Atom-based electromagnetic field sensing element and measurement system

Abstract

Methods and apparatus for sensing or measuring electromagnetic fields. The method causes atoms of a gas occupying a test volume coextensive with the electromagnetic field to be excited into a distribution of Rydberg states. Transmission of at least one probe beam of electromagnetic radiation along a path traversing the test volume is measured at one or more frequencies overlapping a spectral feature, and a physical characteristic of the electromagnetic field is derived based on a change in the spectral feature. In various embodiments, the electromagnetic field can be placed in an interference relationship with other electromagnetic fields. Time-varying electric field amplitudes, frequencies, phases, and noise spectral distributions can be measured, thus producing AM and FM modulated fields as well as magnetic fields of approximately 1 Tesla. Apparatus for measuring electromagnetic fields can be coupled to a probe field and a detector or detector array on a single side.

Description

[0001] This invention was made with government support under Contract No. W911NF-17-C-0007, awarded by the Defense Advanced Research Projects Agency (DARPA) and the U.S. Army. The government may hold rights to certain aspects of this invention.

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

[0003] This invention relates to atom-based field sensing elements, measurement systems and methods, and more particularly to elements, systems and methods for measuring, receiving or imaging RF field amplitude, polarizability or phase, modulated RF signals, incoherent RF noise or RF noise using Rydberg atoms and performing continuous frequency RF field detection. Background of the Invention

[0005] Atoms with quasi-free electrons in high Rydberg states (characterized by high principal quantum numbers, typically n>20) exhibit large polarizability and electric dipole moments, with principal quantum numbers n ranging from ~n. 7 and ~n 2 This makes them extremely sensitive to electric fields. By convention in this paper, atomic states that are not Rydberg states may be referred to as "low-position states".

[0006] The concept of applying the spectral response of Rydberg states in atomic vapor to electric field measurements is already known, at least from the paper "Rydberg States using Electromagnetically Induced Transparency" by Mohapatra et al. Phys.Rev.Lett. Beginning with “vol. 98, 113003 (2007),” this document is incorporated herein by reference. Early work in the prior art relating to atom-based field sensing is the subject of U.S. Patent No. 9,970,973 to Anderson et al. (hereinafter referred to as the “Anderson 973 Patent”), which, along with its references, is incorporated herein by reference. More specifically, the Floquet method has previously been established as a suitable method for simulating the microwave spectrum of Rydberg atoms in vapor chamber experiments, for example in Anderson et al.’s paper “Two-photon microwave transitions and strong-field effects in a room-temperature Rydberg-atom gas,” Phys.Rev.AAs shown in "vol.90,043419(2014)," this document is incorporated herein by reference.

[0007] Electromagnetic induction transparency (EIT) is a quantum interference process in which two excitation paths in a tertiary atomic system destructively interfere and produce an increase in the transmittance of a probe laser beam. For example... Figure 8B In the Rydberg-EIT cascade scheme described in the paper, transparency is formed by the coherent superposition of the ground and Rydberg states. Rydberg-EIT has been realized in both cold atom gases and room-temperature vapor chambers. It has been widely used as a non-destructive optical detection technique for Rydberg spectra, quantum information processing, and weak and strong microwave electric field measurements. The paper by Bason et al., "Enhanced electric field sensitivity of rf-dressed Rydberg dark states,"... New J.Phys. The paper “A Rydberg-level AC Stark displacement using electrodes in a vapor chamber” discusses the use of electrodes in a vapor chamber and is incorporated herein by reference.

[0008] As used herein, the term "sensor" will refer 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 the sensor and a controller or processor used with or from the sensor controller or processor. The term "monolithic sensor," as used herein, refers to a sensor whose entirety is contained on a single substrate or whose components are permanently connected to form a single physical device. Examples of connection include microfabrication, fusion, anodic bonding, and adhesive bonding. To the inventor's knowledge, a monolithic Rydberg sensor has never been proposed.

[0009] However, no method has been proposed to date that proposes a Rydberg spectrum suitable for measuring the phase of an electromagnetic field (relative to a reference phase). The embodiments of the invention described below address this deficiency.

[0010] To realize practical atom-based RF sensing, measurement, or imaging devices, suitable sensing elements are required. All prior art sensing elements described or suggested in earlier work have limitations imposed by physical principles, which can be overcome by the insights described below according to the invention. Prior art sensing elements are taught, for example, by the literature “Optical measurements of strong microwave fields with Rydberg atoms in a vapor cell” by Anderson et al., https: / / arxiv.org / pdf / l60l.02535.pdf (January 11, 2016), which is incorporated herein by reference.

[0011] Other teachings on atom-based electromagnetic field sensing can be found in Gordon et al.'s paper "Millimeter Wave Detection via Autler-Townes Splitting in Rubidium Rydberg Atoms, https: / / arxiv.org / pdf / l406.2936.pdf, (June 11, 2014)" and Simons et al.'s paper "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., The article “vol.108,174101(2016)” was found and both of these articles are incorporated into this paper by reference.

[0012] The performance limitations of existing Rydberg electromagnetic induction transparency (EIT) technology include:

[0013] (1) Low sensitivity; the highest field sensitivity to date has shown a level of 1 mV / m, mainly limited by the EIT linewidth. Furthermore, this sensitivity level can be achieved by monitoring only small changes in the EIT peak lineshape. ETnlike directly measures Rydberg level splitting, where the field can be traced to fundamental constants and invariant atomic parameters. Extracting the RF electric field from detailed EIT lineshape analysis requires a relatively complex model (which depends on experimental parameters such as laser beam power and vapor pressure), thus ruling out absolute field measurements and making it unreliable in routine operation. The highest measurement sensitivity to date (approximately 3 μV / cm / Hz) is... 1 / 2 The shot noise-limited sensitivity has been demonstrated in Kumar et al.'s book "Rydberg-atom based radio-frequency electrometry using frequency modulation spectroscopy in room temperature vapor cells." Opt.Express.In vol. 25, 284263 (January 21, 2017), Fan et al.'s paper, "Effect of Vapor Cell Geometry on Rydberg-Atom-Based Measurements of Radio-Frequency Electric Fields," Phys.Rev. The paper “Appl 044015 (2015)” previously reported a half-order-of-magnitude improvement in sensitivity, and both papers are incorporated herein by reference. The latter work developed an RF-induced EIT enhancement of the Rydberg-EIT line through a weak resonant RF field, a method considered somewhat unreliable in routine field measurement operations because such subtle changes depend on many details, such as laser power and chamber pressure. A more robust method to enhance sensitivity is desired.

[0014] (2) It is impossible to measure the RF field over a continuous frequency range. In weak RF fields, the method is limited by the measurement of the RF field and the transition resonance between the RF field and the Rydberg state allowed by the dipole. It is simply not easy to measure weak RF fields that are non-resonant and far from resonant due to any transition.

[0015] (3) RF polarization measurement currently requires complex analysis of atomic spectra.

[0016] (4) All existing Rydberg-EIT measurements must be field amplitude measurements, and, partly due to the physical limitations discussed herein, it is never possible to obtain information about the RF field phase.

[0017] (5) To date, the form factor of the measuring device used for Rydberg EIT measurements has always required large components, non-portable components or components with large dielectric coverage areas, thus excluding the ability to perform measurements or integrate into existing RF measurement and transmission systems in many practical applications.

[0018] (6) Prior to the invention described below, the Rydberg EIT technique was only used for measuring coherent fields. Previous methods could not measure incoherent fields or noise.

[0019] RF measurements using Rydberg EIT in a vapor chamber typically employ a laser beam backpropagating through atomic vapor to address the Doppler shift of the spectral laser beam in the hot atomic sample. To date, this has presented challenges for implementing Rydberg EIT in a vapor chamber for practical sensor design applications, as it requires the laser beam to propagate through free space or enter and exit the chamber from opposite sides using optical fibers on either side. This results in a large dielectric coverage area and size for the sensor head, which is undesirable for measurement applications. Furthermore, to scale to multi-pixel sensor arrays, the entry of the beam from opposite sides of the chamber limits the achievable pixel density and resolution within the array.

[0020] While unilateral optical coupling into the vapor chamber has been discussed, for example in the context of George et al.'s "Pulsed high magnetic field measurement via a Rubidium Vapor Sensor," https: / / arxiv.org / pdf / l704.00004.pdf, (March 31, 2017), which is incorporated herein by reference, a separate fiber is used for both the input and output beams of the same or similar wavelength. Furthermore, in the prior art, the probe beam always enters on one side of the vapor chamber and exits on the other.

[0021] Although most matter in the observable universe exists in a plasma state, measuring or inferring the properties of the electric field within a plasma region presents unique challenges to science unless the collective motion of the plasma can be observed or unless a physical probe can be inserted into the plasma mass. An example of the former is the inference of the radial electric field in tokomak, inferred from the polar rotation velocity. Without these forms of detection, certain assumptions must be made when using atomic probes. For example, at the intensity ratio of the spectral bands of nitrogen, as discussed by Paris et al., "Intensity ratio of spectral bands of nitrogen as a measure of electric field in plasmas," J.Phys.D. The reference, vol.38, pp.3894-99 (2005), is incorporated into this paper by reference. The calculation requires that nitrogen molecules be excited directly from the ground state mainly through electron bombardment.

[0022] To date, optical diagnostic techniques for measuring plasma fields have primarily involved measuring Stark shifts in plasma molecules via emission and absorption spectra, laser-induced fluorescence, and Raman spectroscopy. While existing methods offer passive, non-invasive measurements, they may require prior knowledge of the optical absorption or emission spectra of the plasma components. This can make it difficult to distinguish the collective plasma phenomena of interest from the few human processes involving component plasma particles in diagnostic readings. It also necessitates tailoring diagnostic tools to the type of plasma being studied, which does not include general techniques capable of performing diagnostics on different plasma systems. Along these lines, some plasmas are expected to have emission profiles with frequencies and emission intensities that are difficult to detect using conventional detectors and spectrometers. For example, in some cases, weak IR emission resulting from vibrational transitions of plasma components may provide useful information, but the detectors required to measure these low IR intensity levels are not yet available. Due to these limitations, applications may require engineering the plasma with certain atomic / ionic particles to achieve well-characterized optical diagnostics. This could pose a significant drawback in fundamental plasma research, where the nature of the plasma itself is the subject of study.

[0023] In situations where the aforementioned types of prior knowledge are not always available, science has been awaiting a more general form for remote measurement of the electric field within plasmas. This form is described in detail below according to embodiments of the invention.

[0024] 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, development, production, and maintenance of strong magnetic systems across various industries. However, no probes were available for measuring such fields; this is first achieved through the invention described below, the atomic vapor or Rydberg-EIT system. The maximum magnetic field strength is at most -10... 3 Gauss, as previously practiced, can measure the maximum magnetic field strength using Zeeman splitting of the hyperfine level based on the Rydberg atomic model via Rydberg EIT analysis.

[0025] As described herein according to the invention, the measurement of stronger magnetic fields requires new strategies. Summary of the Invention

[0026] According to an embodiment of the present invention, a method for sensing or measuring a first electromagnetic field is provided. The method comprises the following steps:

[0027] The atoms of the gas occupying at least part of the test volume, which is within the same range as the first electromagnetic field, are excited into a Rydberg state distribution.

[0028] The first electromagnetic field is constructed by placing it in an interference relationship with at least one other electromagnetic field.

[0029] The propagation of at least one probe beam measuring electromagnetic radiation at one or more frequencies along a path traversing a test volume, wherein one or more frequencies overlap with the spectral characteristics of the atomic gas; and

[0030] The physical properties of the first electromagnetic field can be derived, at least based on the changes in its spectral characteristics.

[0031] According to other embodiments of the invention, the gas may be an atomic vapor, and the atoms of the atomic vapor may be selected from the group consisting of rubidium, cesium, and alkali metals. The step of exciting the atoms into a Rydberg state distribution may include optically exciting the atoms into a Rydberg state distribution and at least one of electromagnetically induced transparency and electromagnetically induced absorption.

[0032] According to other embodiments of the invention, the variation in spectral characteristics may include Autler-Townes splitting, and the physical property of the first electromagnetic field may be field amplitude.

[0033] The first electromagnetic field can be monochromatic, and the physical properties of the first electromagnetic field can be its phase relative to a reference phase.

