperfine levels split into multiple Zeeman sublevels, transitioning from the weak-field (linear Zeeman) region into the Paschen-Back region. The resulting saturation absorption spectrum exhibits significantly more diffuse lines, and cross-resonances disappear due to nuclear separation and electron spin. The absolute line positions and relative separations between them are excellent magnetic field markers.

[0165] The strong magnetic field may be measured, according to the present invention, either by using standard Rydberg-level saturation spectroscopy, as depicted in Figures 24A–24C, or by using a quantum interference process, as shown in Figures 25A–25C, in which two excitation paths within the three-level atomic structure destructively interfere with the transmission of one of the laser beams being utilized, producing an increase. In the individual cases, Figures 24A and 25A show separate quantum level schemes for 2- and 3-level systems, while Figures 24B and 25B show the coupling of the electromagnetic field into the atomic vapor cell 106. Figure 24C plots the saturation spectrum of rubidium in a 0.7 T magnetic field. The line positions and their relative separation reveal the magnetic field present within the spectroscopic cell.

[0166] In the EIT spectroscopic method depicted in Figures 25A-25C, a quantum interference process is employed in which two excitation pathways within the three-level atomic structure destructively interfere with the transmission of one of the laser beams being utilized, producing an increase. The resulting EIT transmission window presents a convenient optical reading for the atomic energy level and its response to an arbitrary external field (here, a magnetic field). In the Rydberg-EIT cascade scheme, the transparency is formed by the coherent superposition of the ground state and the Rydberg state. The Rydberg-EIT is implemented in both cooled atomic gas and room-temperature vapor cells, such as those depicted in Figure 1.

[0167] The atomic state most relevant to the saturation and EIT spectroscopy of rubidium is the 5S state of rubidium. 1 / 2 Basal, 5P 3 / 2 Excitation, and nS 1 / 2 , nD 5 / 2 , and nD 3 / 2 These are Rydberg states. In the magnetic field of interest, all of these lie within the Paschen-Back region of the hyperfine structure. Intermediate states lie within the (linear) Zeeman region of the fine structure, while Rydberg states typically lie within the Paschen-Back region of the fine structure. Furthermore, Rydberg states typically exhibit a strong shift due to atomic diamagnetism.

[0168] Due to their large size, Rydberg atoms undergo a large diamagnetic shift. For the S-type Rydberg state, the Rydberg state energy shift at the atomic level is as follows: [ka] In the formula, n, l, m l , m s These are the principal quantum, angular momentum, magnetic orbit, and spin quantum number, respectively. Regarding the S state, [ka] The coordinates r and q are the spherical coordinates of the Rydberg electron (magnetic field point along z). The displacement consists of a spin-Zeeman term (the first term on the right-hand side) and a diamagnetic term (the second term on the right-hand side). The individual differential magnetic moments are the negative derivatives with respect to the magnetic field B. The Bohr magnetron is 1 / 2 at the atomic level, and the radial matrix elements are n 4 Scaled as such, the diamagnetic differential magnetic moment in the Bohr magnetron is n 4 Please note that it is B / 2. 1 Tesla field (4.25 × 10¹¹ in atomic units) -6 In this case, diamagnetism exceeds the paramagnetic (spin) differential dipole moment when n is greater than approximately 25. Easily attainable, at n=50, diamagnetism exceeds the paramagnetic differential dipole moment by approximately 16 times. Therefore, in strong magnetic fields, the diamagnetic effect of Rydberg atoms results in an increase of several orders of magnitude in sensitivity to small magnetic field fluctuations. Additional aspects, including the role of quantum chaotic behavior, are discussed in Ma et al. “Paschen-Back effects and Rydberg-state diamagnetism in vapor-cell electromagnetically induced transparency” by al. Phys.Rev.A. This is discussed in , vo.95, 061804(R) (June 27, 2017) (incorporated herein by reference).

[0169] A step for quantifying magnetic field attributes according to one embodiment of the present invention is described here with reference to Figure 21. In the first step 2101, a predetermined Rydberg atomic energy level or Rydberg-EIT spectrum in a strong magnetic field is calculated. FM-modulated measurement light is propagated within an atomic vapor cell (2103), and spectral features of the atomic vapor are measured (2105). The measured spectral features are compared with calculated spectral features (2107), and matching spectra are identified (2109). This provides a step for quantifying magnetic field attributes (2111). Atomic-based optical RF power / voltage converters and sensors

[0170] Another aspect of the present invention is described here with reference to Figures 26A and 26B. Figure 26A schematically depicts a hybrid atomic-based optical RF power / voltage converter and sensor, generally designated by the number 2600. The hybrid atomic-based optical RF power / voltage converter and sensor 2600 employs an atomic vapor cell 2602 with an integrated electrode 2604 embedded in an RF receiver or circuit 2608 for the conversion of an RF signal of interest to an in-cell electric field optically measured via spectroscopy of field-sensitive atomic states. By the direct conversion of the RF electrical signal to an atomic-mediated optical reading, the atomic-based converter provides a high-bandwidth (DC~THz) absolute (atomic) measurement of power or voltage. A demonstration of such an atomic-based converter in a 60Hz electrical signal measurement is shown in Figure 26B, which can advantageously be employed as an RF receiver element in the basis of an antenna in microwave interception. In both the measurement and receiver cases, the spectral reading of the atomic cell is used to detect and determine the power equivalent field of the electrical or electromagnetic signal of interest.

