Detection of Radio Frequency Electromagnetic Radiation Using a Vapor Cell Sensor and a Comspectrum

Abstract

In general aspects, a vapor cell sensor can be used to detect radio frequency (RF) electromagnetic radiation. In some aspects, the system includes a laser system configured to generate a laser signal including first and second laser signals. The system also includes an optical comb generator and a vapor cell sensor. The optical comb generator is configured to generate a comb spectrum based on the first laser signal. The comb spectrum includes comb lines at respective comb frequencies. The vapor cell sensor contains vapor and is configured to generate an optical spectrum based on the interaction of the vapor with the comb spectrum and the second laser signal. The system also includes an optical detector configured to detect characteristics of the optical spectrum at one or more of the comb frequencies.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 63 / 392,404, entitled "Detecting Radio Frequency Electromagnetic Radiation Using Vapor Cell Sensors," filed July 26, 2022. This application also claims priority to U.S. Patent Application No. 18 / 296,307, entitled "Detecting Radio Frequency Electromagnetic Radiation Using Vapor Cell Sensors and Comb Spectra," filed April 5, 2023. The disclosures of these priority applications are incorporated herein by reference in their entireties. [Background technology]

[0002] The following description relates to the detection of radio frequency electromagnetic radiation using a vapor cell sensor. Summary of the Invention

[0003] A vapor cell sensor can contain a vapor or gas within an enclosed volume, such as a volume defined by a chamber. The vapor or gas can be used as a medium that interacts with radio frequency (RF) electromagnetic radiation incident on the vapor cell sensor. A beam of light, such as that generated by a laser, can be sent through the vapor or gas to probe and measure the vapor or gas's response to the RF electromagnetic radiation. In this way, the vapor cell sensor can detect RF electromagnetic radiation and can often be useful in determining the characteristics of the RF electromagnetic radiation. [Brief explanation of the drawings]

[0004]

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Mathematics

DETAILED DESCRIPTION OF THE INVENTION

[0005] In a general aspect, this specification describes a system capable of detecting radio frequency (RF) electromagnetic radiation. In many implementations, the system includes a vapor cell sensor configured to detect RF electromagnetic radiation using a vapor having one or more atomic Rydberg states. The vapor can change electromagnetic induced transparency (EIT) or electromagnetic induced absorption (EIA) when interacting with RF electromagnetic radiation. These changes can change the optical transmission spectrum of the vapor. The system also includes an optical comb generator configured to generate a comb spectrum in response to receiving a beam of light (e.g., a beam of laser light). The comb spectrum includes comb lines at respective comb frequencies and is used to probe the vapor at a plurality of comb frequencies.

[0006] The detection of RF electromagnetic fields using atomic Rydberg states is a promising high-sensitivity technique that can provide an exceptional detection bandwidth. A vapor cell sensor containing a vapor of Rydberg atoms or molecules can also provide a fully dielectric structure with minimal perturbation to the RF electromagnetic field. In contrast, an antenna is typically composed of a metallic material and can potentially distort the RF electromagnetic field. In some cases, the systems described herein use, in part, a vapor cell sensor and an optical comb generator to detect RF electromagnetic fields. During operation, the optical comb generator generates an optical signal that detects (e.g., measures) the optical properties of the vapor, including changes in the transparency of the vapor induced by the RF electromagnetic field. The optical signal corresponds to a comb spectrum having comb lines at respective comb frequencies. In many implementations, the system includes a probe laser and a coupling laser. The optical comb generator receives an optical probe beam from the probe laser to generate the comb spectrum. The coupling laser generates an optical coupling beam tuned to the Rydberg excited state of the vapor.

[0007] In some implementations, self-heterodyne spectroscopy is achieved by mixing the comb spectrum with a local oscillator signal obtained from the probe laser and shifted by an acousto-optic modulator. In some variations, an electro-optic modulator and an arbitrary waveform generator are used to emit a chirped sine function. The chirped sine function can generate, for example, a flat frequency comb spectrum with a tooth spacing of 10 kHz and a frequency span of 100 MHz. In these variations, the electromagnetically induced transparency line shape can be resolved with a linewidth of less than 5 MHz, both with and without laser locking. Also, the Autler-Townes splitting of the transmission peak can be measured, with a sensitivity of 2.3 μV·cm -1 Hz -1 / 2 and a sensitivity of 66 μV·cm -1RF fields as low as 1000 kHz can be detected. The corresponding detection method can offer a significant simplification for the readout of Ortler-Townes splitting, since in many cases neither the probe nor the coupling laser needs to be tuned and slow drift of the lasers can be tolerated. This detection method also allows for the detection of pulsed RF fields (e.g., their amplitude) when the incident RF field splits the electromagnetically induced transparency peak by the Ortler-Townes process.

[0008] Referring now to FIG. 1 , a schematic diagram of an example system 100 for detecting radio frequency (RF) electromagnetic radiation is shown. In some implementations, the example system 100 uses an electronic optical comb for Rydberg atom-based electrical measurements with EIT-based or EIA-based transmission spectra. In some implementations, the example system 100 performs self-calibrating absolute power measurements by measuring the frequency division of the spectral lineshape. The spectral lineshape is based on precise electronic transitions of the vapor, and therefore measurements based on its characteristics (e.g., frequency division) are self-calibrating. The frequency division can correspond to the separation of two peaks in the spectral lineshape, an example of which is shown in the lower right portion of FIG. 2B . In these implementations, the example system 100 can experimentally measure the value of the frequency division, such as by operation of an optical detector. The example system 100 can then use this measurement to determine the electric field strength of the RF electromagnetic radiation interacting with the vapor. Equation (1), described below, can be used to calculate the electric field strength (E) of the RF electromagnetic radiation by using a measurement (e.g., Ω). RF ) can be used. Other types of applications and measurements are possible.

[0009] The exemplary system 100 includes a laser system 102 configured to generate a laser signal (e.g., a beam of laser light) including first and second laser signals 104, 106 (e.g., first and second beams of laser light). For example, the laser system 102 may include a probe laser 102a and a coupling laser 102b configured to generate a probe laser signal 104 and a coupling laser signal 106, respectively. Examples of such lasers include semiconductor lasers, fiber lasers, amplified lasers, and the like. The probe laser 102a and the coupling laser 102b may optionally be locked to their respective reference frequencies. Also, the laser system 102 may optionally include a third laser configured to generate a third laser signal. Additional lasers are also possible. The exemplary system 100 can include optical components such as lenses, mirrors, diffraction gratings, beam splitters, etc. to define one or more optical paths of the laser signal. FIG. 1 shows two mirrors 108a, 108b for directing the coupling laser signal 106 along an optical path 110 that is opposite to the probe laser signal 104 (or its derivative). However, other numbers and configurations of optical paths are also possible.

[0010] The exemplary system 100 also includes a vapor cell sensor 112 having vapor therein. In many cases, the vapor is a vapor of a Rydberg atom or molecule, such as a gas of Group IA atoms (e.g., Cs or Rb). The vapor cell sensor 112 can also have a body or housing that encloses an internal volume for containing the vapor. The body or housing can be formed of a dielectric material such as silicon, silicon oxide, or borosilicate glass. Other dielectric materials are also possible. An exemplary configuration of the vapor cell sensor 112, including examples of dielectric materials, is described in U.S. Patent No. 10,859,981, entitled "Vapor Cells Having One or More Optical Windows Bonded to a Dielectric Body".