[0034] According to other embodiments of the invention, constructing the first electromagnetic field may include modulating the electromagnetic field prior to the measurement step. The modulation may be at least one of frequency modulation, amplitude modulation, and step modulation.

[0035] In another embodiment of the invention, the Rydberg state distribution may include at least one pair of states with non-zero dipole moments for interaction between atoms and radio frequency fields.

[0036] According to another embodiment of the present invention, the following additional steps may be included:

[0037] Calculate the predetermined Rydberg atomic energy level or Rydberg-EIT spectrum in the presence of an incoherent RF noise field that exists or constitutes the first electromagnetic field.

[0038] To propagate light into the atomic vapor chamber;

[0039] Spectral characteristics were measured using light propagating through an atomic vapor chamber;

[0040] Identify matching spectra; and

[0041] The properties of the incoherent RF noise field were obtained.

[0042] According to another embodiment of the present invention, the following additional steps may be present:

[0043] Calculate the predetermined Rydberg atomic energy levels or spectrum of atoms in a first electromagnetic field that is identical to a strong static magnetic field or a low-frequency magnetic field;

[0044] At least one other electromagnetic field is used as an optical probe to propagate into the atomic vapor chamber;

[0045] Measure the spectral characteristics of light propagating through the atomic vapor chamber;

[0046] Identify matching spectra; and

[0047] The physical properties of a strong magnetic field were derived.

[0048] It is possible to combine lock detection to modulate the amplitude or frequency of light at a modulation frequency or a multiple of that frequency, and predetermined atomic energy levels or spectra can be used for lower atomic states.

[0049] According to another aspect of the invention, a monolithic sensor is provided for detecting and / or measuring parameters characterizing an electromagnetic field. The sensor has atomic vapor contained within a housing, an excitation source for exciting the atoms of the atomic vapor into a Rydberg state distribution, and at least one waveguide for coupling one or more probe beams into the atomic vapor and for collecting the probe beam after its interaction with the atomic vapor.

[0050] According to other embodiments of the 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 chamber. The enclosure may be partitioned, and more specifically may be linearly or regionally partitioned.

[0051] In other embodiments, different probe beams may be coupled to each compartment of the compartment array, for example, via an array of optical elements, and may be collected after interaction with atomic vapor and coupled to a detector element via an array of optical elements. The housing may include a light-absorbing surface and may also have a temperature regulator.

[0052] According to another aspect of the invention, a one-sidedly coupled monolithic sensor is provided for detecting and / or measuring parameters characterizing an electromagnetic field. The one-sidedly coupled monolithic sensor has an atomic vapor and an excitation source contained within a dielectric housing, the excitation source being used to generate an excitation beam that excites the atoms of the atomic vapor into a Rydberg state distribution. Additionally, the one-sidedly coupled monolithic sensor has a first prism and a second prism, the first prism being used to couple the excitation beam into the atomic vapor and to couple a probe beam exiting from the atomic vapor, and the second prism being used to couple the probe beam into the atomic vapor. The excitation beam and the probe beam can be incident on the respective first and second prisms in substantially parallel directions.

[0053] In another aspect of the invention, a sensor is provided for detecting and / or measuring parameters characterizing an electromagnetic field. The sensor includes at least one material or structure for regulating the electromagnetic field, and atomic vapor contained within a housing disposed within the regulating material or structure. The sensor also includes an excitation source, a detector, and a processor; the excitation source is used to excite atoms of the atomic vapor into a Rydberg state distribution; the detector is used to detect a probe beam traversing the atomic vapor and generate a detector signal; and the processor is used to derive parameters characterizing the electromagnetic field based at least on the detector signal.

[0054] In other embodiments, the material or structure used to modulate the electromagnetic field can be an RF resonator or a waveguide. It can also be a metamaterial.

[0055] Materials or structures used to modulate the electromagnetic field may include antennas or one or more electrodes. The materials or structures may be conductive, and the electromagnetic field can be modulated by converting current or voltage signals into an electromagnetic field within the atomic vapor chamber. The properties of the current or voltage signal can be derived from the detector signal.

[0056] In other embodiments of the invention, the excitation source for exciting the atoms of the atomic vapor into Rydberg states may have one or more light beams to establish electromagnetically induced transparency or electromagnetically induced absorption in the atomic vapor. The enclosure containing the atomic vapor may be a glass vapor chamber.

[0057] In yet another embodiment of the invention, the material or structure used to modulate the electromagnetic field may include a filter or reflector for the electromagnetic field entering or exiting the atomic vapor shell. A detector may be used to detect the electromagnetic field generated by the excitation of the atomic vapor and the emission from the atomic vapor. The electromagnetic field may be associated with at least one of vertical electromagnetic waves and traveling electromagnetic waves.

[0058] According to another aspect of the invention, a sensor is provided for detecting and / or measuring parameters characterizing an electromagnetic field. The sensor has atomic vapor contained within a housing, which in turn has a light-absorbing surface. The sensor also has a source for a heating beam incident on the light-absorbing surface, and an excitation source for exciting the atoms of the atomic vapor into a Rydberg state distribution. The sensor further includes a detector for detecting a probe beam after traversing the atomic vapor and generating a detector signal, and a processor for applying the heating beam to the light-absorbing surface in a manner that regulates the temperature characterizing the atomic vapor.

[0059] In other embodiments of the present invention, the light-absorbing surface may be a film, a polymer, or glass.

[0060] According to another aspect of the present invention, a method for measuring the electric field within a plasma region contained in a housing is provided. The method comprises the following steps:

[0061] Introduce tracer particles of a specified substance into the plasma;

[0062] Excite the tracer particles to a specified Rydberg state;

[0063] At least a probe beam and a coupler beam are applied to obtain the EIT transmission spectrum of the plasma; and

[0064] Based on at least one of field-induced spectral shape change and field-induced spectral shift, the EIT transmission spectrum of the plasma is compared with a spectral model to infer the electric field within the plasma region.

[0065] According to further embodiments of the invention, the method may include additional steps of applying a magnetic field or RF field to the plasma. The tracer particles may be atoms, more specifically including rubidium atoms. The method may also include generating tracer particles from a cold atom source. Attached Figure Description

[0066] The foregoing features of the invention will be more readily understood by referring to the following detailed description and the accompanying drawings, wherein:

[0067] Figure 1 A unilateral optically coupled RF sensing element according to an embodiment of the present invention is schematically depicted.

[0068] Figure 2A This illustrates the use of a pen-shaped backward EIT configuration obtained according to an embodiment of the present invention. 87 EIT spectrum of Rb in 30D Rydberg state.

[0069] Figure 2B A single-sided atomic vapor sensor according to an embodiment of the present invention is shown, wherein the excitation beam and the probe beam are coupled to the vapor chamber via a prism.

[0070] Figure 3 A microwave imaging array comprising a single vapor chamber sensor element coupled on one side is shown according to an embodiment of the present invention.

[0071] Figure 4A The calculation of the RF field enhancement factor for several frequencies along the axis of a 125 μm diameter tip is shown according to an embodiment of the present invention. Figure 4B The skin depth associated with the conductive tip is shown.

[0072] Figure 5A and Figure 5B A hybrid atomic cavity structure of one type according to an embodiment of the present invention is shown.

[0073] Figure 6 This shows the near-resonant 4GHz incident RF field at 1V / m. Figures 5A-5B Calculation of the electric field in the hybrid atomic cavity structure shown.

[0074] Figures 7A-7D A hybrid atomic resonator device according to an embodiment of the present invention is shown. Figure 7A The resonator electrodes / cavity inside the spectrum chamber are shown; Figure 7B This is a top view of the resonator, showing the ceramic pins used for electrode alignment and stabilization; Figure 7C It is a side view of a resonator with the indicated glass spacers and gaps; and Figure 7D The resonator electrode / cavity structure inside the rubidium vapor chamber is shown. The resonator electrode / cavity structure has connecting leads for external voltage / current control or to ground / short-circuit the electrodes.

[0075] Figure 8A An experimental apparatus for measuring field properties according to an embodiment of the present invention is shown, while Figure 8B The relevant Rydberg EIT energy level diagram is shown.

[0076] Figures 9A-9D This illustrates field enhancement in a hybrid atomic cavity according to an embodiment of the present invention. Figure 9A Plot the 31-s Rydberg EIT spectrum measured at a fixed -10 dBm injected power as a function of RF / microwave frequency. Plot the RMS electric field E with respect to the applied electric field. RMS With 31S 1 / 2 The Stark mapping is calculated with the Rydberg state as the center. Figure 9C Drawing use Figure 9A and Figure 9B The obtained microwave E RMS Regarding frequency, and Figure 9D Plot the EIT lines for measurements at 2.5 GHz and 4.35 GHz microwave, respectively.

[0077] Figure 10A and Figure 10B The diagram shows a side view and an end view of a field measurement system having an atomic vapor chamber inside a waveguide, according to an embodiment of the present invention.

[0078] Figure 11A The experiment shows that, with a fixed injection power, the Rydberg AC-Stark energy shift varies with the applied microwave frequency at different angular positions θ relative to the vertical axis. Figure 11B Plotting the microwave electric field at 4.35 GHz as... Figure 11A The θ variation in the data shown.

[0079] Figure 12A The calculation results of the electric field amplitude according to an embodiment of the present invention are shown, and Figures 12B-12D Show Figures 7A-7D The calculated results of the electric field vector direction in the hybrid atom-cavity structure.

[0080] Figure 13A and Figure 13B The experimental and calculated DC Stark maps of the 30D Rydberg states for an applied DC electric field are shown respectively.

[0081] Figure 14 Floquet calculations depicting the AC Stark energy transfer of rubidium-47S and rubidium-47P classes in a 100MHz RF field.

[0082] Figure 15 Plot the RF intensity and electric field calibration under the rubidium 47S state.

[0083] Figure 16 The measured EIT spectrum of the microwave frequency (detuned from 37.51663492 GHz) was plotted at a fixed -14 dBi microwave intensity (individually calibrated) for four different injected RF powers, at a state of 47 s.

[0084] Figure 17 The plot shows how the center of the measured cross-traversal changes with the applied RF electric field for a series of measurements (approximately 200 V / cm).

[0085] Figure 18A The simulated electric field generated inside four different open annular cavity structures with varying applied frequency is shown for an incident field of 1 V / m. Figure 18B The figure illustrates a measurement channel within the gap of an open annular cavity structure according to an embodiment of the present invention. Figure 18C and Figure 18D Simulated resonance curves of an open-loop resonator with a geometry that produces resonance around 100 GHz are shown.

[0086] Figure 19A and Figure 19B The IR glass capsule 1901 is shown, which surrounds the atomic vapor chamber 1903 with an inner diameter of 4 mm. Figure 19C The fully optical heating test platform is shown.

[0087] Figure 20A The back end and operating principle of a sensing element for phase-sensitive measurement of RF electric fields according to an embodiment of the present invention are schematically depicted. Figure 20B The quantum mechanical level scheme and optical / RF excitation path used in phase-sensitive RF electric field measurements are depicted.

[0088] Figure 21 This is a flowchart depicting the steps in a Rydberg-EIT measurement of magnetic field properties (which is now possible for the first time) according to an embodiment of the present invention.

[0089] Figure 22 This is a flowchart of the steps in measuring RF noise properties in a Rydberg-EIT range within a specified frequency range (which is now possible for the first time) according to an embodiment of the present invention.

[0090] Figures 23A-23C An EIT employing Rydberg atom tracing, according to an embodiment of the present invention, is schematically depicted to detect electromagnetic fields within a plasma.

[0091] Figures 24A-24C The diagram schematically depicts the measurement of strong magnetic fields using the saturation absorption spectrum method of a two-stage Rydberg quantum system according to an embodiment of the present invention.

[0092] Figures 25A-25C The diagram schematically depicts the measurement of strong magnetic fields using the saturation absorption spectrum method of a three-level Rydberg quantum system according to an embodiment of the present invention.

[0093] Figure 26A A hybrid atom-based optical RF power / voltage transducer and sensor according to an embodiment of the present invention is schematically depicted. Figure 26B The diagram shows signal curves obtained at various voltage levels applied across the electrodes of the transducer and sensor.

[0094] Figure 27A An atomic vapor chamber with opposing windows, according to an embodiment of the present invention, is schematically depicted. The opposing windows are used for wavelength-selective transmission of electromagnetic waves. Figure 27B Show Figure 27A Images of atomic vapor chamber compartments.

