Sensing of radio frequency electromagnetic fields

Abstract

We provide a system for sensing radio frequency (RF) electromagnetic fields. [Solution] In a general embodiment, a system for sensing a radio frequency (RF) electromagnetic field is described. The system includes a laser system that generates a probe laser signal and a coupled laser signal. The system also includes an RF source that generates a reference RF electromagnetic field. The reference RF electromagnetic field is part of a composite RF electromagnetic field that also includes a perturbed RF electromagnetic field. A vapor cell sensor in the system generates an optical signal in response to the probe laser signal, the coupled laser signal, and the composite RF electromagnetic field interacting with the vapor in the vapor cell sensor. In addition, the system includes a control system that adjusts the coupled laser signal and the reference RF electromagnetic field for each transition of the vapor. Based on the optical signal, the control system generates a value that represents the characteristics of the perturbed RF electromagnetic field.

Description

Technical Field

[0001] Cross - reference to Related Applications This application claims priority to U.S. Provisional Patent Application No. 63 / 504,406, filed May 25, 2023, entitled "Sensing Multichromatic Radio Frequency Fields". This application also claims priority to U.S. Patent Application No. 18 / 650,804, filed Apr. 30, 2024, entitled "Sensing Radio Frequency Electromagnetic Fields". The disclosures of the priority applications are hereby incorporated herein by reference in their entirety.

[0002] The following description relates to sensing radio frequency (RF) electromagnetic fields.

Background Art

[0003] Sensors can be used to determine the characteristics of RF electromagnetic fields. However, in certain environments, sensors may sense additional RF electromagnetic fields. In these environments, interference from the additional RF electromagnetic fields can interfere with or prevent accurate measurement of the characteristics of the RF electromagnetic fields.

Brief Description of the Drawings

[0004] [Figure 1] It is a schematic diagram of an example system for sensing a multichromatic RF field. [Figure 2] It is a schematic diagram of the example system of FIG. 1 where a Tx antenna is integrated into a second rubidium vapor - based sensor of the example system. [Figure 3] It is a schematic diagram of the example system of FIG. 1 where a second RF source generates a perturbed RF field at two or more signal frequencies. [Figure 4] It is a schematic diagram of the example system of FIG. 1 where the perturbed RF field is generated by a test - target device and the environment of the example system. [Figure 5A] It is a schematic diagram of an example system for sensing an RF electromagnetic field. [Figure 5B] This is a schematic diagram of an example set of electronic states of Rb atom vapor. [Figure 5C] This is a schematic diagram of a set of examples illustrating the electronic state of Cs atom vapor. [Figure 6A] This is a schematic diagram of the fourth level system of the electronic transition example. [Figure 6B] Figure 6A is a schematic diagram of an example single-dressed system showing only the single-photon Jaynes-Cummings states for electronic states |3> and |4>. [Figure 6C] Figure 6A is a schematic diagram of the example double-dressed system based on the Example 4 level system. [Figure 6D] This is a schematic diagram of the example bonding base derived from the example double-dressed system in Figure 6C. [Figure 7A] This is a graph of transmittance data for various Ω2 scanning and calculation examples. [Figure 7B] This is a graph of transmittance data for various Ω2 scanning and calculation examples. [Figure 7C] This is a graph of transmittance data for various Ω2 scanning and calculation examples. [Figure 7D] This is a graph of transmittance data for various Ω2 scanning and calculation examples. [Figure 8A] This is a contour map of the example spectrum as a function of Δ2 when Ω1 = 70.6 MHz and Ω2 = 19.8 MHz. [Figure 8B] Figure 8A is a graph of the transmittance peak. [Figure 8C] This is a contour map of the example spectrum as a function of Ω1 when Δ2 = -70.0 MHz and Ω2 = 12.5 MHz. [Figure 8D] Figure 8C is a graph of the transmittance peak. [Figure 9A] This is a contour graph of the Ω2 scan in the example for various magnitudes of Δ2 when Ω1 = 72.9 MHz. [Figure 9B] This is a contour graph of the Ω2 scan in the example for various magnitudes of Δ2 when Ω1 = 72.9 MHz. [Figure 9C] This is a contour graph of the Ω2 scan in the example for various magnitudes of Δ2 when Ω1 = 72.9 MHz. [Figure 9D] Figures 9A to 9C show graphs of the average resolution R for each of the doublet pairs. [Figure 10A] This is a contour graph of the example transmittance map generated by scanning Δ2 and Δc when Ω1 = 70.56 MHz and Ω2 = 19.84 MHz. [Figure 10B] This graph shows the peak transmittance positions from the transmittance map of the example in Figure 10A. [Figure 11A] This graph shows the peak transmittance position in the double-dressed state example when Ω1 = 72.9 MHz and Δ2 = -40 MHz. [Figure 11B] This graph shows the peak transmittance position in the double-dressed state example when Ω1 = 72.9 MHz and Δ2 = -73 MHz. [Figure 12A] This is a contour map of the RF1 Rabi frequency scanning measurement in the example where Δ2 = Ω1 / n, for n = -1, Ω1 = -60 MHz, and Ω2 = 7.1 MHz. [Figure 12B] This graph shows the peak transmittance positions generated from the measurement data of the example in Figure 12A. [Figure 12C] This is a contour map of the RF1 Rabi frequency scanning measurement in the example where Δ2 = Ω1 / n, for n = -1, Ω1 = -60 MHz, and Ω2 = 8.9 MHz. [Figure 12D] This graph shows the peak transmittance positions generated from the measurement data of the example in Figure 12C. [Figure 12E] This is a contour map of the RF1 Rabi frequency scanning measurement in the example where Δ2 = Ω1 / n, for n = -1, Ω1 = -60 MHz, and Ω2 = 12.5 MHz. [Figure 12F] Figure 12F is a graph showing the peak transmittance positions generated from the measurement data of the example in Figure 12E. [Figure 13] This is a flowchart of the example measurement process for determining Δ2 and Ω2 of an out-of-band RF field. [Figure 14] This table shows the dependence of ΔEmin on different example conditions for Δ1 and Δ2. [Figure 15A] These are graphs of the transmittance maps of the example, generated by scanning Ω1 and Δc, respectively. [Figure 15B] These are graphs of the transmittance maps of the example, generated by scanning Ω1 and Δc, respectively. [Figure 16A] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc=0MHz. [Figure 16B] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc=0MHz. [Figure 17A] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc = 20 MHz. [Figure 17B] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc = 20 MHz. [Figure 17C] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc = 20 MHz. [Figure 17D] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc = 20 MHz. [Figure 18A] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc=20MHz when Δ2=40MHz. [Figure 18B] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc=20MHz when Δ2=40MHz. [Figure 18C] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc=20MHz when Δ2=40MHz. [Figure 18D]This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc=20MHz when Δ2=40MHz. [Figure 18E] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 at Δc=20MHz when Δ2=40MHz. [Figure 18F] This graph compares the difference Tπ-T0 for different Ω2 sizes in various examples. [Figure 19A] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 near Δ2=40MHz at Δc=0MHz for different relative phases. [Figure 19B] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 near Δ2=40MHz at Δc=0MHz for different relative phases. [Figure 19C] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 near Δ2=40MHz at Δc=0MHz for different relative phases. [Figure 19D] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 near Δ2=40MHz at Δc=0MHz for different relative phases. [Figure 19E] This is a graph of the example probe transmittance map generated by scanning Ω1 and Δ1 near Δ2=40MHz at Δc=0MHz for different relative phases. [Figure 19F] This graph shows the transmittance profile for various relative phases Φ at Δ1=Δ2, as a function of Ω1. [Figure 20A] This graph shows the transmittance peaks generated by scanning Ω1 for different example sizes of Ω2, when Δc=0MHz, Δ1=Δ2=40MHz, and Φ=π. [Figure 20B]Figure 20A is a graph showing the linear relationship between Ω1, where the transmittance peak is observed in the example, and the corresponding Ω2. [Figure 21] This is a flowchart of the example measurement process for obtaining Δ2 and Ω2 by scanning Δ1 and Ω1. [Modes for carrying out the invention]