[0011] In some embodiments, the probe laser signal 104 has a probe frequency that matches the probe photoelectron transition of the vapor, and the coupling laser signal 106 has a coupling frequency that matches the coupling photoelectron transition of the vapor. The coupling photoelectron transition may share an energy level common to the probe photoelectron transition. For example, the vapor may include first, second, and third electronic energy levels, each having progressively higher energy. The probe photoelectron transition can be defined by a first energy gap between the first and second electronic energy levels, and the coupling photoelectron transition can be defined by a second energy gap between the second and third electronic energy levels. However, other configurations of the electronic energy levels (e.g., a configuration in which one or more subsequent electronic energy levels are lower than the starting electronic energy level) are also possible.

[0012] In these embodiments, the vapor includes RF electron transitions configured to change the absorption of light by one or both of the probe and coupling photoelectron transitions in response to absorption of RF electromagnetic radiation. The RF electron transitions can correspond to electron transitions defined by a pair of electronic energy levels at least one of which is different from the first, second, and third electronic energy levels. The RF electron transitions can each have a third energy gap that is smaller in magnitude than the first and second energy gaps of the first and second photoelectron transitions, respectively. In an embodiment where the laser system 102 is configured to generate a laser signal in addition to the probe laser signal and the coupling laser signals 104, 106, the additional laser signal can have respective frequencies matched to different photoelectron transitions of the vapor. In certain cases, the absorption of light by these photoelectron transitions can also be changed by the RF electron transitions.

[0013] FIG. 2A shows a schematic diagram of an exemplary vapor cell sensor 200 positioned proximate to an antenna 202 configured to generate RF electromagnetic radiation. The exemplary vapor cell sensor 200 is configured to receive an input optical signal (e.g., a laser signal) and generate one or more output optical signals in response thereto. In FIG. 2A, the exemplary vapor cell sensor 200 receives a probe laser signal 204 and a coupling laser signal 206. The probe laser signal 204 and the coupling laser signal 206 are generated by respective lasers. Examples of such lasers include semiconductor lasers, fiber lasers, amplified lasers, wavelength tunable semiconductor lasers, and the like. The probe laser signal 204 and the coupling laser signal 206 pass through the exemplary vapor cell sensor 200 along a common optical path. The direction of travel along the common optical path may be the same for both beams. However, in some variations as shown in FIG. 2A, the laser signals travel in opposite directions along the common optical path. Other optical configurations are possible by angularly tuning the laser signals to cancel Doppler shifts.

[0014] While passing through the exemplary vapor cell sensor 200, the probe laser signal and the coupling laser signals 204, 206 interact with the vapor contained within the sealed container of the exemplary vapor cell sensor 200. The face 208 of the sealed container facing the antenna 202 can be formed of a dielectric material that is transparent to electromagnetic radiation and thereby functions as a window for electromagnetic radiation. The other faces of the sealed container can also be formed of a dielectric material. Along with the reception of the probe laser signal 204 and the coupling laser signal 206, the exemplary vapor cell sensor 200 can also receive RF electromagnetic radiation from the antenna 202 through the face 208 of the sealed container. The RF electromagnetic radiation can change the optical transmission of the probe laser signal 204 passing through the exemplary vapor cell sensor 200, which is detected (e.g., measured) by an optical detector 210 (e.g., a photodiode). The measurement of the optical transmission or the probe laser signal 204 can enable the exemplary vapor cell sensor 200 to detect and measure the characteristics of the RF electromagnetic radiation. In many cases, this change is caused by the RF electromagnetic radiation changing the absorption coefficient of the vapor (e.g., with respect to the wavelength of the probe laser signal 204).

[0015] The measurement of the characteristics of the RF electromagnetic radiation can depend on two or more photoelectronic transitions associated with the vapor. For example, FIG. 2B shows a schematic diagram of an exemplary electronic energy level structure for two-photon measurements based on Rb atoms in the vapor state. In FIG. 2B, a laser beam is used to access the photoelectronic transitions from 5S 1 / 2 to 5P 3 / 2 and from 5P 3 / 2 to 53D 5 / 2 For example, a probe laser signal having a frequency of approximately 780 nm can be used to access the photoelectronic transition from 5S 1 / 2 to 5P 3 / 2 and a laser beam is used to access the photoelectronic transition from 5P 3 / 2 to 53D 5 / 2A coupling laser signal having a frequency of about 480 nm can be used to access the optoelectronic transition. However, other types of lasers or laser systems can also be used. The lower right inset of FIG. 2B shows the spectral line shape of the optical transmission of the probe laser signal through the Rb vapor. The upper part of the inset corresponds to the state where there is no RF electromagnetic radiation, and the lower part of the inset corresponds to the state where there is RF electromagnetic radiation. Thus, the inset shows that the spectral line shape can change when the RF electromagnetic radiation interacts with the Rb vapor. In some cases, such as shown in FIG. 2B, the frequency range of the spectral line shape is centered on the frequency of the probe laser signal. In some cases, the spectral line shape is symmetric about this center.

[0016] During the measurement of the RF electromagnetic radiation, the transmission of the light from the probe laser 204 is recorded in the presence of the light from the coupling laser 206. For example, RF electromagnetic radiation of about 14 GHz changes the magnitude of the transmission such that the 54P of the vapor 3 / 2 to 53D 5 / 2It can interact with photo - electron transitions. When the RF electromagnetic radiation does not interact with the Rb vapor, as shown in the upper graph of the inset in FIG. 2B, a narrow peak is observed in the light transmission of the probe beam of light that would normally be absorbed. Such a phenomenon is sometimes called electromagnetically induced transparency (EIT). EIT can arise from the interference between different possible absorption paths set by the interaction of the vapor and the light - irradiated field. The absorption by the vapor is suppressed by such interference, thereby enhancing the transmission through the vapor that would normally absorb. Other phenomena can also occur. For example, electromagnetic induced absorption (EIA) can also arise from the interference between different possible absorption paths, in which case the absorption (less transmission) of the vapor is enhanced. In some cases, a third laser signal can be used to induce EIA. In these cases, the probe laser signal and the coupling laser signal produce EIT, but a third laser signal is used to induce absorption characteristics within the EIT spectral line shape. Also, by applying different detunings of the laser signal relative to the photo - electron transition of the vapor, it is possible to set the laser signal so as to form a mode in which EIT is used to measure the characteristics of the RF electromagnetic radiation.

[0017] When the RF electromagnetic radiation interacts with the Rb atoms in the vapor, and particularly when the RF electromagnetic radiation has an electric - field component that is near - resonant or resonant with a third photo - electron transition of the Rb vapor, absorption characteristics are induced within the narrow peak of the probe light transmission, as shown in the lower part of the inset. The absorption characteristics can split the narrow peak of the probe light transmission into two transmission peaks. Since the Rubidium atomic transition has a large transition dipole moment and the amplitude is converted into a frequency difference, the measurement of the narrow peak and the absorption characteristics can be sensitive to the RF electromagnetic radiation received by the exemplary vapor cell sensor 200. Since EIT is a coherent multi - photon process, it is sub - Doppler and can thus be performed in the vapor cell sensor with high spectral resolution.