[0095] Implementation of the invention

[0096] Definitions: Unless otherwise stated in the context, the following terms shall have the meanings indicated:

[0097] Some embodiments of the present invention relate to atom-based field sensing elements, which are also referred to herein by the same names as “sensing elements”, “field sensing elements”, and “sensors”.

[0098] In this document and in the appended claims, “modulation” means the restriction, guidance, manipulation, or filtering of an electromagnetic field or its physical properties (including its modes, electric field amplitude, polarization, frequency, phase, and spectral components).

[0099] When referring to electromagnetic waves, the term "enhancement" should be defined as the modulation of electromagnetic waves in a way that increases the value of any physical property of the electromagnetic waves.

[0100] "Monochromatic field" should refer to a static field or an electromagnetic field characterized by a frequency range not exceeding 1% of the center frequency.

[0101] An electromagnetic field is called "constructed" if and only if it is monochromatic and interferes with at least one other electromagnetic field. Therefore, a "constructed" electromagnetic field is one in which the field is positioned to interfere with one or more other electromagnetic fields.

[0102] In this document, an atom-based field sensing element is referred to as "integrated" if and only if it contains a structure or at least one material used to modulate the RF field, wherein the term "modulation" is as defined above. The modulated RF field may be referred to as the "RF field of interest" in this document.

[0103] As used in this article, when referring to a set, whether continuous or discrete, the word "distribution" should include the case of a single element. Thus, for example, the distribution of the atomic population in a Rydberg state also includes a single state.

[0104] As used herein, in the spectrum (the term refers to any function of frequency v in this document), "spectral characteristic" should refer to the behavior acting on a defined continuous frequency subdomain, where the values ​​of the function at the boundaries of the subdomain constitute local minima or maxima of the function.

[0105] The "splitting" of spectral characteristics refers to the shrinking of local maxima of a function due to physical effects, resulting in the emergence of two new local maxima, one at a frequency higher than the original local maximum and the other at a frequency lower than the original local maximum. Where appropriate, the term "splitting" can also indicate the frequency difference between the locations of the new local maxima that replace the original local maximum.

[0106] The term "electromagnetic" encompasses both DC and AC fields.

[0107] In this article, “RF” can be used synonymously to refer to “microwave”, “millimeter wave”, “terahertz”, or any electromagnetic radiation with frequencies above DC to THz.

[0108] If it is higher than ~10 -3 Tesla (10G), the magnetic field should be represented as "strong" in 10... -3 At Tesla, the m-degeneracy of some atomic hyperfine levels, disrupted by the magnetic field, begins to transition from the weak-field (linear Zeeman) state to the Paschen-Bak state.

[0109] "Electromagnetically induced transparency" (EIT) refers to the physical phenomenon in which a coherent optical field tuned to interact with (at least) three states of an optical system induces transparency at wavelengths corresponding to absorption by additional quantum transitions in the medium. This is described in Marangos's "Topical review: Electromagnetically induced transparency". J.Mod.Opt. , vol.45, pp.471-503 (1998) Review of the Physics and Terminology of EIT, which is incorporated herein by reference.

[0110] As used in this document, “dielectric” is defined as a material or substance that transmits electrical energy but does not conduct electricity (insulator).

[0111] Atom-based electromagnetic field sensing elements and measurement systems

[0112] According to certain embodiments of the invention, a single-sided optically coupled RF sensing element (otherwise referred to herein as a "sensor" and "pencil configuration") is provided, which is generally indicated as marked 100 and referenced to Figure 1 Describe it. Figure 1 The pencil-shaped linear sensor design described herein uses a single entrance port 102 to fiber-couple the desired laser beams 103, 104 into and out of a vapor chamber volume 108 contained within a housing 106. The vapor chamber volume 108 is also referred to herein as a “vapor chamber” or “atomic vapor chamber.” The vapor chamber volume 108 contains atomic or molecular gases. The region of gas within the vapor chamber volume 108 probed by beams 103 and 104 may be referred to herein and in the appended claims as a “test volume.”

[0113] Using a sensor 100 that enters from one side to measure the effective volume, Figure 1 The configuration ensures that the effective measurement volume 110 is unobstructed regarding the incident RF / microwave field 112 from all surfaces except one. Figure 1 In the described embodiment, the linearly polarized probe 103 and coupler 104 beams are transmitted through a single-polarization-holding fiber 120 and collimated by a lens 122 to approximately 200 μm full width at half maximum (FWHM) in the vapor chamber 106. The probe and coupler beams 103 and 104 co-propagate through the atomic vapor chamber 106, with the probe beam 103 then selectively back-reflected back through the cell by a short-pass dichroic mirror coating 130, while the coupler beam passes through the cell and is blocked by a thin dielectric beam-absorbing block 132. The back-reflected probe beam 134 retraces its path, overlaps with the outgoing coupler beam, and is recoupled back into the fiber 120 by the lens 122. A quarter-wave plate 140 positioned before the back-reflection (…) Figure 1 (between the lens and the vapor chamber) ensures that the linearly polarized incoming probe beam is rotated 90 degrees on the back-reflected outgoing beam, so that it can be selectively separated for readout using a polarization selection element (not shown) after the polarization-maintaining (PM) fiber.

[0114] Compared to other embodiments of the vapor chamber EIT prior to this invention, Figure 1The sensor 100 described herein offers several advantages. First, the linear single-sided design allows for a small, thin probe tip and a sensor element with a small dielectric package. The design also reduces the need for any optical components to redirect the beam out of the fiber and into the unit. Compared to typical implementations of vapor chamber EITs, using a single lens for input and output coupling of a larger beam diameter advantageously improves measurement accuracy and sensitivity by providing a smaller interaction time and therefore a higher achievable spectral resolution, and improves operational stability by reducing the device's sensitivity to misalignment through reverse coupling of the readout probe beam into the same fiber.

[0115] Figure 2A Showing the use Figure 1 The pen shape is configured with 100 back EIT. 87 The EIT spectrum of the 30D Rydberg state of Rb is typically indicated by label 200. The single-sided EIT configuration may be referred to herein as the "backward EIT configuration". The separation of fine structural features 204 is evident. The coupler beam 104 reflects from the interior of the inner chamber wall, resulting in a repeating EIT spectrum 202. The spectrum is acquired without performing lock-on detection of the silicon photodiode signal.

[0116] At the center of the Doppler profile, the repeating spectrum 202 is blue-shifted from the main EIT line 200 by an amount equal to the frequency detuning of the probe 103 relative to the atom at velocity v = 0. Repeating spectra resulting from internal reflections within the vapor chamber are commonly observed in vapor chamber EIT experiments. These can be avoided by positioning the chamber at an angle to the perpendicular incidence of the EIT beam or by having a chamber window at an angle relative to the incident beam.

[0117] Figure 2B One embodiment of the sensing element is shown, generally indicated by designation 230, having single-sided fiber coupling via a rubidium vapor capsule 232. A sensing element according to another embodiment of the invention is implemented with a first prism 212 and a second prism 214 redirecting a single-sided fiber-coupled excitation beam 216 and a single-sided fiber-coupled probe beam 218 to the vapor capsule 232. Prisms 212 and 214 are coupled via lenses 235 to the respective optical fibers guiding beams 216 and 218.

[0118] According to other embodiments of the invention, a single-sided optically coupled vapor chamber RF / microwave sensing element can be extended to a multi-sensor array, wherein single-sided coupling of the chamber array is achieved jointly by using a large single beam impacted onto a lens microarray for both the coupler and the probe. Reference now is made to... Figure 3One such embodiment is described. Again, the one-sided entry of the beam from coupler 104 and probe 103 allows for dense encapsulation of single elements in the array and makes the effective measurement volume / surface unobstructed from the incident RF / microwave radiation to be measured or imaged. For low-density arrays, within the scope of the invention, methods such as... Figure 1 and Figure 3 The grid of those individual single-sided elements shown in the figure.

[0119] Figure 3 A microwave imaging array, typically indicated by the label 300, is shown. The microwave imaging array 300 consists of single-sided couplings of individual vapor chamber sensor elements 302 arranged in a linear or regional (two-dimensional) array. Optical couplers 304 and probe 306 EIT beams are separated from each other using a dichroic mirror 308. A laser beam array 310 is obtained from a large-diameter laser beam 312 passing through a microlens array (ML array) 314. The microlens array is commercially available. The laser beam array is accompanied by a planar array of sub-chambers 316 containing atomic vapor (layer thickness approximately equal to a portion of the RF wavelength of interest, with a sub-chamber period less than 1 mm). A dielectric coating 318 on the vapor chamber array reflects the 780 nm probe laser beam and transmits the 480 nm coupler laser beam and microwave field. The image of the probe beam reflected by a polarized beam splitter contains microwave information. It is recorded using a CCD camera 320 and analyzed using an image processor 322. A polarized beam splitter (PBS) 324 is also known.

[0120] Cavity-enhanced field sensitivity

[0121] The concept of a hybrid atom detector as defined above for RF detection is now presented, wherein atomic Rydberg vapors are integrated with different resonant materials or structures to tune the RF field of interest. The hybrid atom detector according to the invention can advantageously achieve detection capabilities.

[0122] Near-field effects are known to produce regions of enhanced electric fields. For example, the above-described concept of a hybrid atom detector, first described according to the invention, can be advantageously used for plasmonic resonance in nanoparticles. An example of a hybrid atom detector according to the invention employs a gap ring resonator. A simple near-field enhancement device is a metal tip with a subwavelength diameter. The tip enhances the RF electric field, approximating the enhancement of the electric field near a lightning rod during a thunderstorm. Figure 4A The calculations for the RF field enhancement factor along the axis of a 125 μm diameter tip 401 are shown for some frequencies. The illustrations and curves demonstrate that simple structures (such as metal tips integrated into atomic vapor chambers) can enhance the field by a factor of approximately 3, corresponding to 9.5 dB in intensity. For enhancement, it is important that the tip diameter exceeds [a certain value]. Figure 4BThe skin depth described in the figure, for the cases of interest (Cr, beryllium copper, etc.), is on the order of 1 μm in the 10 to 100 GHz range (and according to 1 / frequency). 0.5 (And scaling). The result is that hybrid devices, such as those with metal ends implanted in atomic vapor chambers, enhance field sensitivity through localized near-field enhancement.

[0123] Cavity structures resonating with RF fields provide another means for localized field enhancement. Cavity structures can readily provide increased control over RF field parameters such as RF field polarization and frequency. Within the scope of this invention, cavities can be designed to reduce inhomogeneities in the atom-RF field interaction volume, which may be desirable in applications and is difficult to achieve when developing near-field effects using pointed structures.

[0124] Now for reference Figure 5A and Figure 5B A novel concept for a hybrid atom-cavity structure for sensing in the Rydberg EIT is described, illustrating an example-type hybrid atom-cavity structure (generally indicated by the designation 500) and its operating principle for RF field enhancement. Structure 500 consists of two solid metal frames 502, also referred to herein as “electrodes,” separated by a gap 504 in front of a rubidium vapor chamber 506. References Figure 5B The gap 504 between the two metal frames 502 forms a cavity 510 that resonantly couples to the impact RF field 508, and the impact RF field 508 compresses the corresponding RF electric field 512 locally within the cavity volume. The word "cavity" is used broadly in this paper to refer to a structure that imposes any kind of boundary condition on the solution of Maxwell's equations over a specified spatial volume. In this paper, "cavity" can also be synonymously referred to as a "resonator" or "resonant structure".

[0125] The Rydberg atomic vapor inside cavity 510 is optically interrogated for measurement of field 512. Figure 6 Shown by reference Figure 5A and Figure 5B as well as Figures 7A-7D The calculations show and describe the field enhancement provided by a hybrid atom-cavity structure 500 with a conventionally fabricated electrode having a rubidium vapor chamber. Structure 500 has a gap size of 460 μm, which locally enhances the field along the Y-axis within the gap 504 by a factor of approximately 10. Figure 5BThe electric field 512 of a linearly polarized 4 GHz microwave (vertical direction) corresponds to an intensity of 20 dB. Utilizing an EIT laser beam waist in the 50 to 100 μm range, the enhanced electric field maintains fairly uniformity within the effective measurement volume of the measurement channel, which measures approximately 0.46 × 0.5 × 9 mm. The 9 mm long “cavity channel” (the term used herein is synonymous with “gap” and “cavity”) provides a sufficiently long interaction volume for higher light absorption during measurement and also advantageously provides an improved signal-to-noise ratio in the EIT spectrum.