[0171] Figure 26B shows plots of readings from an atomic-based optical RF power / voltage converter of a 60 Hz electrical signal applied to an electrode for six voltage levels. The optical laser is near-resonant with a field-sensitive atomic Rydberg state, and the transmission of the probe laser through vapor is detected. The field equivalent power is then determined by comparing the detected transmission signal with a known atomic response. Depending on the detailed geometry of the selected electrodes and structures, as well as the electrical and thermal properties of the selected materials used, the atomic detector readings may be used for atomic calibration of the RF power / voltage.

[0172] Generally, the atomic-based optical RF power / voltage converter and sensor, designated by the number 2700, is described with reference to Figures 27A and 27B. The atomic-based optical RF power / voltage converter and sensor 2700 consists of a small cylindrical cesium vapor cell with an integrated internal conductive plate. The conductive plate, or electrode, is a 0.5 mm thick ring spaced 4 mm apart, fused to the cell body on one side and to a window on the other. As a result, the total path length through the cell is 5 mm. The inner and outer diameters of the cell are 3.4 mm and 5 mm, respectively, while the inner and outer diameters of the electrode rings are 2 mm and 5 mm, respectively. Thus, two 0.7 mm thick ring electrodes are embedded within the vapor cell and to which external electrical connections are made.

[0173] The atomic vapor 2701 is contained within an atomic vapor cell compartment 2703, which has a window 2705 transparent to an optical beam used for exciting atoms into the Rydberg state, and another integrated window 2707 transparent to the EM field generated by the optically excited atomic medium for extraction of the generated EM field. An EM filter 2710 prevents the transmission of the Rydberg-EIT probe and coupler beams 103 and 104.

[0174] The embodiments described herein are intended to be illustrative only, and modifications and alterations will be obvious to those skilled in the art. All such modifications and alterations are intended to be within the scope of the present invention as defined in any appended claims.

[0175] Further teachings relating to the subject matter of the present invention can also be found in the following publications, which are incorporated herein by reference. · Anderson et al., “A vapor-cell atomic sensor for radio-frequency field detection using a polarization-selective field enhancement resonator,” Appl. Phys. Lett. , vol. 113, 073501 (2018) · Simons et al., “Electromagnetically Induced Transparency (EIT) and Autler-Townes (AT) splitting in the presence of band-limited white Gaussian noise,” J. Appl. Phys. , vol. 123, 203105 (2018).

Claims

1. A method for detecting or measuring a first electromagnetic field, wherein the method is: a. Exciting atoms and / or molecules of the gas within the enclosure into a Rydberg state distribution, wherein the enclosure is exposed to the first electromagnetic field, b. Structuring the first electromagnetic field by arranging it in an interfering relationship with at least one other electromagnetic field, c. Measuring the transmission of at least one probe beam of electromagnetic radiation along a path traversing the enclosure, d. Deriving the physical characteristics of the first electromagnetic field based at least on the measured transmission. Methods that include...

2. The method according to claim 1, wherein the gas is an atomic vapor or a molecular vapor.

3. The method according to claim 2, wherein the atoms of the atomic vapor include rubidium, cesium, alkali metals, alkaline earth metals, or a combination thereof.

4. The method according to claim 1, wherein the distribution of Rydberg states includes one or more Rydberg states.

5. The method according to claim 1, wherein exciting the gas into the distribution of Rydberg states includes optically exciting the gas into the distribution of Rydberg states.

6. The method according to claim 1, wherein exciting the gas in the distribution of the Rydberg state includes electromagnetic wave-induced transparency, electromagnetic wave-induced absorption, or both.

7. The method according to claim 1, wherein the physical properties of the first electromagnetic field are at least partially based on a change in the spectral characteristics of the gas, the change in the spectral characteristics includes Autler-Townes splitting.

8. The method according to claim 1, wherein the physical characteristics of the first electromagnetic field include the field amplitude.

9. The method according to claim 1, wherein the physical characteristics of the first electromagnetic field include its phase with respect to a reference phase.

10. The first electromagnetic field is monochromatic, The method according to claim 1, wherein the physical characteristics of the first electromagnetic field include its phase with respect to a reference phase of an external radio frequency (RF) field that modulates the at least one other electromagnetic field.

11. The method according to claim 1, wherein structuring the first electromagnetic field includes placing the first electromagnetic field in resonance with atomic transitions by superimposing a static field or an RF field.

12. The method according to claim 1, wherein structuring the first electromagnetic field comprises modulating the first electromagnetic field prior to the step of measuring it.