[0018] Returning now to FIG. 1 for reference, the exemplary system 100 includes an optical comb generator 114 configured to generate a comb spectrum 116 in response to receiving a probe laser signal 104 (or a portion 104a thereof). In the embodiment shown in FIG. 1, the comb spectrum 116 is an optical signal generated by the optical comb generator 114, and the optical signal has a comb-shaped frequency profile defined by comb lines at respective comb frequencies. The optical comb generator 114 can be based on an electro-optic modulator, a mode-locked laser, an optical microresonator, a nonlinear optical fiber, or an acousto-optic modulator. Other types of optical comb generators are also possible. In some variations, the optical comb generator 114 includes an electro-optic modulator (EOM) 114a and an arbitrary waveform generator (AWG) 114b. The electro-optic modulator 114a can communicate with the arbitrary waveform generator 114b. FIG. 1 shows a single electro-optic modulator 114a communicating with a single arbitrary waveform generator 114b, but other configurations of these components are possible. For example, the optical comb generator 114 may include two or more electro-optic modulators communicating with a single arbitrary waveform generator. As another example, the optical comb generator 114 may include a plurality of electro-optic modulators communicating with different respective arbitrary waveform generators. These configurations may enable the optical comb generator 114 to increase the number of comb lines in the comb spectrum 116, or increase the bandwidth of the comb spectrum 116, or both. Other advantages may also exist.

[0019] The vapor of the vapor cell sensor 112 is configured to generate an optical spectrum 118 based on the interaction between the comb spectrum 116 and the coupling laser light 106 and the vapor. In the embodiment shown in FIG. 1, the optical spectrum 118 is an optical signal supplied to the optical detector 120 (e.g., a photodiode). The exemplary optical spectrum 118 represents the optical transmission of the vapor at the comb frequency. The optical spectrum 118 also includes characteristics (e.g., amplitude, polarization, phase, etc.) that change in response to RF electromagnetic radiation interacting with the vapor. Such a change in the optical spectrum 118 caused by the vapor cell sensor 112 may correspond to a change in the characteristics of the RF electromagnetic radiation (e.g., changes in power, angular direction, angular shift, etc.). In many cases, a detectable change in the characteristics of the optical spectrum 118 enables the exemplary system 100 to detect the RF electromagnetic radiation incident on the vapor cell sensor 100 and determine one or more characteristics of the RF electromagnetic radiation.

[0020] The exemplary system 100 includes an optical detector 120 configured to detect (e.g., measure) the characteristics of the optical spectrum 118 at one or more of the comb frequencies. In some variations, the optical detector 120 is configured to detect the characteristics of the optical spectrum 118 at multiple comb frequencies (e.g., a subset of the comb frequencies, all of the comb frequencies, etc.). For example, the optical detector 120 may be configured to detect the characteristics of the optical spectrum 118 at two or more comb frequencies, and such detection can be performed simultaneously (e.g., in parallel) at those two or more comb frequencies. In some cases, the optical detector 120 is configured to simultaneously detect the characteristics of the optical spectrum 118 at all of the comb frequencies. Examples of characteristics include the amplitude of the optical spectrum 118, or the polarization of the optical spectrum 118, or the phase of the optical spectrum 118, or combinations thereof. Other characteristics of the optical spectrum 118 are also detectable.

[0021] During operation, the optical comb generator 114 can enable the exemplary system 100 to determine the profile of an EIT-based or EIA-based peak over a wide bandwidth. For example, each comb frequency of the comb spectrum 116 can enable the exemplary system 100 to simultaneously measure peaks at multiple frequencies over the range of frequencies occupied by the peak. Such simultaneous measurements are significantly faster than repeatedly measuring individual frequencies over that range. The simultaneous measurements can also enable the exemplary system 100 to more accurately determine the profile of the peak, particularly in situations where the peak changes rapidly in response to variations in RF electromagnetic radiation.

[0022] FIG. 3 shows a schematic diagram of an exemplary electronic energy level structure for two-photon measurements based on Cs atoms in the vapor state. 6S 1 / 2 energy level to 6P 3 / 2 As indicated by a plurality of comb lines extending towards the 6S 1 / 2 to 6P 3 / 2 photoelectron transition, the comb spectrum is used for the interaction. The comb spectrum is generated from a probe laser signal having a frequency of about 852 nm and may be similar to the comb spectrum 116 described with respect to FIG. 1. 6P 3 / 2 to 55D 5 / 2 A coupling laser signal having a frequency of about 509 nm is used for the interaction with the photoelectron transition from 6P

[0023] Cs atoms in the vapor state are also in 53F 7 / 2 to 55D 5 / 2has a photoelectron transition thereto. RF electromagnetic radiation can interact with this transition, thereby 1 / 2 from 6S 3 / 2 to 6P 3 / 2 and from 6P 5 / 2 to 55D 1 / 2 changing the absorption of light by one or both of the photoelectron transitions. For example, as shown in FIG. 3, RF electromagnetic radiation of about 19.5 GHz may be used to change the absorption of the comb spectrum by the photoelectron transition from 6S 3 / 2 to 6P. Such absorption can serve as the basis for the detection of RF electromagnetic radiation and the measurement of its characteristics. The presence of multiple comb lines enables the simultaneous decomposition of the profile of the EIT peak (e.g., its spectral line shape) at multiple frequencies. This function contrasts with the probe laser light shown in FIG. 2B, for which it is necessary to vary its single frequency to iteratively decompose the all-optical transmission spectrum. The accuracy of such an iterative scan is susceptible to the effects of changes in the optical transmission spectrum or the laser during the scan period.

[0024] Next, referring back to FIG. 1, in some implementations, the exemplary system 100 includes a spectrum analyzer 122 that communicates with an optical detector 120. The spectrum analyzer 122 is configured to generate data representing the characteristics of the optical spectrum 118 at one or more comb frequencies. In many variations, the spectrum analyzer 122 is configured to generate data representing the characteristics of the optical spectrum 118 at multiple comb frequencies (e.g., a subset of comb frequencies, all comb frequencies, etc.). For example, the optical detector 120 can be configured to detect the characteristics of the optical spectrum 118 at two or more comb frequencies, and the spectrum analyzer 122 is configured to generate data representing the characteristics of the optical spectrum 118 at the two or more comb frequencies. In further implementations, the exemplary system 100 can include a computer 124 that communicates with the spectrum analyzer 122. The computer 124 can have one or more processors and a memory configured to store instructions for the one or more processors. When executed by the one or more processors, the instructions can be configured to perform operations such as determining the amplitude of RF electromagnetic radiation, or the polarization of RF electromagnetic radiation, or the phase of RF electromagnetic radiation, or a combination thereof, based on the data generated by the spectrum analyzer 122.

[0025] In some implementations, the exemplary system 100 includes an acousto-optic modulator (AOM) 126 configured to split the probe laser signal 104 into a first portion and a second portion 104a, 104b. The first portion 104a is received by the optical comb generator 114 and used to generate the comb spectrum 116. The second portion 104b can have a frequency higher than that of the first portion and can be received by the optical detector 120.