[0126] Now for reference Figures 7A-7D A hybrid atom-resonator device (generally indicated as 700) is described according to an embodiment of the present invention. Figure 7A The perspective view shown highlights the spectral chamber 702 (otherwise referred to as the "atom vapor capsule"), whose internal structure corresponds to the Stark tuner / compressor 704. Figure 7B This is a top view of the Hybrid Atom-Resonator Device 700. Figure 7C The side view shows the upper electrode 706 and the lower electrode 707 separated by spacer 708 to form a gap 710 (also called a “cavity”). Figure 7D The perspective view of the hybrid atom-resonator device 700 depicted in the figure shows electrode wire leads 712 coupled to the vapor capsule 702 via electrode connections 714.

[0127] To demonstrate the field enhancement for high-sensitivity atom-based RF field measurements using hybrid atom-cavity devices, it is possible to... Figure 8A The experimental setup shown in the figure utilizes Figures 7A-7D The hybrid atom-resonator device 700 uses a Rydberg EIT as the cavity within the 710. 85 A highly efficient, non-destructive optical probe is used to measure the RF field within cavity 710 by inducing the shift of the field-induced energy level of the high-position Rydberg state of Rb atoms. Figure 8B The illustration shows the relevant rubidium-Redburg EIT energy level diagram. (See illustration.) Figure 5B and 8A As shown, two laser beams with λ = 780 nm (720) and 480 nm (722) propagate toward each other and overlap through the center of cavity 710. In an exemplary embodiment of the invention, the 780 nm beam 720 is focused to a half-width of 70 micrometers and has a power of 8 μW at the center of chamber 702, while the 480 nm beam 722 is focused to a half-width of 70 nm and has a power of 40 mW. Rydberg EIT spectroscopy is performed by monitoring the 780 nm transmission through the vapor, wherein the laser frequency is stabilized at... 85 Rb 5S 1 / 2 (F=3) to 5P 3 / 2(F=4) transitions are performed, and the frequency of the 480 nm laser is linearly scanned across selected Rydberg levels at a repetition rate of several Hz. An optical frequency reference is derived from the 480 nm laser beam 720 to calibrate the Rydberg EIT spectrum.

[0128] According to embodiments of the invention, modulation spectroscopy can be implemented to improve the signal-to-noise ratio in the EIT spectrum. As used herein, modulation includes any of frequency modulation, amplitude modulation, step modulation, or combinations thereof. For example, a 480 nm beam 720 can be amplitude modulated using a ~20 kFlz square wave pulse with a 50 / 50 duty cycle, and the 780 nm signal 730 obtained by detection of the 780 nm beam using a photodetector 732 can be demodulated, for example, using a lock-in amplifier (not shown). The hybrid atom-cavity structure 700 is maintained at an ambient temperature of approximately 45 °C for enhanced rubidium vapor density and 780 nm absorption. The two electrodes 706 and 707 forming the cavity 710 are electrically coupled to ground externally to the chamber 702. In one example, an RF field is generated using a signal generator, amplified by 20 dB, and fed into a WR229 open waveguide (2.577 to 5.154 Hz) 735 (otherwise referred to herein as a “guide”). The measurement channel / cavity 710 through which the Rydberg EIT laser beams 720, 722 pass is positioned approximately 1 cm in front of the guide 735. In the example shown, the RF beam and the beam are linearly polarized, with the polarization oriented parallel to the minor axis (Y) of the cavity 710.

[0129] Figure 9A The diagram shows the relative shift of the 31S Rydberg EIT spectral line as a function of the RF / microwave frequency for a fixed injected microwave power of -10 dBm. The 31S Rydberg level was chosen such that, for the microwave frequency range of 2.5 to 5.2 GHz spanned in the experiment, the applied microwave is far detuned to any Rydberg transition, and the 31S state exhibits an AC-Stark shift proportional to the microwave electric field amplitude. Figure 9A On the far left of the plot shown, the laser frequency axis is centered on the 31S line, with a 2.5 GHz microwave field applied. For increasing microwave frequencies, the 31S level begins to shift significantly around 3.5 GHz to a large microwave cavity-induced field resonance at 4.35 GHz (4.37 ± 0.01 GHz in high-resolution scans, not shown). Other features are evident in the spectrum, including a significant resonance at 4.85 GHz. This is due to the complexity of the cavity structure (e.g., the inclusion of three holes 740 in the aluminum rod for electrode / cavity alignment). Figure 7B As shown in the diagram, and the long electrode line 712 behind each electrode 706, 707, the multiple resonances from this device are not accidental.

[0130] Figure 9B Describe the root mean square (RMS) electric field E for the applicationRMS , with 31S 1 / 2 Strak diagram of computation centered on Rydberg states. Figure 9C Depicting Use Figure 9A and 9B The obtained microwave E RMS Regarding frequency, and Figure 9D Plot the EIT lines (plot line 902 and plot line 904) for measurements of 2.5 GHz microwave and 4.35 GHz microwave, respectively.

[0131] The examples discussed herein illustrate the adaptability of the geometry of a hybrid device for high electric field measurement sensitivity at desired application-specific RF / microwave frequencies (as a design choice for those skilled in the art). In this example, the frequency displacement is converted to an electric field value by line-fitting the microwave-induced AC-Stark displacement measured by a spectroscopic method to a Gaussian function and calculating the Stark displacement using rubidium 31S Rydberg states. Figure 9B This shows the effect of an applied electric field on a field with no electric field for 31 seconds. 1 / 2 The Stark mapping is calculated with the Rydberg state as the center. Figure 9C The diagram shows the variation of the microwave electric field as a function of microwave frequency, measured inside the cavity. At the resonance point of 4.35 ± 0.05 GHz, the cavity-enhanced microwave field E is measured. RMS >= 13.5V / cm, relative error < 0.3V / cm, given by the fitting uncertainty of < 0.1MHz at the peak position.

[0132] exist Figure 9A In this case, the EIT linewidth increased from 21.7MHz at 2.5GHz to 84.0MHz at 4.35GHz (see also...). Figure 9D This increase is attributed to field inhomogeneities in the measurement volume, since the EIT beams 720, 722, and cavity channel 710 are of similar size, and near-field effects at the cavity edges are sampled by the beam. Edges and corners at the ends 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 widening of the inhomogeneous field can be mitigated by implementing a cavity structure with a larger cavity volume and / or by using a smaller beam size for more spatially localized measurements.

[0133] To estimate the cavity enhancement factor used for the electric field, the above reference can be used. Figures 9A-9D The cavity-enhanced 4.35 GHz field measurement described is compared with the field measured outside cavity 710. For this purpose, the EIT beams 720 and 722 are moved by Δz = -0.9 mm from the center of cavity 710 toward the front of vapor chamber 702 and waveguide 735. To obtain a measurable linear displacement at this location outside the cavity, the injected microwave power is increased from -10 dBm to -5 dBm. Figures 9A-9D Compared to the comparison used in the discussion, this is a factor of 3.16 higher in power (1.78x higher in the field). Under these conditions, the AC-stark displacement induced by a 4.35 GHz microwave field at -3.80 MHz was measured, corresponding to E RMS =1.47V / cm. Using this value for the RF field outside the cavity results in an increased injection power and neglects the change in the field emitted from the waveguide on the small Δz (|Δz| / d = 0.03 << 1, where |Δz| = 0.9mm is the beam position relative to the cavity, and d = 29.1mm is the minor axis of the waveguide), thus obtaining... The cavity field enhancement factor is equivalent to a 24 dB increase in sensitivity.

[0134] The simulation is discussed below with reference to Figure 12, simulating the field within a hybrid atom-cavity structure incident with a 4.37 GHz microwave field (with an amplitude of 1 V / m linearly polarized along the y-axis). This simulation yields an enhancement factor of 18.6, approximately 14% higher than the measured value for a 4.35 GHz field. This difference can be explained by the 0.02 GHz frequency difference between the measured and simulated fields. The simulation does not account for microwave losses due to the dielectric cell 702, which depend on the accurate cell geometry (including wall dimensions) and the material dielectric constant for the microwave frequency of interest.

[0135] In complementary implementations of hybrid devices, within the scope of this invention, instead of inserting the resonant structure 510 into a chamber containing atomic vapor, the atomic vapor can also be incorporated into the resonant structure. This may be desirable, for example, in applications where atomic measurements need to be integrated into existing RF systems (speaker receivers, waveguides, etc.) for absolute leveling of RF power and fields. As an example, see reference... Figure 1 The sensing element 100 under discussion (containing a similar narrow dielectric capsule 232 of atomic vapor) can be incorporated into the measurement channel 710 of the resonant structure 510, similar to... Figures 5A-5B Or as shown in 7A-7D. Within the scope of this invention, the resonant structure 510 can be any type of RF resonator or component.

[0136] Now for reference Figure 10A and 10BAnother implementation of a vapor chamber 1002 within a waveguide 1004, within the scope of this invention, is described, with side and end views of the field measurement system, typically indicated by the designation 1000, shown respectively. An aperture 1006 in the waveguide 1004 provides a pathway for the beam of the EIT coupler 1008 and the probe 1010. This system has been used for high-intensity field measurements within waveguides. Such hybrid systems can be advantageously integrated into existing RF circuits for the absolute level measurement of power passing through the circuit. As an example, hybrid devices incorporating atomic vapor into horn, diode, and waveguide structures provide a versatile, compact internal module for measurement, calibration, or power modulation in microwave sources, transmission systems, and other instruments in land-based, sea-based, air-based, and space-based applications.

[0137] By achieving Rydberg levels with higher principal and orbital quantum numbers and Rydberg states resonantly coupled to a cavity-enhanced RF field, the absolute sensitivity achievable using hybrid atom-resonator devices as described herein can be tailored and further enhanced, all within the design capabilities of those skilled in the art. All these enhancements are within the scope of this invention. Field enhancements and sensitivity can be further tailored, for example, by designing resonant structures other than those described above and hybrid devices with metamaterials known in the art or discussed in the future. Complementary implementations of vapor chambers incorporated into resonant structures, also within the scope of this invention, can offer particular advantages when integrating atomic measurement capabilities into existing RF systems (horn receivers, waveguides, etc.) and DC circuits / components.

[0138] Polarization selectivity in hybrid systems

[0139] Another feature of the hybrid devices described above is their ability to distinguish different RF / microwave polarizations to achieve polarization-selective, atom-based field measurements. For Figures 5A-5B And the cavity structure shown in 7A-7D, cavity 710 is used as an RF polarization filter, in which an RF field with only a linear resonant component along the cavity axis Y is coupled into the cavity and the field is amplified within the effective measurement volume.

[0140] Figure 11A This illustrates the experimental 31S Rydberg AC-Stark displacement of the microwave field polarization vector relative to the vertical (Y-axis) at different angular positions Θ with a fixed injection power, varying with the applied microwave frequency. This is achieved by rotating waveguide 735 counterclockwise about the Z-axis in the XY plane from Θ = 0° (along the short waveguide axis of Y) to 90° in 10° steps. At Θ = 0°, the microwave polarization is aligned with the cavity axis of cavity 710 for maximum coupling into the cavity. Figure 11A Curve 1102 shown in the figure is obvious. As Θ increases, the signal decreases because the linear (Θ = 0°) component of the microwave field parallel to the cavity axis decreases. Figure 10B Describing for Figure 11A The data in the figure show the microwave electric field at 4.35 GHz as a function of Θ (obtained from the 31S line displacement and calculated as described previously in the Stark plot). The field decreases as Θ increases because the Θ = 0° component of the microwave field vector (the component coupled to the resonance) decreases with cosΘ dependence. Figure 10B Curve 1110 in the figure confirms this expectation with a cosine fit to the data, although the 4.35 GHz field in the cavity does not reach zero at Θ = 90° due to cavity defects (e.g., slight electrode misalignment and surface quality). As a result, the power of the linearly polarized resonant electromagnetic wave coupled to the resonator and detected by atoms in the resonator gap has a cosine similarity to that of the resonator. 2 The Θ dependency, where Θ is the microwave polarization angle as defined above, shows that this cavity resonator simulates the function of an integrated microwave polarizer.