13. The method according to claim 12, wherein the modulation includes frequency modulation, amplitude modulation, step modulation, or a combination thereof.

14. The method according to claim 1, wherein the first electromagnetic field includes an amplitude modulation field, a frequency modulation field, a polarization modulation field, a phase modulation field, or a combination thereof.

15. The method according to claim 1, wherein the physical characteristics of the first electromagnetic field include the amplitude, frequency, polarization, phase, or combination thereof of the time-varying electric field of the first electromagnetic field.

16. The method according to claim 1, wherein the at least one other electromagnetic field is introduced by an external RF reference wave.

17. The method according to claim 1, wherein the at least one other electromagnetic field is introduced by an electrode integrated into the enclosure or cavity structure.

18. The method according to claim 1, wherein an external reference wave is introduced to the location of the atom and / or molecule.

19. The method according to claim 1, wherein the physical properties of the first electromagnetic field include the sum of the electric fields of the first electromagnetic field and the reference field.

20. The method according to claim 19, wherein the magnitude of the sum of the electric fields of the first electromagnetic field and the reference field is at least partially based on the phase difference between the first electromagnetic field and the reference field.

21. The method according to claim 19, wherein the physical characteristics of the first electromagnetic field include a beat frequency resulting from the sum of the electric fields of the first electromagnetic field and the reference field.

22. The method according to claim 1, wherein the physical properties of the first electromagnetic field include a beat frequency resulting from structuring the first electromagnetic field by arranging the first electromagnetic field in an interfering relationship with at least one other electromagnetic field.

23. The method according to claim 1, wherein the physical properties of the first electromagnetic field include laser-induced fluorescence.

24. A sensor for detecting and measuring a parameter for characterizing a first electromagnetic field, wherein the sensor is a. Excitation source and, b. An enclosure comprising a gas of atoms and / or molecules, wherein at least a subset of the gas can be excited into a distribution of Rydberg states by the excitation source, c. A detector arranged to detect the transmission of the probe beam after the probe beam has crossed the gas, d. A processor configured to derive parameters for characterizing the first electromagnetic field based on the detected transmission of the probe beam. A sensor equipped with the following features.

25. The sensor according to claim 24, wherein the transmission of the probe beam is sensitive to evaluating the phase characteristics of the first electromagnetic field.

26. The sensor according to claim 24, wherein the transmission of the probe beam is sensitive to the phase of transitions between Rydberg states in the distribution of Rydberg states characterized by a specific Rabi frequency.

27. ​​The sensor according to claim 24, wherein the parameter for characterizing the first electromagnetic field varies continuously over time.

28. The sensor according to claim 24, wherein the gas includes molecular vapor.

29. The sensor according to claim 24, wherein the excitation source is configured to induce transitions between Rydberg states in the distribution of Rydberg states at a specific Rabi frequency.

30. The sensor according to claim 24, wherein the parameter for characterizing the first electromagnetic field includes the propagation direction.

31. The sensor according to claim 24, wherein the parameters for characterizing the first electromagnetic field include amplitude, frequency, phase, polarization, or a combination thereof.

32. The sensor according to claim 24, wherein the parameters for characterizing the first electromagnetic field include amplitude modulation, frequency modulation, phase modulation, polarization modulation, or a combination thereof.

33. The sensor according to claim 24, wherein the parameter for characterizing the first electromagnetic field includes the phase of the first electromagnetic field with respect to a reference phase.

34. The sensor according to claim 24, further comprising a second electromagnetic field arranged in an interference relationship with the first electromagnetic field.

35. The sensor according to claim 34, wherein the phase of the second electromagnetic field is introduced by an external radio frequency (RF) reference source.

36. The sensor according to claim 24, wherein the phase of the first electromagnetic field is with respect to an RF-modulated light beam.

37. The sensor according to claim 24, wherein the phase of the first electromagnetic field is with respect to an external RF reference wave.

38. The sensor according to claim 24, further comprising an RF reference wave.

39. The sensor according to claim 24, wherein the parameter for characterizing the first electromagnetic field includes the sum of the electric fields of the first electromagnetic field and the reference field.

40. The sensor according to claim 39, wherein the magnitude of the sum of the electric fields of the first electromagnetic field and the reference field is at least partially based on the phase difference between the first electromagnetic field and the reference field.

41. The sensor according to claim 39, wherein the transmission parameters of the probe beam are sensitive to the beat frequency resulting from the sum of the electric fields of the first electromagnetic field and the reference field.

42. The sensor according to claim 24, wherein the transmission of the probe beam is sensitive to beat frequencies resulting from structuring the first electromagnetic field by arranging the first electromagnetic field in an interfering relationship with at least one other electromagnetic field.

43. The sensor according to claim 24, wherein the transmission of the probe beam is sensitive to laser-induced fluorescence.

44. The sensor according to claim 24, wherein the distribution of Rydberg states includes one or more Rydberg states.

45. The sensor according to claim 24, wherein the parameter for characterizing the first electromagnetic field includes characteristics of the source of the first electromagnetic field.

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