[0026] In some implementations, RF electromagnetic radiation (e.g., RF pulses or other forms of RF radiation) is received by the vapor cell sensor 112. The RF electromagnetic radiation can be generated by an antenna or other types of RF generating devices that are remote from the exemplary system 100. The antenna or device can operate independently of the exemplary system 100. In some cases, the exemplary system 100 can include a source of RF electromagnetic radiation. The source of RF electromagnetic radiation can be configured to radiate RF electromagnetic radiation towards the vapor cell sensor 112. In FIG. 1, the source of RF electromagnetic radiation is shown as a horn antenna 128. However, other types of sources (e.g., other types of antennas) are also possible. In further implementations, the exemplary system 100 can include a pulse generator 130 and an RF generator 132. The pulse generator 130 can communicate with the RF generator 132 and can be configured to generate a signal representing each pulse of the RF electromagnetic radiation (e.g., its shape). For example, the pulse generator 130 can generate a square wave with a frequency of 1 Hz and a duty cycle of 50%. However, other types of signals (e.g., sine waves, sawtooth waves, etc.) are also possible. The RF generator 132 is configured to generate a pulse of RF electromagnetic radiation in response to receiving a signal from the pulse generator 130. In the embodiment shown in FIG. 1, the RF pulse is radiated by the horn antenna 128, e.g., as a short burst of RF energy radiated from the horn antenna 128.

[0027] During operation, the exemplary system 100 can be used to detect RF electromagnetic radiation (e.g., pulses of RF electromagnetic radiation). Such detection may include determining the characteristics of the RF electromagnetic radiation. For example, the exemplary system 100 can receive RF electromagnetic radiation at the vapor cell sensor 112. The RF electromagnetic radiation can be generated by any source of RF electromagnetic radiation (e.g., horn antenna 128, unknown source, remote source, etc.). The exemplary system 100 can also generate a comb spectrum 116 in response to receiving the probe laser signal 104 (or its first portion 104a) at the optical comb generator 114. The exemplary system 100 can further generate an optical spectrum 118 by interacting the comb spectrum 116 and the coupling laser signal 106 with the vapor in the vapor cell sensor 112.

[0028] The optical detector 120 enables the exemplary system 100 to detect (e.g., measure) the characteristics of the optical spectrum 118 at one or more comb frequencies. In many variations, the optical detector 120 enables the exemplary system 100 to detect the characteristics of the optical spectrum 118 at a plurality of comb frequencies (e.g., a subset of comb frequencies, all comb frequencies, etc.). Such detection can be performed simultaneously. For example, the exemplary system 100 can simultaneously detect the characteristics at all comb frequencies. The characteristics of the optical spectrum 118 can be the amplitude of the optical spectrum 118, or the polarization of the optical spectrum 118, or the phase of the optical spectrum, or a combination thereof. However, other characteristics are also possible. The exemplary system 100 can also generate data representing the characteristics of the optical spectrum 118 at one or more comb frequencies by operation of the spectrum analyzer 122. When the RF electromagnetic radiation is received by the vapor cell sensor 112, the computer 124 can determine the amplitude of the RF electromagnetic radiation, or the phase of the RF electromagnetic radiation, or the polarization of the RF electromagnetic radiation, or a combination thereof.

[0029] In some embodiments, the performance of the exemplary system 100 can be improved by removing the background optical spectrum from the optical spectrum 118. For example, the exemplary system 100 can generate a background optical spectrum by the interaction of the comb spectrum 116 and the vapor in the absence of the coupling laser signal 106. The background optical spectrum represents, at least in part, the background optical transmission of the vapor at the comb frequencies of the comb spectrum 116. The exemplary system 100 also detects the characteristics of the background optical spectrum at one or more comb frequencies (e.g., a subset of the comb frequencies, all of the comb frequencies, etc.). The characteristics can be the amplitude of the background optical spectrum, the polarization of the background optical spectrum, or the phase of the background optical spectrum, or a combination thereof. Other characteristics are possible. The spectrum analyzer 122 can then generate first and second data. The first data represents the optical characteristics of the optical spectrum 118 at one or more comb frequencies. Similarly, the second data represents the optical characteristics of the background optical spectrum at one or more comb frequencies. Using the difference between the first data and the second data, when RF electromagnetic radiation is received by the vapor cell sensor 112, the computer 124 can determine the amplitude of the RF electromagnetic radiation, or the phase of the RF electromagnetic radiation, or the polarization of the RF electromagnetic radiation, or a combination thereof.

[0030] In some implementations, the exemplary system 100 can generate a reference optical signal from the probe laser signal 104. The reference optical signal can function as a local oscillator for the exemplary system 100 and can enable the exemplary system 100 to perform self-heterodyne spectroscopy. For example, the exemplary system 100 can use an acousto-optic modulator 126 to split the first laser signal 104 into a first portion and a second portion 104a, 104b. The first portion 104a is received by an optical comb generator 114 to generate a comb spectrum 118. The second portion 104b is shifted to a frequency higher than that of the first portion 104a by the operation of the acousto-optic modulator 126. The second portion 104b, which functions as a reference optical signal (or local oscillator), can then be combined with the optical spectrum 118 from the vapor cell sensor 112 to generate a heterodyne optical spectrum 134. The exemplary system 100 can then detect the characteristics of the heterodyne optical spectrum 134 at one or more comb frequencies (e.g., a subset of the comb frequencies, all of the comb frequencies, etc.). Examples of the characteristics of the heterodyne optical spectrum 134 include the amplitude of the heterodyne optical spectrum 134, the polarization of the heterodyne optical spectrum 134, and the phase of the heterodyne optical spectrum 134. Other characteristics are possible.

[0031] The exemplary system 100 can provide advantages over standard techniques for detecting RF electromagnetic radiation. For example, when the vapor cell sensor 112 is in the Autler-Townes detection mode, standard techniques typically require scanning at least one of the probe laser and the coupling lasers 102a, 102b over an optical transmission spectrum to make measurements. When a pulse of RF electromagnetic radiation is detected, the pulse can split EIT-based or EIA-based peaks, and only changes in optical transmission are observed. The fact that it is not necessary to scan the probe laser or the coupling lasers 102a, 102b can be a significant advantage. The comb spectrum 116 can overcome the challenges associated with scanning the probe laser and the coupling lasers 102a, 102b. There can be other advantages as well.

[0032] In some implementations, the comb spectrum 116 is generated using an electro-optic modulator 114a, which is further driven by an arbitrary waveform generator 114b. The form of the drive signal from the arbitrary waveform generator 114b generates a comb spectrum having a controllable frequency spread (or overall bandwidth) and comb tooth spacing. The comb spectrum 116 is defined by a series of "teeth" or comb lines that can be large enough such that the density within the frequency range (or bandwidth) is quasi-continuous across the frequency of interest of the probe laser. For example, the comb spectrum 116 can correspond to the total amount of comb lines at discrete positions within the frequency range. Thus, one or both of the spacing between the comb lines of the comb spectrum 116 and the bandwidth can be controlled to make the comb spectrum 116 quasi-continuous. In some cases, the quasi-continuous comb spectrum 116 corresponds to a spacing greater than half the linewidth of the probe laser signal 104a. In some cases, the comb spectrum 116 can be based on a frequency spacing between adjacent comb lines that does not exceed 100 kHz. In further cases, such as when a third laser signal is used, the frequency spacing does not exceed 10 kHz.

[0033] The probe laser 102a is selected as the light source of the comb spectrum 116 because it may be necessary to resolve the optical transmission associated with each comb line or detuning from resonance. To that end, after passing through the vapor cell sensor 112, the comb spectrum 116 can be heterodyned (or synthesized) using the reference optical signal 104b (or local oscillator). The heterodyne optical spectrum 134 is based on the fundamental frequency of the probe laser 102a but is frequency-shifted so that the bandwidth of the comb spectrum 116 is detectable by the spectrum analyzer 122.