[0141] DC field tuning capability of the vapor chamber integrated with electrodes

[0142] A major limitation of weak RF field measurements based on Rydberg atoms is that they typically require the RF field to resonate with dipole-allowed Rydberg transitions, which provides large electric dipole moments and strong atomic responses to electric fields. Therefore, weak field measurements can only be performed on 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 the atomic energy levels and transitions to resonance or near-resonance with the RF field of interest, thus providing sufficient atomic sensitivity for the measurement. The hybrid atom-resonator, first proposed according to the invention, provides a practical means of applying localized fields to atoms using a cavity / antenna / electrode structure itself designed for this purpose.

[0143] Using the hybrid atom-resonator 700 described above, and according to a further embodiment of the invention, the same electrodes described above in the context of RF field enhancement are used simultaneously or separately to apply a DC electric field to the Stark-tuned Rydberg transition frequency that resonates with the weak RF field. Figure 13A and 13B Experimental and calculated DC-Stark plots of the 30D Rydberg state for the applied DC electric field are shown, respectively. Note that the Stark plots are symmetric about the zero field. Measurements were performed by grounding one electrode and applying a voltage to the other electrode in measurement channel 510 (…). Figure 5B (As shown in the figure) the cavity that generates the DC field to obtain Figure 13A The spectrum of the experiment. Figure 13A The diagram illustrates the three sublevels |mj| = 0.5, 1.5, and 2.5 for the fine structure component at j = 2.5, and the two sublevels |mj| = 0.5 and 1.5 for the fine structure component at j = 1.5. Using a zero-field and linearly polarized beam, due to the m-mixing of the 5P³ / ² hyperfine structure, Figure 5BThe rubidium EIT ladder scheme described in the paper selectively excites Rydberg sublevels of |mj| = 0.5 and 1.5. The appearance of weak Rydberg levels of j = 2.5 and |mj| = 2.5 in the experimental spectrum may be due to slight misalignment or ellipticity of the beam polarization.

[0144] Figure 13A and 13B Provide proofs of DC electric field tuning of Rydberg levels and transitions using hybrid atom-cavity structures or similar structures with electrodes integrated with atomic vapor or gas. As an example, consider 30D. 5 / 2 and 30D 3 / 2 Two RF photon transitions between mj = 1.5. Using an applied electric field of 0 V / cm, this corresponds to resonance at -540 MHz and dipole-allowed transitions in the second stage using two -270 MHz RF photons. At an electric field of + / -10 V / cm, the energy difference between states increases to ~h*700 MHz (where h is Planck's constant in appropriate units), and dipole-allowed transitions are achieved using two -350 MHz RF photons. By applying an electric field from 0 to + / -10 V / cm, RF photon resonances can be continuously tuned anywhere between -270 and 350 MHz. Within the scope of this invention, the range of tunability can be extended, for example, by using higher field values, different atomic states with different polarizability and electric dipole moments, and multiphoton excitation processes. AC-Stark tuning using external electrodes.

[0145] Continuous frequency measurement of weak Ka-band microwave electric fields can be similarly achieved by AC-Stark tuning of the Rydberg transition using a low-frequency RF with internal or external tuning electrodes (both as described above). In one embodiment of the invention, an AC-Stark tuned 100 MHz RF field is applied to a vapor chamber using external electrodes to tune the transition Stark to microwave resonances with and without RF field detuning. Figure 14 The Floquet spectra (1401 and 1403) calculated for the 47S and 47P states modulated by a 100MHz RF field are shown. The 47S and 47P plots are superimposed and referenced to the same zero-field frequency to show the RF-induced differential shift of the 47S1 / 2 to 47P3 / 2 transition. Thus, it can be expected that the resonant microwave transition will be tuned down continuously at approximately 200MHz from 0 to 200V / cm of the applied 100MHz RF.

[0146] Figure 15The figure shows the RF intensity and electric field calibration in the 47S state, mapping the incident RF power to the 47S state displacement at different Stark detunings of the excitation beam. The experimental and calculated plots agree well, producing a dBi-to-dBm conversion of dBi = dBm + 50.5 and using 1 = I0 * 10 dBI / 10 =1 / 2εcE0 2 The electric field (E0) is calibrated, where I0 = 1 W / m. 2 ε is the vacuum permittivity, and c is the speed of light. Then, using... Figure 15 The calibration is used to set the desired difference shift for the 47S to 47P transition (where the Ka-band microwave is tuned to resonance). Figure 14 The RF electric field of curve 1405 in the figure.

[0147] Avoidance crossover has been used in the interpretation of electric field-induced / mixing populations in high-state states, as exemplified by Zhang et al., “Stark-induced L-mixing interferences in ultracold cesium Rydberg atoms,” Phys.Rev.A As reported in , vol.87, 033405 (2013). Figure 16 The figure shows that for four different injected RF powers / field strengths in the room, with a fixed microwave intensity of -14 dBi (individually calibrated), the measured EIT spectra of the 47S state are detuned to a microwave frequency of 37.51663492 GHz (no RF transition frequency). This is achieved by not applying RF ( Figure 16 (Top plot in the figure) As the microwave frequency is scanned across the resonant transition without RF field, the 47S line exhibits the expected Auttler-Townes behavior. The center of the avoidance cross is located at 0 MHz detuning, where the Auttler-Townes splitting peak is symmetrically split. As the RF power / field increases (bottom plot in the figure), the avoidance cross shifts to a larger microwave detuning, tracing the AC-Stark tuned transition frequency. At the applied -38.2 dBm RF ( Figure 16 (Bottom image in the image) shows the microwave resonating with the transition at a detuning point of approximately 60 MHz.

[0148] exist Figure 17 In this study, the center of the measured crossover is depicted as a function of the applied RF electric field (a series of values ​​up to approximately 200 V / cm). An uncertainty bar is set for the approximate EIT linewidth of + / -10 MHz. Figure 14The calculated difference shifts shown here are again depicted by curve 1701 for comparison with the experimental shifts. The match between the experimental and calculated shifts is excellent across almost the entire range, with the measured AC-Stark shifts exhibiting the expected quadratic relationship to the applied RF field. At the highest RF field, the coupling between the modulation sidebands of the 47S and 47P states, as well as variations in the atomic-microwave field coupling strength, make it difficult to discern the centers of avoidance crosses in the spectrum under certain experimental conditions (large optical Rabi frequencies and EIT linewidths), leading to deviations between the depicted measurements and the calculated values. Continuous AC-Stark tuning with ~200 MHz microwave detuning is possible, where transitions between other Flokai states and modulation sidebands in strong fields can also be used.

[0149] It should be understood that, within the scope of this invention, AC-Stark tuning can also use electrodes in the sensing element but outside the vapor chamber for continuous frequency microwave electric field measurement.

[0150] Integrated Gap Ring Resonator

[0151] Within the scope of this invention, by reference Figures 18A-18D The described gap ring resonator 1801 provides an example of a field-tuned structure. The gap ring resonator 1801 is a simple resonant structure of metamaterials commonly used in microwave, millimeter-wave fields, and the THZ region of the electromagnetic spectrum. The gap ring field amplifier shares conceptual similarities with the plasmonic resonance of microspheres used in the optical and infrared spectral ranges for spectroscopy and light harvesting applications. An atomic vapor chamber in a quantum RF sensing element with an integrated gap ring structure designed to achieve low-noise field amplification, high sensitivity, and polarization selectivity in atom-based electric field sensing applications constitutes another embodiment of an atom-cavity structure for advanced sensing capabilities.

[0152] Figure 18A The diagram illustrates the structure of a basic type of gap-ring structure: a tubular ring with a single slit. At resonance, the electric field of the incident millimeter-wave field 1803 is compressed at the slit (or “gap”) 1805. The gap 1805 also defines a measurement channel 710, in which atomic vapor is optically probed for measuring the amplified field. This operating principle is... Figure 18B The image is shown in the illustration, depicting a 1×0.2×0.2 mm slit / gap for the gap ring, with vertically polarized microwaves incident on the cavity from the right side. Figure 18AIn this paper, we describe the simulated electric field values ​​within the gaps of this resonator type for three different gap sizes and geometries as a function of the incident microwave field frequency (a fixed 1 V / m incident field amplitude). These gap rings exhibit resonance at 14, 44, and 54 GHz, with field amplification factors of 46.8x, 74.1x, and 27.3x, respectively. The resonant frequency can be designed using simple geometric parameters of the gap rings. Figure 18C and 18D The simulated resonant behavior of other gap ring resonator structures is depicted, including a square tube structure that provides amplification at 42.5, 125, and 94 GHz, with corresponding 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 the upper limit for the sensitivity of the target field measurement without amplification, a hybrid device providing 81.9x field amplification at 42.5 GHz microwaves can achieve an effective sensitivity at the level of 0.01 mV / m (for the incident field).

[0153] Other gap ring resonator structures applied to field measurements in vapor chambers, as well as other types of resonators (such as coaxial high-Q microwave cavities), are within the scope of this invention.

[0154] Non-contact optical heating for temperature-stable steam chambers

[0155] Now for reference Figures 19A-19C The described contactless, all-optical vapor chamber heating can be a necessary component as an active vapor pressure control system for Rydberg RF sensors and hybrid devices, for which the temperature control hardware (electronics, wires) must not alter the detector's RF field response. According to embodiments of the invention, one or more light-absorbing materials are incorporated into the chamber. The light-absorbing material is heated via absorption or inelastic scattering of the incident light beam, which in turn heats the atomic vapor (or solid metal) within the chamber for higher atomic vapor densities. By using, for example, a chamber constructed of IR-absorbing glass, atoms can be thermally contacted with the light-heated element, or indirectly heated via the light-absorbing material element in thermal contact with the vapor shell.

[0156] Besides heating, it is important to stabilize the chamber temperature during operation. This can be critical when measurements are performed in environments where the external air temperature can significantly alter the chamber temperature. This is particularly important when using small chambers (on the order of millimeters) (whose atomic temperatures and densities are more susceptible to ambient temperature fluctuations due to their small volume). To address this, within the scope of this invention, active stabilization can be implemented by actively monitoring changes in the atomic vapor temperature or density of the chamber via light absorption through a second laser beam that resonates with atomic transitions. This absorption signal provides active feedback on the amount of photoheating power required to achieve the desired temperature and density. Furthermore, the chamber can be made thermally insulated from the environment, for example, by incorporating an insulating vacuum layer between the photoheated chamber and the environment.

[0157] refer to Figures 19A-19C According to the all-optical vapor chamber heating method integrated into the Rydberg RF sensor, the internal temperature of the atomic vapor chamber is increased by irradiating the IR-absorbing glass capsule with a strong light source. Figure 19A and 19B The IR glass capsule 1901 surrounding the atomic vapor chamber 1903 with an inner diameter of 4 mm is shown. Figure 19C A fully optical heating test platform is shown. A light source 1905 (such as a 50W halogen bulb) is imaged onto the capsule, and the temperature of the IR glass capsule 1901 is monitored using a temperature sensor (such as a thermistor (not shown)) placed within the IR glass capsule volume. A feedback loop is implemented between the thermistor and the light source intensity to regulate the temperature within the capsule, providing a stable operating temperature for uniform heating of the atomic vapor chamber. In one embodiment, a steady-state temperature of up to 130°C is achieved with uniform distribution within the capsule. Active temperature stabilization of the capsule temperature at 50°C (a typical operating temperature when using a small 4mm inner diameter Rb chamber) has been achieved.

[0158] RF phase measurement capability using modulated laser fields

[0159] A method for extracting the phase of an RF field using a sensing element is now described. According to embodiments of the invention, a phase-sensitive record of a coherent electromagnetic field on a surface can advantageously allow for field reconstruction in all spaces. This reconstruction principle has numerous applications, including optical holography, interferometric radar (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 the antenna under test. In the last listed application, measurements are performed on a surface and a near-field to far-field conversion is applied to calculate the field in all spaces.

[0160] To achieve phase sensitivity in field measurements, holographic methods are typically employed. Here, the reference wave interferes with the wave emitted by the object. In this case, the object under consideration is the antenna under test, which emits an RF field requiring full characterization. The reference wave, with well-defined amplitude and phase, is preferably a planar RF field that interferes with the object wave within an atomic vapor chamber or hybrid atomic cavity structure. The chamber is constructed such that the atomic field interaction volume spans any given direction and is measured in any given direction at a distance less than one RF wavelength. 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 sum of the electric fields of the object and the reference millimeter-wave or microwave field is then measured using accepted methods.

[0161] The magnitude of the measurement 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 a vapor chamber sensor element across a suitable grid with a spatial resolution much smaller than the RF wavelength. The phase-sensitive electric field value measured on the grid then allows for a complete three-dimensional reconstruction of the object wave. To obtain the far field of the antenna under test, a near-field / far-field conversion can be performed using known algorithms. This measurement method can be readily extended to include fully polarized sensitivity of the electric field vector using hybrid atomic cavity structures (see above) or other spectral techniques.

[0162] In RF field phase measurements, the generation of a well-characterized reference wave presents considerable challenges. For comparison, we first consider optical holography. Here, the reference wave is typically an extended, near-perfect plane-wave laser beam that interferes with scattering by objects within the photosensitive emulsion (or equivalent) layer. It is well-known in optical holography that the purity of the reference wave is crucial. The system should be essentially free of diffraction rings caused by dust particles and other defects. False reflections of the reference wave from a smooth glass surface are an even greater problem. In the case of RF measurements, this condition is difficult to meet even with state-of-the-art anechoic chambers. For quantitative work, it is also important that the reference wave has a fixed amplitude or at least a known slowly varying amplitude function. The preparation of a defect-free RF reference wave with smooth amplitude behavior on a large surface presents significant challenges and is not always possible.

[0163] Figure 20AThe diagram schematically illustrates the rear end of a sensing element (generally indicated as 2000) according to an embodiment of the invention and the operating principle for phase-sensitive measurements of RF electric fields. A microwave horn 2002 (MW) represents any wave from the antenna under test or other object of interest. An fiber optic modulator 2004, driven by an RF source 2006, coherently imprints an RF reference beat onto a coupler beam 104, which is then transmitted to atoms in a vapor chamber 106. The RF reference beat replaces the reference beam typically required in phase-sensitive (holographic) field measurements. The vapor chamber 106 in the atom-based RF sensing element is approximately 1 mm in size and is fiber-coupled to laser beams at 780 nm and 480 nm. A single-sided fiber-coupled sensing element 100 is mounted on a sensor rod (not shown) with minimal dielectric profile. The sensing element and rod are the only parts of the detector actually located in the RF field. The fiber optic modulator and optical phase control element are integrated with a sensor remote control station (not shown) located outside the sensing element 100, and the remote control station includes a laser, signal readout electronics, and a computing unit for analysis. Figure 20B The quantum mechanical level scheme and optical / RF excitation path used in phase-sensitive RF electric field measurements are depicted.

[0164] To meet these practical measurement needs, the solution is integrated into an atom-based RF sensing element and measurement. The working principle involves imprinting a phase-coherent RF reference onto an optically coupled laser beam via electro-optic modulation. A commercially available fiber optic high-frequency modulator is used, operating at a frequency ω that is the same as the frequency of the RF field to be measured. RF The coupler beam is frequency-modulated or amplitude-modulated. In one implementation, the field frequency is chosen such that it is also the same as half the spacing between two adjacent S-type Rydberg levels. The energies of the levels and their spacing are known with very high precision. There are many options for this transition. Furthermore, the carrier frequency of the coupler laser beam 104 is tuned so that it resonates between the S-levels with transition 2010 to nP. 3 / 2 Rydberg stages. The Rydberg nP stage is not exactly located at the midpoint between the two S Rydberg stages, resulting in the modulation coupler frequency 2012 being resonantly detuned Δ from the S state. In rubidium, these detunings are approximately 100 MHz and are typically greater than the Rabi frequency of any of the transitions involved. Therefore, the absorption via a coupled laser photon and the absorption of RF photons are described ( Figure 20B Channel B in the middle) or stimulated emission ( Figure 20B The two photon Rabi frequencies of channel A) transitioning from 5P to nP are given below:

[0165]

[0166]

[0167] Here, Ω 5PnS and Ω 5P(n+1)S It is the Rabi frequency at which the optical coupler laser transitions to the S-Rydberg level, Ω RF* It is the RF jump from the S-Rydberg level to the nP level. 3 / 2 The rabbi frequency of the Reedburg class, and It is the phase of the RF field. Similarly, and This represents the phase of the modulation sideband of the coupled laser. Note that in the above equation... The preceding symbols are significantly different. Furthermore, the RF field amplitude E... RF Included in Ω RF* In the middle, because Ω RF* =E RF d * / n, where d * These are the known RF electric dipole transition matrix elements used for RF Rydberg-to-Rydberg transitions. The net coupling Ω between the 5P state and the nP Rydberg state. C Then by Figure 20B The total coherence of channels A and B is given.

[0168]

[0169] For simplicity, we assume Ω. 5PnS and Ω 5P(n+1)S The two RF Rabi frequencies are identical (both are approximately good). These assumptions are not important, but they help to clarify the mathematics. Optical phase and It is well-defined and not easily drifted because all frequency components of the modulated coupler laser beam follow exactly the same geometric path. As a useful optical component, the prism phase control element or equivalent in the modulated coupler laser beam is used to control the optical phase. and The difference between them. As can be seen from the previous equations, the net coupling form is...

[0170]

[0171] Where Ω C0 It is a (complex) phase-independent pre-factor and Φ is a displacement phase that can be adjusted in the coupler beam using the dispersion control element 2003 (in Figure 20A In this process, it is accomplished by moving the prism unit 2005 left and right. Since the intensity of the Rydberg-EIT line observed in the spectrum is typically related to... Proportional, therefore the strength of the EIT line is... Proportional. Therefore, the EIT line intensity carries phase information about the RF field. We note that the transition from 5P to nP is forbidden; therefore, the coupler beam carrier (the thin blue line in Figure 24b) will not introduce additional terminology in the analysis. In a more general case, such terminology may, of course, be included. Furthermore, the pre-factor Ω can be determined by finding the peak EIT line intensity while varying Φ using a dispersion control element in the coupled beam. C0 The size of Ω. C The obtained peak value is then displayed as Ω. C0 This generates the magnitude of the RF electric field. In this way, E can be measured. RF and Both.

[0172] The specification states that the RF field phase (and amplitude) measurement capability is achieved by introducing an RF reference wave via optical frequency modulation. The novelty of this method lies in its elimination of the need for an external RF reference wave by utilizing optical modulation applied directly to the atoms in the quantum RF sensing element using a laser beam, instead of an external RF reference wave. In practice, methods such as... Figure 5A and Figure 5B The chamber-integrated electrode or cavity structure (hybrid system) shown can be used to sense the position of atoms by introducing a reference wave into an atom-based RF sensing element using an external reference wave.

[0173] Modulated RF detection in an atomic vapor chamber

[0174] For telecommunications applications, the detection of modulated RF fields is desirable. Since the EIT response time is less than 100 ns, atom-based sensing elements can be used as RF / optical transducers to directly detect the amplitude and frequency modulation of high-frequency fields without resorting to quantum interference. Similarly, RF phase modulation detection follows the phase detection capability described above. Typical cases are described below.

[0175] AM modulation at the audio frequency: In the Floquet mapping diagram, most Rydberg states (at any carrier frequency between -100 MHz and several 100 GHz) exhibit a differential dynamic dipole moment, with a magnitude range reaching thousands of Debye. The EIT line on the mapping diagram has a linewidth specified by the coupler and probe Rabi frequencies. For modulation purposes, a moderate probe and a large coupler Rabi frequency can be used to maintain a fast EIT response time to AM and broaden the EIT line to several tens of MHz. By applying a carrier RF to the EIT test cell and selecting a working point for the coupler-laser frequency at one of the inflection points of the Rydberg-EIT line, the AM of the RF signal will result in a direct response of the photodiode reading of the EIT sensing element. For a differential dipole moment d, the AM depth dE of the electric field must satisfy dE < h×dL / d, where dL is the EIT linewidth. Therefore, the relative modulation depth dE / E < h×dL / (Ed). This value may range from several 10% to 1%, depending on the precise conditions and sensitivity requirements.

[0176] According to an embodiment of the present invention, an acoustic signal can be converted using a microphone, a linear amplifier, and a voltage-controlled RF attenuator to generate an AM-modulated RF test field. An antenna or a microwave horn is used to transmit the EIT test signal. The EIT cell acts as a receiver. With the working point selected as described, the EIT probe photodiode signal is transmitted through a passband that covers the acoustic frequency range. The detected signal is amplified and sent to a recording device and / or a speaker. Note that in this method, no demodulation is required at the receiver end (processing of the EIT cell and the EIT probe laser signal). The EIT physics acts as the demodulator. The same receiver principle can be applied when detecting AM-modulated transmissions from other sources. Since the EIT sensor cell operating in the antenna receiver is optically coupled, an AM receiver based thereon has very high EMI and EMP resistance, can withstand high-voltage spikes, and constitutes a sensitive AM radio receiver under normal operating conditions. Modulation of FM fields can be implemented in a similar manner.

[0177] Capability for measuring incoherent RF fields and RF noise

[0178] Before the present invention, Rydberg-EIT systems were only capable of characterizing coherent RF fields, since Autler-Townes splitting requires the interaction of coherent fields. As now described, this physical constraint is lifted for the first time according to the present invention. Reference is now made to Figure 22The steps for quantifying RF noise properties according to embodiments of the present invention are described. In a first step 2201, a predetermined Rydberg atomic level or Rydberg-EIT spectrum is calculated in the presence of an incoherent RF noise field. The following sections present a Rydberg-EIT model in the presence of noise. Measurement light is propagated in an atomic vapor chamber 2203, and the spectral characteristics of the atomic vapor are measured 2205. The measured spectral characteristics are compared with the calculated spectral characteristics 2207, and matching spectra are identified 2209. This provides a quantification of the presence of incoherent RF noise and the properties 2211 of the RF noise, including spectral noise density, spectral power, electric field amplitude, polarization, RF noise field propagation direction, and source characteristics such as horn antenna gain (which may emit such RF noise).

[0179] In RF electric field measurements in atomic vapor using Rydberg EIT and Autler-Townes, the EIT probe beam couples two atomic levels |1> and |2>, the EIT coupling beam couples level |2> to a Rydberg level |3>, and the RF field to be measured couples level |3> to another Rydberg level |4>. Then, an RF-driven transition Ω... RF The Rabi frequency becomes apparent in the Autler-Towns (AT) split of the two lines (observed in the EIT spectrum), which in turn yields the electric field via basic atomic physics calculations. To account for the effects of broadband RF field noise in such atom-based RF electric field measurement, a quantitative description of the impact of broadband microwave noise is needed. The considerations are likely quite general, as microwave amplifiers typically add broadband noise to the amplifier's output; this noise will then affect the atom-based electric field measurement.

[0180] To conform to typical experimental testing conditions, this approach 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 greater than the horn's far-field limit. The basic theory described here is sufficient to explain the physical phenomena of noise-induced effects. This theory can later be extended to cover more general types of field geometry, thus opening up a wider range of applications (without adding substantially new insights into fundamental physics).

[0181] The effect of broadband noise on Rydberg atomic systems consists of two main parts. Rydberg levels |3> and |4> populated by coherent sources (lasers, coherent microwave radiation) can transition to other Rydberg levels because the frequency components of the noise spectrum resonate with the transitions between Rydberg states. This process is analogous to blackbody radiation-driven decay. The usual approach is to quantize the radiation field and obtain the transition rates according to Fermi's golden rule, then sum over the possible field polarizations and available final angular momentum states. This usual approach needs to be modified to apply to noise fields with well-defined polarizations and propagation directions (specified by the geometry of the microwave horn). Similarly, the blackbody energy density of the field must be replaced by the noise characteristics under specific conditions. At the atom's location, the noise has a spectral intensity, i.e., the noise intensity per frequency interval, expressed in W / (m²). 2 The unit is Hz, which may be a known or actual subject of research.

[0182]

[0183] To model a hypothetical RF field test scenario where the coherent microwave field to be measured and noise are applied to an atom via the same microwave horn, and the atom is located in the far field of the horn, we quantize the field in only one dimension (the propagation direction of the microwave field emanating from the horn) and assume a fixed field polarization. For the noise-induced transition rate R from the initial state |i> to the final state |f>... fi Analysis shows

[0184]

[0185] Where n is the field polarization unit vector, ν fi It is the transition frequency (E) f -E i ) / h, where E f and E i These represent the energies of the initial and final Rydberg stages. These rates are in the International System of Units (SI) and have units of "atoms per second". Note R. if =R fi For a given state of interest (labeled as |3> and |4> in the current case), we compute the known noise spectrum I. ν The rate R of (|v|) fi .