[0034] For example, if the bandwidth of the comb spectrum 116 is 100 MHz, the comb spectrum 116 may be upshifted by 120 MHz so that the entire bandwidth of the heterodyne frequency is detectable by a high-speed photodiode (e.g., optical detector 120). A swept-frequency spectrum analyzer can be used, or a real-time spectrum analyzer can be used. At frequencies below 5 GHz, real-time digital signal processing techniques may be convenient for a device that can be used in the actual field. This method can be useful because in the amplitude method where the amplitude of the optical spectrum 118 is used to estimate the RF electromagnetic field amplitude, the entire line shape can be measured, whereby small frequency fluctuations at the center of the peak are observable and can be compensated for, reducing noise. Similar principles can be used to perform comb spectroscopy using a three-photon process by modulating the probe laser 102a. Other multi-photon schemes are also possible.

[0035] In some implementations, the exemplary system 100 enables frequency comb spectroscopy that does not require tuning the probe laser and the coupling lasers 102a, 102b. To measure substantially all actual detunings simultaneously, sufficient power can be allocated to each comb line in the comb spectrum 116. Also, signal processing can compensate for large laser fluctuations up to 10 MHz, and thus the lasers do not need to be precisely locked (although locking can still be advantageous). However, in certain cases, one or both of the probe laser and the coupling lasers 102a, 102b are locked to a reference frequency. The reference frequency may be different for the probe laser and the coupling lasers 102a, 102b.

[0036] In the pulsed detection mode, it may be advantageous to know the absolute amplitude of the pulse of RF electromagnetic radiation. When the pulse divides a transmission peak, the signal received by the optical detector 120 may saturate the optical detector 120 and the pulse amplitude is unknown. By measuring with the comb spectrum 116, the Autler-Townes peak splitting can be measured and the pulse amplitude is determined. In the amplitude mode, the change in peak height can be fitted to a model, leading to a better determination of the pulse amplitude, so the measurement of the entire peak can also be useful for determining the pulse amplitude. Thus, since the pulse amplitude is important for applications such as clutter removal in radar, the exemplary system 100 may be useful for detecting pulses of RF electromagnetic radiation. Currently, considering the drift and fluctuations of standard radar antennas, pulse amplitude detection is not feasible. The exemplary system 100 can provide the possibility of using pulse amplitude detection in radar for applications such as clutter removal.

[0037] Next, referring to FIGS. 4A to 4E, graphs showing examples of comb spectra and optical transmission peaks are shown. Specifically, FIG. 4A shows a graph showing an example of a comb spectrum determined by simulation (top) and experiment (bottom). FIG. 4B shows an enlarged portion of the graph of FIG. 4A showing the individual teeth of an exemplary comb spectrum measured and simulated by experiment in the frequency range of 150.00 MHz to 150.10 MHz. The exemplary comb spectrum consists of 10,000 teeth having a frequency span of 100 MHz and a power variation of 3.06 dB. The experimentally measured comb spectrum has a slight change in the power of the teeth across the comb width but has excellent similarity to the simulated comb spectrum.

[0038] The exemplary comb spectra of FIGS. 4A to 4B can be used to generate optical transmission peaks. For example, FIG. 4C shows a graph showing an example of an optical transmission peak in the absence of an RF electromagnetic field. This peak is obtained using the comb spectra of FIGS. 4A to 4B with both the probe laser and the coupling laser locked. However, the background spectrum has been removed from the transmission signal to generate the peak. The average of 50 scans with a duration of 200 ms per scan was taken. The resulting Lorentz fit of the transmission peak having a full width at half maximum of 4.9 MHz is shown.

[0039] To show the possibility of measuring the transmission signal without locking the laser, the transmission signals in the state where neither the coupling laser nor the probe laser is locked were also collected. The data was obtained from the exemplary comb spectra of FIGS. 4A to 4B, and the free-running laser is shown in the graph of FIG. 4D. Due to the drift of the non-locked laser wavelength, the scanning time was shortened to 1 ms and no averaging was performed. Although the signal-to-noise ratio decreases, the peak can be clearly seen. The optical transmission peak has a full width at half maximum of 4.7 MHz. The data shown in FIG. 4D demonstrates that the frequency comb enables the measurement of the transmission peak without laser locking. To show the influence of laser drift and jitter on the transmission spectrum, four consecutively collected transmission peaks are shown in the graph of FIG. 4E. The ability to probe the transmission spectrum without the need to lock the probe laser or the coupling laser is an advantage of frequency comb spectroscopy. Also, the fact that there is no need to scan the laser greatly simplifies the optical control system required for measurement in some use cases.

[0040] FIG. 5 shows a graph showing an example of asymmetry in three frequency combs (or comb spectra) that are varied by the background absorption of Cs vapor in the vapor cell. As a result of such background absorption, a Doppler-broadened spectrum may occur. For example, the frequency comb can be affected by the Doppler-broadened Cs background by detuning the frequency comb to different respective center frequencies. "Modulation" can be used in addition to the spectrum to detune the frequency comb and map the Doppler-broadened spectrum of Cs. In FIG. 5, the comb spectrum is passed through the vapor cell in the absence of the coupling laser signal.

[0041] In some variants, an RF electromagnetic field can induce auto-Lorentz splitting of the peaks that gives rise to two transmission windows with separated frequencies 55D 5 / 2 The frequency separation can be represented by the following equation (1) in certain cases.

[0042] [Number] In Equation (1), the transition dipole moment is d = 6294ea0, and E is the electric field strength of the RF electromagnetic field. Figure 6A shows the splitting of the EIT peak calculated using Equation (1) as a function of the RF electric field strength in the Autler-Townes regime. When the probe laser is scanned, the spectral splitting due to the Doppler effect can be changed by a factor of λ p / λ c . To account for the slope of the comb profile shown in Figure 4A, the split peaks can be leveled by removing the linear background fit. Since the power output of the horn antenna is related to the electric field strength (e.g., P ∝ E 2 ), the square root of the RF electromagnetic power (P) can have a linear relationship with respect to the spectral splitting of the EIT characteristic as shown in Figure 6C.

[0043] At low RF electric field strengths, the magnitude of the transmission peak splitting may be difficult to measure directly, but it causes a decrease in the amplitude of the transmission peak. Figure 6B shows the change in the peak amplitude for the case of low radio frequency electromagnetic field power. The peak amplitude difference obtained by averaging the peak amplitude over a 0.4 MHz span centered at 162 MHz can be quadratic in the amplitude regime for certain cases. Figure 6C shows an example of this quadratic relationship. The weakest detectable electromagnetic field that can be defined as the last measured value before the change in the peak amplitude drops below zero is 66 ± 0.4 μV / cm -1 .

[0044] To determine the system's sensitivity limit and how fast data can be obtained, the acquisition time can be shortened. The spectrum analyzer scan time can also be shortened to 1 ms, and the scan range can be reduced to 10 MHz. Next, the average of five scans is taken for each point. The bandwidth of the spectrum analyzer is also increased to 5 kHz, thereby reducing the signal-to-noise ratio. To make the sensitivity more comparable to other results, the sampling range is reduced to 0.1 MHz during post-processing. Taken together, these changes can shorten the effective scan time per measurement from 20 s to 100 μs while still allowing the observation of the total transmission peak. Figure 7A shows the change in the transmission peak amplitude induced by the RF electromagnetic field obtained using these measurement settings as a function of the RF electromagnetic field strength. The difference in peak amplitudes is shown in Figure 7B, and this difference is 234 ± 1.2 μV / cm -1 of the minimum detectable RF electromagnetic field strength and 2.3 ± 0.02 μV / cm -1 Hz -1 / 2 of the sensitivity. The comb spectrum generated from the probe laser provides sensitivity and accuracy of identification compared to single-frequency experiments. The recovery of the full spectral line shape allows for the observation of slight frequency variations at the peak center and can be used to correct the measurements. The observation of the full spectrum can be used to reduce noise compared to single-frequency amplitude-mode measurements.

[0045] In some aspects of what is described, the system can be illustrated by the following examples. The system can be used to detect radio frequency electromagnetic radiation in certain cases.

[0046] (Example 1) A laser system configured to generate a laser signal including first and second laser signals, and An optical comb generator configured to generate a comb spectrum based on the first laser signal, the comb spectrum including comb lines at respective comb frequencies, the optical comb generator A vapor cell sensor configured to contain vapor and generate an optical spectrum based on the interaction of the vapor with a comb spectrum and a second laser signal, wherein the optical spectrum at least partially represents the optical transmission of the vapor at the comb frequency, the optical spectrum includes characteristics that vary in response to radio frequency (RF) electromagnetic radiation that interacts with the vapor, a vapor cell sensor, and an optical detector configured to detect characteristics of the optical spectrum at one or more of the comb frequencies, a system.

[0047] (Example 2) A system according to the system of Example 1, wherein the characteristic of the optical spectrum includes the amplitude of the optical spectrum.

[0048] (Example 3) A system according to the system of Example 1 or Example 2, wherein the characteristic of the optical signal includes the polarization of the optical spectrum.

[0049] (Example 4) A system according to the system of Example 1 or any one of Examples 2 to 3, wherein the characteristic of the optical signal includes the phase of the optical spectrum.

[0050] (Example 5) A system according to the system of Example 1 or any one of Examples 2 to 4, including a spectrum analyzer configured to communicate with the optical detector and generate data representing characteristics of the optical spectrum at one or more of the comb frequencies.

[0051] (Example 6) A system according to the system of Example 5, including a computer having one or more processors and a memory that communicates with the spectrum analyzer, and when the memory is executed by the one or more processors, A system that stores instructions configured to perform operations including determining the amplitude of RF electromagnetic radiation, or the polarization of RF electromagnetic radiation, or the phase of RF electromagnetic radiation, or a combination thereof, based on data.

[0052] (Example 7) A system according to Example 1 or any one of Examples 2 to 6, comprising a source of RF electromagnetic radiation configured to emit RF electromagnetic radiation towards a vapor cell sensor.

[0053] (Example 8) A system according to Example 7, wherein the source of RF electromagnetic radiation includes a pulse generator and an RF generator, the pulse generator is in communication with the RF generator and is configured to generate a signal representing each pulse of the RF electromagnetic radiation, and the RF generator is configured to generate a pulse of RF electromagnetic radiation in response to receiving the signal.

[0054] (Example 9) A system according to Example 1 or any one of Examples 2 to 8, wherein the optical communication generator includes an electro-optic modulator and an arbitrary waveform generator.

[0055] (Example 10) A system according to Example 1 or any one of Examples 2 to 9, wherein the first laser signal has a first frequency that matches a first photoelectronic transition of the vapor, the second laser signal has a second frequency that matches a second photoelectronic transition of the vapor, and the second photoelectronic transition shares an energy level common to the first photoelectronic transition, and the vapor includes an RF electronic transition configured to change the absorption of light by one or both of the first and second photoelectronic transitions in response to absorption of the RF electromagnetic radiation.

[0056] (Example 11) A system according to Example 1 or any one of Examples 2 to 10, including an acousto-optic modulator configured to split a first laser signal into a first part and a second part, wherein the first part is received by an optical comb generator to generate a comb spectrum, and the second part has a frequency higher than that of the first part.

[0057] In some aspects of what is described, the method can be illustrated by the following examples. The method can be used to detect radio frequency electromagnetic radiation in certain cases.

[0058] (Example 12) In response to receiving the first laser signal in the optical comb generator, generating a comb spectrum including comb lines at respective comb frequencies; Generating an optical spectrum by interacting the comb spectrum and a second laser signal with vapor in a vapor cell sensor, wherein the optical spectrum at least partially represents the optical transmission of the vapor at the comb frequencies, and the optical spectrum includes characteristics that change in response to radio frequency (RF) electromagnetic radiation interacting with the vapor; generating the optical spectrum; and detecting characteristics of the optical spectrum at one or more of the comb frequencies. A method comprising.

[0059] (Example 13) The method of Example 12, wherein detecting the characteristics of the optical spectrum includes detecting the characteristics of the optical spectrum at two or more of the comb frequencies (e.g., a subset of the comb frequencies, all of the comb frequencies, etc.).

[0060] (Example 14) The method of Example 13, wherein the characteristics of the optical spectrum are detected simultaneously at two or more of the comb frequencies.

[0061] (Example 15) A method according to any one of Example 12 or Examples 13 to 14, wherein the characteristics of the optical spectrum include the amplitude of the optical spectrum.

[0062] (Example 16) A method according to any one of Example 12 or Examples 13 to 15, wherein the characteristics of the optical spectrum include the polarization of the optical spectrum.

[0063] (Example 17) A method according to any one of Example 12 or Examples 13 to 16, wherein the characteristics of the optical spectrum include the phase of the optical spectrum.

[0064] (Example 18) A method according to any one of Example 12 or Examples 13 to 17, including receiving RF electromagnetic radiation in a vapor cell sensor, wherein generating an optical spectrum includes interacting the RF electromagnetic radiation with vapor in the vapor cell sensor.

[0065] (Example 19) A method according to the method of Example 18, wherein receiving RF electromagnetic radiation includes receiving a pulse of RF electromagnetic radiation in a vapor cell sensor.

[0066] (Example 20) A method according to the method of Example 18 or Example 19, generating data representing the characteristics of the optical spectrum at one or more comb frequencies by operation of a spectrum analyzer, and determining the amplitude of the RF electromagnetic radiation, or the polarization of the RF electromagnetic radiation, or the phase of the RF electromagnetic radiation, or a combination thereof based on the data.

[0067] (Example 21) A method according to any one of Example 12 or Examples 13 to 20, wherein the optical comb generator includes an electro-optic modulator and an arbitrary waveform generator.

[0068] (Example 22) The method according to any one of Example 12 or Examples 13 to 21, generating a background light spectrum by interacting a comb spectrum with vapor in a vapor cell sensor, the background light spectrum representing at least partially the background light transmission of the vapor at the comb frequencies, and detecting characteristics of the background light spectrum at one or more comb frequencies.

[0069] (Example 23) The method according to Example 22, wherein the characteristics of the background light spectrum include the amplitude of the background light spectrum.

[0070] (Example 24) The method according to Example 22 or Example 23, wherein the characteristics of the background light spectrum include the polarization of the background light spectrum.

[0071] (Example 25) The method according to Example 22 or any one of Examples 23 to 24, wherein the characteristics of the background light spectrum include the phase of the background light spectrum.