[0186] In the assumed measurement scenario, the coherent microwave field to be measured drives the transition between Rydberg states |3> and |4>. If the noise spectrum covers the transitions |3> and |4>, then the noise-induced transitions must proceed at equal rates (R0, R0, R0). 34 =R 43The two noise-induced bidirectional attenuation terms are included in the main equation. R must also be included. 34 and R 43 This includes the coherence decay rate of any off-diagonal density matrix element (which involves levels |3> or |4> or both).

[0187] For transitions |3>→|f> and |4>→|f> (unlike the coherently driven transitions |3>←→|4>), the noise is expressed as R f3 =R 3f and R f4 =R 4f The per-atom rate drives the transitions. Note that the levels |f> with the noise population are incoherent with each other and with any of the levels |1> to |4>, because the noise-induced transitions have random quantum phases. Therefore, all levels |f> with the level |3> population may be merged into the virtual level |d> due to the noise. Similarly, all levels |f> with the level |4> population are merged into the virtual level |e>. Due to the electric dipole selection rule, there is no overlap between the levels merged into the virtual level |d> (which becomes the noise population from |3>) and the levels merged into the virtual level |e> (which becomes the noise population from |4>).

[0188] The net rate of entry into the virtual level is

[0189]

[0190]

[0191] It is also R d3 =R 3d and R e4 =R 4e Noise also induces AC displacements based on the same field quantization model and calculated using second-order perturbation theory. Displacements of level |i>=|3> or |4> were found to be

[0192]

[0193] Integral limit ν min and ν max Choose a sufficiently wide frequency range to cover the entire noise spectrum. Note that the sign of the transition frequencies varies depending on the term. Important (as expected). The AC displacements of levels |3> and |4> will need to be added to the master equation as noise-induced detuning terms. The noise-induced AC displacements of all other Rydberg levels included in the model are not important, as they are incorporated into the dummy levels |d> and |e>.

[0194] Comparing the three equations above, we see that AC displacement is more difficult to calculate than attenuation. For attenuation, only transitions with frequencies located within the noise band take effect, and only the noise spectral density is needed at these frequencies. Typically, only a few (and sometimes none) Rydberg-Rydberg transitions involving levels |3> or |4> occur within the noise band. Conversely, all permissible transitions involving levels |3> or |4> (including transitions at frequencies outside the noise band) are, in principle, related to the equations above. Similarly, for each of these transitions, the integral over the entire noise band needs to be evaluated. For transitions within the noise band, extra care must be taken regarding the poles.

[0195] To evaluate the above equation, the noise spectral intensity function I is needed. ν (ν). In many cases, it is possible for the user to use a spectrum analyzer to measure the power spectral density function dP / dν of the noise injected into the speaker.

[0196] The propagation equation available in textbooks produces I ν The equation of (ν),

[0197]

[0198] Where dP / dν is interpolated in W / Hz and the distance from the horn x is in meters. The spectral power dP / dν is normalized so that it integrates to the total noise power injected into the horn (in watts). The linear gain g of the horn. L(ν) This is usually provided by the speaker manufacturer's specifications. Then, I... ν The result of (ν) is input into the above equation to obtain the noise-induced attenuation rate and AC-level displacement.

[0199] Based on the results of the above equations, the fourth-order master equation of the problem can be extended to include the effects of noise up to second order. The state space of the master equation is modified by virtual "levels" |d> and |e>, which will maintain the net population ρ transmitted by noise from the corresponding levels |3> and |4> (levels coupled by the coherent microwave signal whose electric field is to be measured). dd and ρ ee The revised master equation includes additional terms in the equations for the energy level populations of the Rydberg states |3> and |4>.

[0200]

[0201]

[0202] The equations for attenuation involving coherence levels |3> and / or |4> also need to be modified to include all terms R. 3d - R 3e - and R34 - The new equations for virtual levels |d> and |e> are:

[0203]

[0204]

[0205] The modified master equations do not include any equations concerning coherence at the virtual stage (coherence at the virtual stage is always zero). After modifying the standard fourth-order master equations using all these terms, solving them using standard methods yields the coherence ρ as a function of the coupler-laser frequency. 12 Extracting the EIT spectrum requires ρ 12 .

[0206] For example, the Beer absorption coefficient α(Δ) can be calculated. C The model EIT spectrum is obtained, showing the Beer absorption coefficient in the medium as a function of coupler-laser detuning for a given atomic vapor and the chamber temperature used. Note that this involves an integral over the Maxwell velocity distribution in the chamber, as each velocity class has its own Doppler displacement of the coupler beam and probe beam. The ratio of input probe power to output probe power is then calculated using e-. -αL Given, where L is the chamber length. It is important to note that the atomically specified matrix elements are used for all noise-driven transitions in all experimentally available inputs and computations.<f|r|i> After that, no suitable parameters remain to adjust the model results. This will lead to an absolutely unfitted consistency when comparing the measured spectrum and the modeled spectrum of the Rydberg-EIT-AT spectrum under broadband noise.

[0207] Capability to measure continuous-frequency RF electric fields using strong atomic field interaction states

[0208] As used herein, the term "strong atom-field interaction state" refers to a microwave field characterized by an electric field strength exceeding that of an Autler-Townes state, where a two-stage treatment is sufficient to describe the observed spectral line splitting. For measuring the RF electric field in a strong atom-field interaction state, the Floquet state is considered to exhibit a high-density state, altering the differential dynamic dipole moment throughout and in multiple avoidance crossovers. This treatment is proposed for the first time according to an embodiment of the invention.

[0209] Plasma Diagnostics

[0210] Some methods according to embodiments of the present invention may be referred to as plasma diagnostics, using electromagnetically induced transparency (EIT) to measure plasma fields, particle interactions, and parameters of particles or plasma components embedded in plasma. One method for plasma field measurement and diagnostics is described, employing electromagnetically induced transparency (EIT) or electromagnetically induced absorption (EIA) as a high-resolution plasma optical probe for measuring the energy level shifts of Rydberg atoms embedded in plasma, where the Rydberg atoms act as sensitive local electric field sensors with a large dynamic range.

[0211] Now for reference Figures 23A-23C An embodiment of EIT-based plasma diagnostics is described. Rubidium or other tracer particles suitable for EIT are incorporated into plasma 2300 during their generation. The tracer atoms are optically interrogated using EIT, wherein, as shown, the EIT beam 2303 spatially overlaps with the tracer atoms within the plasma. Figure 23C The diagram illustrates the atomic-level structure of rubidium atoms and the Rydberg-EIT configuration, consisting of a 780 nm probe laser beam 2320 and a backpropagating 480 nm coupler beam 2322. The frequency of the probe laser beam 2320 resonates with the 5S¹ / ² to 5P³ / ²D² transition, while the frequency of the coupler beam scans near the 5P³ / ² to Rydberg state transition. In this example, the 58 s Rydberg state is selected. The EIT beams are overlapped and focused at the beam waist to optimize the EIT signal intensity and the desired spatial resolution within the plasma 2300 (typically ~100 μm). Probe transmittance is detected on a photodetector 2306 for reading. As the coupler beam is scanned across the Rydberg state resonance, the tracer atoms become transparent to the probe light when the coupler frequency matches the 5P state resonance with the Rydberg state and a decrease in probe transmittance is detected. In this way, Rydberg-EIT spectral analysis is performed on tracer atoms within the plasma that are susceptible to the influence of the plasma environment (fields, particles). Information about the plasma field and particles is obtained from the EIT spectrum, and then from the plasma-induced Rydberg linear displacement and linear shape changes, which can be calculated with high precision.

[0212] The polarizability of the low-angular momentum Rydberg state is calibrated as ~n 7 , where n is the principal quantum number. By tuning the coupler laser frequency to the Rydberg level for desired measurements, this powerful scaling provides a wide range of field measurements and sensitivity for diagnostics.

[0213] In plasma science and applications, magnetic fields that directly influence plasma properties can be used to confine plasmas. Furthermore, the magnetic field induced by the charged current within the plasma is itself of interest. Following the same approach, EIT plasma diagnostics can also be used to measure plasma magnetic fields. The calculated spectra of Rydberg atoms in a magnetic field, as well as their spectra in combined magnetic and electric fields, allow mapping of the EIT spectrum measured from tracer atoms in, for example, magnetically confined plasmas, to their corresponding electric and / or magnetic fields.

[0214] In another embodiment of the diagnosis, reference is made to... Figure 23B The description describes a tracer atomic beam 2330 generated from a cold atomic source 2332 (such as atoms collected in a magneto-optical trap) and injected into the plasma of interest using a pulsed pusher beam 2334. Similarly, pulsed beams of hot atoms or molecules can be used. Atoms are seeded into the plasma, where they can interact with the plasma and its environment. The atoms are then optically interrogated using a Rydberg-EIT optical probe 2336, which overlaps spatially and temporally with the atomic beam within the plasma. Similarly, the transmittance of the optical probe is detected on a photodetector 2306 for reading and analysis. In this configuration, a particle collector / detector 2340, such as a microchannel plate (MCP), can also be integrated and used to measure the flux of the atomic beam through the plasma, and to provide additional information about the plasma density via losses caused by collisions during the interaction of the atomic beam with the plasma, or similarly by detecting the charge / molecules generated by the interaction between the atoms and plasma components.

[0215] Atomic strong magnetic field sensor and measurement method

[0216] According to a further embodiment of the present invention, a method is disclosed as the basis for a new detection technique for high magnetic field sensing and measurement.

[0217] The field measurement method disclosed in this paper is based on atomic spectroscopy of low-density atomic vapor encapsulated in a small (approximately 1 cm in diameter or less) glass chamber. In this atomic-based field measurement method, a laser beam is used to measure the magnetic field-induced shifts in atomic energy levels caused by the Zeeman effect. In an advanced implementation, we propose also utilizing the exaggerated diamagnetic response of highly excited Rydberg atoms to a magnetic field to achieve even higher sensitivity in strong fields. Magnetic fields several times greater than 0.1 T split the hyperfine levels of the Rydberg states into multiple Zeeman sublevels and transitions from weak-field (linear Zeeman) states to Paschen-Back states. The resulting saturated absorption spectra exhibit significantly more dispersed lines, and cross resonances disappear due to the decoupling of nuclear and electron spins. The absolute line positions and their relative separation are good indicators of the magnetic field.

[0218] Figure 25ASaturated spectroscopy, as depicted in [the text], is a known method for eliminating the broadening of inhomogeneous lines caused by the Doppler effect. It is widely used in science and technology where precise spectroscopic information about atomic and molecular transitions and their shifts due to external fields is required. In the saturated spectroscopy of alkali metal atoms in a weak magnetic field, the hyperfine levels of the excited states (in [the text]) are [determined]. Figure 25A The symbolic indication is that |2> and |2'>) are split by a width smaller than the Doppler width, resulting in multiple saturation peaks and cross resonances in the probe laser spectrum of a given Doppler-broadened absorption line. As is known from quantum mechanics textbooks, in magnetic fields several times greater than 0.1 T, hyperfine levels are split into multiple Zeeman sublevels and transition from weak-field (linear Zeeman) states to Paschen-Back states. The resulting saturated absorption spectrum exhibits significantly more dispersed lines, and cross resonances disappear due to the decoupling of nuclear spin and electron spin. The absolute line positions and their relative separation are good indicators of the magnetic field.

[0219] According to the present invention, it can be used Figures 24A-24C The standard saturated spectra of the Rydberg levels depicted in the figure, or using, for example Figures 25A-25C The quantum interference process shown (in which two excitation paths in the tertiary atomic structure destructively interfere and produce an increase in the transmission of one of the laser beams) is used to measure strong magnetic fields. In the corresponding case, Figure 24A and Figure 25A The corresponding quantum energy level schemes for two-level and three-level systems are shown, while Figure 24B and 25B The electromagnetic field is shown to be coupled into the atomic vapor chamber 106. Figure 24C The saturation spectrum of rubidium in a 0.7T magnetic field is depicted. The positions of the lines and their relative separation reveal the magnetic field present in the spectroscopic chamber.