[0072] (Example 26) The method according to Example 22 or any one of Examples 23 to 25, receiving RF electromagnetic radiation in a vapor cell sensor, by the operation of a spectrum analyzer, generating first data representing characteristics of an optical spectrum at one or more comb frequencies and second data representing characteristics of a background light spectrum at one or more comb frequencies, and determining the amplitude of the RF electromagnetic radiation, or the polarization of the RF electromagnetic radiation, or the phase of the RF electromagnetic radiation, or a combination thereof, based on a difference between the first data and the second data, A method, wherein generating an optical spectrum includes interacting the RF electromagnetic radiation with a vapor in a vapor cell.

[0073] (Example 27) A method according to Example No. 12 or any one of Examples Nos. 13 to 26, wherein the first laser signal has a first frequency matched to a first photoelectron transition of the vapor, the second laser signal has a second frequency matched to a second photoelectron transition of the vapor, and the second photoelectron transition shares an energy level common to the first photoelectron transition, wherein the vapor includes an RF electron transition configured to change light absorption by one or both of the first and second photoelectron transitions in response to absorption of the RF electromagnetic radiation.

[0074] (Example 28) A method according to Example No. 12 or any one of Examples Nos. 13 to 27, including generating the first and second laser signals by operation of a laser system.

[0075] (Example 29) A method according to Example No. 28, wherein generating the first and second laser signals includes locking one or both of the first and second laser signals to respective reference frequencies.

[0076] (Example 30) A method according to Example No. 28 or Example No. 29, including splitting the first laser signal into a first portion and a second portion, wherein the first portion is received by an optical comb generator to generate an optical comb spectrum, and shifting the second portion of the first laser signal to a frequency higher than the frequency of the first portion.

[0077] (Example 31) The method of Example 30, comprising combining a second portion of a first laser signal with an optical spectrum from a vapor cell sensor to generate a heterodyne optical spectrum, wherein detecting a characteristic of the optical spectrum comprises detecting a characteristic of the heterodyne optical spectrum at one or more comb frequencies.

[0078] (Example 32) The method of Example 31, wherein the characteristic of the heterodyne optical spectrum comprises the amplitude of the heterodyne optical spectrum.

[0079] (Example 33) The method of Example 31 or Example 32, wherein the characteristic of the heterodyne optical spectrum comprises the polarization of the heterodyne optical spectrum.

[0080] (Example 34) The method of Example 31 or any one of Examples 32 to 33, wherein the characteristic of the heterodyne optical spectrum comprises the phase of the heterodyne optical spectrum.

[0081] In some aspects of what is described, the method can be illustrated by the following examples. The method can be used to detect radio frequency signals.

[0082] (Example 35) receiving, in a vapor cell sensor, an RF signal including an RF pulse; receiving, in the vapor cell sensor, an optical signal including an optical comb; acquiring an optical spectrum based on an output signal generated by the vapor cell sensor in response to the RF signal and the optical signal; and determining a characteristic of the RF pulse based on a spectral line shape change of the optical spectrum.

[0083] (Example 36) The method of Example 35, The optical spectrum is the electromagnetically induced transparency (EIT) transmission spectrum of the vapor in the vapor cell sensor, or the electromagnetically induced absorption (EIA) transmission spectrum of the vapor in the vapor cell sensor, and acquiring the optical spectrum includes acquiring a plurality of frequencies of the EIT transmission spectrum in parallel, or acquiring a plurality of frequencies of the EIA transmission spectrum in parallel, a method.

[0084] (Example 37) A method according to the method of Example 36, wherein determining the characteristics of the RF pulse includes determining the amplitude of the RF pulse based on the Autler-Townes splitting of the Rydberg state energy of the vapor.

[0085] (Example 38) A method according to the method of Example 36 or Example 37, wherein determining the characteristics of the RF pulse includes determining the phase of the RF pulse based on the Autler-Townes splitting of the Rydberg state energy of the vapor.

[0086] (Example 39) A method according to the method of Example 36 or any one of Examples 37 to 38, wherein determining the characteristics of the RF pulse includes determining the polarization of the RF pulse based on the Autler-Townes splitting of the Rydberg state energy of the vapor.

[0087] (Example  40) A method according to the method of Example 36 or any one of Examples 37 to 39, wherein determining the characteristics of the RF pulse includes determining the amplitude of the RF pulse based on a change in the amplitude of the optical spectrum.

[0088] (Example 41) A method according to any one of Example 36 or Examples 37 to 40, wherein determining the characteristics of the RF pulse includes determining the phase of the RF pulse based on the change in the amplitude of the optical spectrum.

[0089] (Example 42) A method according to any one of Example 36 or Examples 37 to 41, wherein determining the characteristics of the RF pulse includes determining the polarization of the RF pulse based on the change in the amplitude of the optical spectrum.

[0090] (Example 43) A method according to any one of Example 35 or Examples 37 to 42, wherein determining the characteristics of the RF pulse includes obtaining a self-calibration measurement of the amplitude of the RF pulse.

[0091] (Example 44) A method according to any one of Example 35 or Examples 3� to 43, wherein the optical comb includes a quasi-continuous optical comb.

[0092] (Example 45) A method according to any one of Example 35 or Examples 36 to 44, including generating an optical comb from a probe laser signal and obtaining an optical spectrum using self-heterodyne spectroscopy based on the output signal and the probe laser signal.

[0093] Although this specification contains many details, these should not be construed as limitations on the scope of the claimed subject matter, but rather as descriptions of features specific to particular embodiments. The particular features described or illustrated herein in the context of separate implementations may be combined. Conversely, the various features described or illustrated herein in the context of a single implementation may be implemented separately or in any suitable sub-combination in multiple implementations.

[0094] Similarly, although the operations are depicted in the figures in a particular order, this should not be construed as requiring that the operations be performed in the particular order or sequence shown in order to obtain a desirable result, or that all of the illustrated operations be performed. In certain circumstances, multitasking and parallel processing may be advantageous. Also, the separation of various system components in the above-described implementations should not be understood as necessarily requiring such separation in all implementations, and the described program components and systems may generally be integrated into a single product or packaged into multiple products.

[0095] Some embodiments have been described above. Nevertheless, it should be understood that various modifications can be made. Accordingly, other embodiments are also within the scope of the following claims.

Claims

1. A laser system configured to generate a laser signal including first and second laser signals, An optical comb generator configured to generate an optical comb spectrum based on the first laser signal, the optical comb spectrum including optical comb lines at respective optical comb frequencies, A vapor cell sensor configured to contain vapor and generate an optical spectrum based on an interaction between the vapor, the optical comb spectrum, and the second laser signal, The optical spectrum at least partially representing light transmission of the vapor at the optical comb frequencies, The optical spectrum including characteristics that vary in response to radio frequency (RF) electromagnetic radiation interacting with the vapor, The vapor cell sensor, A system including an optical detector configured to detect the characteristics of the optical spectrum at one or more of the optical comb frequencies.

2. The system of claim 1, wherein the characteristics of the optical spectrum include the amplitude of the optical spectrum, or the polarization of the optical spectrum, or the phase of the optical spectrum.

3. The system of claim 1 or 2, including a spectrum analyzer configured to communicate with the optical detector and generate data representing the characteristics of the optical spectrum at the one or more optical comb frequencies.

4. A computer having one or more processors and a memory, the memory storing instructions that, when executed by the one or more processors, perform operations including communicating with the spectrum analyzer and, based on the data, determining the amplitude of the RF electromagnetic radiation, or the polarization of the RF electromagnetic radiation, or the phase of the RF electromagnetic radiation, or a combination thereof, the system of claim 3.

5. The system of claim 1 or 2, including a source of the RF electromagnetic radiation configured to emit the RF electromagnetic radiation toward the vapor cell sensor.

6. The source of the RF electromagnetic radiation, Includes a pulse generator and an RF generator, The pulse generator is configured to communicate with the RF generator and generate a signal representing each pulse of the RF electromagnetic radiation, The RF generator is configured to generate the pulses of the RF electromagnetic radiation in response to receiving the signal, the system of claim 5.

7. ​ The system according to claim 1 or 2, wherein the optical comb generator includes an electro-optic modulator and an arbitrary waveform generator.

8. The first laser signal has a first frequency that matches a first photoelectron transition of the vapor, The second laser signal has a second frequency that matches a second photoelectron transition of the vapor, and the second photoelectron transition shares an energy level common to the first photoelectron transition, The system according to claim 1 or 2, wherein the vapor includes an RF electron transition configured to change the absorption of light by one or both of the first and second photoelectron transitions in response to absorption of the RF electromagnetic radiation.

9. The system according to claim 1 or 2, comprising an acousto-optic modulator configured to divide the first laser signal into a first portion and a second portion, the first portion being received by the optical comb generator to generate the comb spectrum, and the second portion having a frequency higher than the frequency of the first portion.

10. Generating a comb spectrum including comb lines at respective comb frequencies in response to reception of a first laser signal in an optical comb generator; Generating an optical spectrum by interacting the comb spectrum and a second laser signal with vapor in a vapor cell sensor, The optical spectrum at least partially represents light transmission of the vapor at the comb frequencies, The optical spectrum includes characteristics that change in response to radio frequency (RF) electromagnetic radiation that interacts with the vapor; Generating an optical spectrum; A method comprising detecting the characteristics of the optical spectrum at one or more of the comb frequencies of the comb frequencies.

11. The method according to claim 10, wherein detecting the characteristics of the optical spectrum includes detecting the characteristics of the optical spectrum at two or more of the comb frequencies of the comb frequencies.

12. The method according to claim 11, wherein the characteristics of the optical spectrum are detected simultaneously at the two or more comb frequencies.

13. The method according to any one of claims 10 to 12, wherein the characteristics of the optical spectrum include an amplitude of the optical spectrum, or a polarization of the optical spectrum, or a phase of the optical spectrum.

14. Receiving the RF electromagnetic radiation in the vapor cell sensor, The method according to any one of claims 10 to 12, wherein generating an optical spectrum comprises interacting the RF electromagnetic radiation with the vapor in the vapor cell sensor.

15. Generating data representing the characteristics of the optical spectrum at the one or more comb frequencies by operation of a spectrum analyzer; Determining the amplitude of the RF electromagnetic radiation, or the polarization of the RF electromagnetic radiation, or the phase of the RF electromagnetic radiation, or a combination thereof, based on the data, the method according to claim 14.

16. Generating a background optical spectrum by interacting the comb spectrum with the vapor in the vapor cell sensor, the background optical spectrum at least partially representing background optical transmission of the vapor at the comb frequencies; Detecting characteristics of the background optical spectrum at the one or more comb frequencies, the method according to any one of claims 10 to 12.

17. The method according to claim 16, wherein the characteristics of the background optical spectrum include the amplitude of the background optical spectrum, or the polarization of the background optical spectrum, or the phase of the background optical spectrum.

18. Receiving the RF electromagnetic radiation in the vapor cell sensor; By operation of a spectrum analyzer, Generating first data representing the characteristics of the optical spectrum at the one or more comb frequencies; Generating second data representing the characteristics of the background optical spectrum at the one or more comb frequencies; And Determining the amplitude of the RF electromagnetic radiation, or the polarization of the RF electromagnetic radiation, or the phase of the RF electromagnetic radiation, or a combination thereof, based on a difference between the first data and the second data, The method according to claim 16, wherein generating an optical spectrum comprises interacting the RF electromagnetic radiation with the vapor in the vapor cell sensor.

19. The first laser signal has a first frequency that is matched to a first photoelectronic transition of the vapor, The second laser signal has a second frequency that is matched to a second photoelectron transition of the vapor, and the second photoelectron transition shares an energy level common to the first photoelectron transition, The method according to any one of claims 10 to 12, wherein the vapor includes an RF electron transition configured to change absorption of light by one or both of the first and second photoelectron transitions in response to absorption of the RF electromagnetic radiation.

20. The method according to any one of claims 10 to 12, including generating the first and second laser signals by operation of a laser system.

21. The method according to claim 20, wherein generating the first and second laser signals includes locking one or both of the first and second laser signals to respective reference frequencies.

22. Dividing the first laser signal into a first portion and a second portion, wherein the first portion is received by the optical comb generator to generate the comb spectrum, The method according to claim 20, including shifting the second portion of the first laser signal to a frequency higher than the frequency of the first portion.

23. Including combining the second portion of the first laser signal with the optical spectrum from the vapor cell sensor to generate a heterodyne optical spectrum, The method according to claim 22, wherein detecting the characteristics of the optical spectrum includes detecting the characteristics of the heterodyne optical spectrum at the one or more comb frequencies.

24. The method according to claim 23, wherein the characteristics of the heterodyne optical spectrum include the amplitude of the heterodyne optical spectrum, or the polarization of the heterodyne optical spectrum, or the phase of the heterodyne optical spectrum.

25. Receiving, in a vapor cell sensor, an RF signal including an RF pulse; Receiving, in the vapor cell sensor, an optical signal including an optical comb; Obtaining an optical spectrum based on an output signal generated by the vapor cell sensor in response to the RF signal and the optical signal; A method including determining characteristics of the RF pulse based on a change in spectral line shape of the optical spectrum.

26. The optical spectrum is the electromagnetically induced transparency (EIT) transmission spectrum of the vapor in the vapor cell sensor, or the electromagnetically induced absorption (EIA) transmission spectrum of the vapor in the vapor cell sensor, comprising obtaining the optical spectrum parallelly for a plurality of frequencies of the EIT transmission spectrum, or parallelly for a plurality of frequencies of the EIA transmission spectrum, including obtaining Determining the characteristics of the RF pulse includes determining the amplitude of the RF pulse based on the Autler-Townes splitting of the Rydberg state energy of the vapor. The method according to claim 25.

27. The optical spectrum is the electromagnetically induced transparency (EIT) transmission spectrum of the vapor in the vapor cell sensor, or the electromagnetically induced absorption (EIA) transmission spectrum of the vapor in the vapor cell sensor, comprising obtaining the optical spectrum parallelly for a plurality of frequencies of the EIT transmission spectrum, or parallelly for a plurality of frequencies of the EIA transmission spectrum, including obtaining Determining the characteristics of the RF pulse includes determining the amplitude of the RF pulse based on a change in the amplitude of the optical spectrum. The method according to claim 25 or 26.

28. Determining the characteristics of the RF pulse includes obtaining a self-calibration measurement value of the amplitude of the RF pulse. The method according to claim 25 or 26.

29. The optical comb includes a quasi-continuous optical comb. The method according to claim 25 or 26.

30. generating the optical comb from a probe laser signal, and obtaining the optical spectrum using self-heterodyne spectroscopy based on the output signal and the probe laser signal. The method according to claim 25 or 26.

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