[0220] exist Figures 25A-25C In the spectroscopic method of EIT described in [the text], a quantum interference process is used, in which two excitation paths in the tertiary atomic structure destructively interfere and produce an increase in the transmission of one of the laser beams utilized. The resulting EIT transmission window reveals conventional optical readings for the atomic energy levels and their response to any external field (here, a magnetic field). In the Rydberg-EIT cascade scheme, transparency is achieved through the coherent superposition of the ground state and the Rydberg state. [The text then discusses] already applied to cold atomic gases and room-temperature vapor chambers (such as...). Figure 1 The implementation of the Reedburg-EIT (described in the text) is carried out in China.

[0221] The atomic state most relevant to rubidium saturation and EIT spectroscopy is the 5S state of rubidium. 1 / 2 ground state, 5P 3 / 2 Excited state, and nS 1 / 2 、nD 3 / 2 and nD 5 / 2Rydberg states. In the magnetic field of interest, these are all Paschen-Back states of hyperfine structure. Intermediate states are (linear) Zeeman states of fine structure, while Rydberg states are typically Paschen-Back states of fine structure. Moreover, Rydberg states typically exhibit strong shifts due to atomic diamagnetism.

[0222] Due to their large size, Rydberg atoms experience large diamagnetic shifts. For an s-type Rydberg state, the energy level shifts of the Rydberg state are measured in atomic units.

[0223]

[0224] Where, n, l, m l m s These are the principal quantum number, angular momentum quantum number, magnetic orbital quantum number, and spin quantum number, respectively. For the S state, l = m l = 0. Coordinates r and q are the spherical coordinates of the Rydberg electron (the point along the z-field). The displacement consists of a spin Zeeman term (the first term on the right) and a diamagnetic term (the second term on the right). The corresponding differential magnetic moment is a negative deviation with respect to the magnetic field B. Note that the Bohr magneton is 1 / 2 (in atomic units), and the radial matrix element has a size of n. 4 The diamagnetic differential magnetic moment in the Bohr magneton is n 4 B / 2. In a 1 Tesla field (4.25 × 10⁻⁶) -6 In the atomic unit, when n is greater than about 25, the diamagnetic effect exceeds the paramagnetic (spin) differential dipole moment. At n = 50 (easily achievable), the diamagnetic effect exceeds the paramagnetic differential dipole moment by a factor of about 16. Therefore, in strong magnetic fields, the diamagnetic effect of the Rydberg atom provides an order-of-magnitude increase in sensitivity to small magnetic field variations. Additional aspects, including quantum chaotic behavior, are discussed in Ma et al., “Paschen-Back effects and Rydberg-state diamagnetism invapor-cell electromagnetically induced transparency.” Phys.Rev.A. The discussion is in ,vo.95,061804(R), (June 27, 2017), which is incorporated herein by reference.

[0225] Now for reference Figure 21 The steps for quantifying magnetic field properties according to an embodiment of the present invention are described. In the first step 2101, a predetermined Rydberg atomic energy level or Rydberg-EIT spectrum in a strong magnetic field is calculated. 2103 FM-modulated measurement light is propagated in an atomic vapor chamber, and 2105 the spectral characteristics of the atomic vapor are measured. 2107 The measured spectral characteristics are compared with the calculated spectral characteristics, and 2109 matching spectra are identified. This provides 2111 for quantifying magnetic field properties.

[0226] Atom-based optical RF power / voltage transducers and sensors.

[0227] Now for reference Figure 26A and Figure 26B Another aspect of the invention will be described. Figure 26A A hybrid atom-based optical RF-power / voltage transducer and sensor, typically designated 2600, is schematically depicted. The hybrid atom-based optical RF-power / voltage transducer and sensor 2600 employs an atomic vapor chamber 2602 with integrated electrodes 2604, which are integrated into an RF receiver or circuitry 2608 for converting the RF signal of interest into an electric field within the chamber. The RF signal is optically measured via a field-sensitive atomic state spectral method. By directly converting the RF electrical signal into an atom-mediated optical reading, the atom-based transducer provides high-bandwidth (DC to terahertz), absolute (atomic) measurements of electrical power or voltage. Proof of this atom-based transducer in 60Hz electrical signal measurements is shown in [examples omitted]. Figure 26B As shown, it can be advantageously used as an RF receiver element as an antenna base in microwave pickup. In the measurement and receiver case, the spectral readings of the atomic chamber are used to detect and determine the equivalent power field of the electrical or electromagnetic signal of interest.

[0228] Figure 26B This diagram shows graphs of readings from an atom-based optical RF power / voltage transducer at six voltage levels for a 60 Hz electrical signal applied to the electrodes. An optical laser resonates near-field-sensitive Rydberg states of atoms, and the transmission of the probe laser through vapor is detected. The equivalent field power is then determined by comparing the detected transmission signal with known atomic responses. Depending on the detailed geometry of the selected electrodes and structure, as well as the electrical and thermal properties of the chosen materials, the atom detector readings can be used for atomic calibration of the RF power / voltage.

[0229] Atom-based optical RF power / voltage transducers and sensors, typically indicated as Mark 2700, and referenced Figure 27A and Figure 27B The description is as follows. The atom-based optical RF power / voltage transducer and sensor 2700 consists of a small cylindrical cesium vapor chamber with an integrated internal conductive plate. The conductive plate, or electrode, is a 0.5 mm thick ring spaced 4 mm apart, with one side of each ring fused to the chamber body and the other side fused to a window. As a result, the total path length through the chamber is 5 mm. The inner and outer diameters of the chamber 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. Therefore, two 0.7 mm thick ring electrodes are embedded within the vapor chamber, which is electrically connected to the outside.

[0230] Atomic vapor 2701 is contained within atomic vapor chamber compartment 2703, which has a window 2705 transparent to the beam used to excite atoms into Rydberg states, and another integrated window 2707 transparent to the EM field generated by the optically excited atomic medium for extracting the generated EM field. An EM filter 2710 blocks the transmission of the Rydberg EIT probe and coupler beams 103 and 104.

[0231] The embodiments of the invention described herein are intended to be exemplary only; the invention is not limited to the disclosed embodiments. Various changes and modifications will be apparent to those skilled in the art. All such variations and modifications are intended to fall within the scope of the invention as defined by any of the appended claims.

[0232] Additional teachings relating to the subject matter of this invention can also be found in the following publications, which are incorporated herein by reference:

[0233] ·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)

[0234] ·Simons et al., "Electromagnetically Induced Transparency(EIT)andAutler-Townes(AT)splitting in the presence of band-limited white Gaussiannoise," J.Appl Phvs .vol.123,203105(2018).

Claims

1. A method for sensing or measuring a first electromagnetic field, the method comprising: a. Excite the atoms of a gas occupying at least a portion of the test volume, which is within the same range as the first electromagnetic field, into a Rydberg state distribution; b. Construct the first electromagnetic field by placing it in an interference relationship with at least one other electromagnetic field; c. The propagation of at least one probe beam, which measures electromagnetic radiation at one or more frequencies, along a path traversing a test volume, wherein one or more frequencies overlap with the spectral characteristics of the atomic gas; d. Based at least on the changes in spectral characteristics, derive the phase of the first electromagnetic field as a physical property; as well as The phase of the first electromagnetic field is determined by: obtaining the net coupling based on the coherent sum of the Rabi frequencies of the two photons transitioning from the 5p state to the np state in the Rydberg state distribution, wherein the EIT line intensity carries phase information about the radio frequency (RF) field, and the phase of the first electromagnetic field is measured.

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

3. The method according to claim 2, wherein the atoms of the atomic vapor are selected from the group consisting of alkali metal atoms and alkaline earth metal atoms.

4. The method of claim 1, wherein the step of exciting atoms into a Rydberg state distribution comprises optically exciting atoms into a Rydberg state distribution.

5. The method of claim 1, wherein the step of exciting atoms into a Rydberg state distribution comprises electromagnetically induced transparency or electromagnetically induced absorption.

6. The method of claim 1, wherein the variation in spectral characteristics includes Autler-Townes splitting.

7. The method according to claim 1, wherein the physical characteristic of the first electromagnetic field is field amplitude.

8. The method of claim 1, wherein the first electromagnetic field is monochromatic, and wherein the physical property of the first electromagnetic field is its phase relative to a reference phase.

9. The method of claim 8, wherein the physical property of the first monochromatic electromagnetic field is its phase relative to a reference phase of the radio frequency (RF) field, which modulates one of the other electromagnetic fields using nonlinear optical elements.

10. The method of claim 1, wherein constructing the first electromagnetic field includes superimposing an additional static field or radio frequency (RF) field to place the first electromagnetic field in resonance with atomic transitions.

11. The method of claim 1, wherein constructing the first electromagnetic field includes modulating the first electromagnetic field prior to the measurement step.

12. The method of claim 11, wherein modulation comprises frequency modulation, amplitude modulation, step modulation, or a combination thereof.

13. The method of claim 1, wherein the Rydberg state distribution comprises at least one pair of states having non-zero dipole moments for interaction between atoms and radio frequency (RF) fields.

14. The method according to claim 1, further comprising the following step: a. Calculate the predetermined Rydberg atomic level or Rydberg-electromagnetically induced transparent EIT spectrum in the presence of an incoherent radio frequency (RF) noise field that exists in or constitutes the first electromagnetic field. b. To propagate light into the atomic vapor chamber; c. Spectral characteristics are measured using light propagating through an atomic vapor chamber; d. Identify the matching spectrum; and e. Determine the properties of the incoherent RF noise field.

15. The method according to claim 1, further comprising the following step: a. Calculate the predetermined Rydberg atomic energy levels or spectrum of atoms in a first electromagnetic field identical to a strong static magnetic field or a low-frequency magnetic field; b. Transmit at least one other electromagnetic field as an optical probe into the atomic vapor chamber; c. Measure the spectral characteristics of light propagating through the atomic vapor chamber; d. Identify the matching spectrum; and e. Derive the physical properties of a strong static magnetic field.

16. The method of claim 15, wherein the light is amplitude modulated or frequency modulated.

17. The method of claim 15, wherein the predetermined Rydberg atomic energy level or spectrum is used for the Rydberg atomic state or for the lower atomic state.

18. The method of claim 15, wherein one or more atomic isotopes or nuclides are used to obtain small magnetic field variations in a strong static magnetic field.

19. A sensor for detecting and / or measuring parameters characterizing an electromagnetic field, the sensor comprising: a. At least one of the materials and structures used to modulate electromagnetic fields; b. Atomic vapor contained within a shell, which is set within a conditioning material or structure; c. Excitation source, used to excite the atoms of atomic vapor into a Rydberg state distribution; d. A detector used to detect the probe beam after it has traversed the atomic vapor and generate a detector signal; as well as e. A processor for deriving parameters characterizing the electromagnetic field, based at least on detector signals. The electromagnetic field is monochromatic, and The parameter characterizing the electromagnetic field is its phase relative to a reference phase.

20. The sensor of claim 19, wherein at least one of the materials and structures used for regulating the electromagnetic field is a radio frequency (RF) resonator.

21. The sensor of claim 19, wherein at least one of the materials and structures used for regulating the electromagnetic field is a waveguide.

22. The sensor of claim 19, wherein at least one of the materials and structures used to modulate the electromagnetic field is a metamaterial.

23. The sensor of claim 19, wherein at least one of the materials and structures used for regulating the electromagnetic field includes an antenna.

24. The sensor of claim 19, wherein at least one of the materials and structures used for regulating the electromagnetic field is one or more electrodes.

25. The sensor according to claim 19, wherein: At least one of the materials and structures is conductive, and the electromagnetic field is modulated by converting current or voltage into an electromagnetic field within atomic vapor, and wherein the current or voltage or associated power through the resistor is derived from the detector signal.

26. The sensor of claim 19, wherein the excitation source for exciting the atoms of the atomic vapor into a Rydberg state distribution comprises one or more light beams to establish an electromagnetically induced transparent (EIT) or an electromagnetically induced absorbed (EIA) in the atomic vapor.

27. The sensor of claim 19, wherein the housing containing atomic vapor is a glass vapor chamber.

28. The sensor of claim 19, wherein the material or structure for regulating the electromagnetic field comprises a frequency-selective filter or reflector for the electromagnetic field entering or exiting the atomic vapor shell.

29. The sensor of claim 19, wherein the detector is used to detect the electromagnetic field generated by the excitation of atomic vapor and the emission from atomic vapor.

30. The sensor of claim 19, wherein the electromagnetic field is associated with at least one of a vertical electromagnetic wave and a traveling electromagnetic wave.

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