[0005] In common embodiments, radio frequency (RF) local oscillators may be used to read Rydberg vapor-based sensors. In some implementations, the RF local oscillator is used to maintain the self-calibration characteristics of the Rydberg vapor-based sensor and, in specific cases, to avoid or mitigate other limitations, such as limitations associated with the bandwidth of the antenna providing the local oscillator. In some implementations, the self-calibration characteristics of the Rydberg vapor-based sensor are maintained even when a multicolor RF field (e.g., a combination of two or more RF fields) is incident on the Rydberg vapor-based sensor. Furthermore, models may be used that represent the physical properties of the multicolor RF field interacting with the vapor in the Rydberg vapor-based sensor. In the embodiments described herein, the vapor includes Rydberg atoms or molecules having Rydberg electronic states. In some implementations, by using pseudo-crossings between Rydberg energy levels of the states of atoms or molecules dressed by the RF field, the model can maintain self-calibration in the Rydberg vapor-based sensor.

[0006] In some implementations, a polychromatic RF field includes two RF fields (e.g., two-color fields). The two RF fields may, in specific cases, each have frequencies ranging from 100 MHz to 1 THz. In these implementations, the first RF field functions as a reference RF field (e.g., a control RF field), while the second RF field has one or more unknown properties (e.g., amplitude, phase, frequency, etc.). The second RF field may be a perturbative RF field (e.g., an interfering RF field). In some implementations, a polychromatic RF field includes three or more RF fields. In some implementations, a Rydberg vapor-based sensor is sensitive to nearby perturbative RF signals. Thus, the frequency and amplitude of nearby perturbative RF fields can be determined. Therefore, Rydberg vapor-based sensors may be better suited for sensing electromagnetic interference (EMI) in constrained environments such as aircraft fuselages or other environments.

[0007] The RF local oscillator and perturbed RF field may interact simultaneously with the vapor of Rydberg atoms or molecules in a Rydberg vapor-based sensor. In these cases, the RF local oscillator can be tuned in several different ways with respect to the electronic levels of the vapor, and the characteristics of the perturbed RF field can be determined. For example, the power of the RF local oscillator can be tuned to match the pseudocrossing or systematically beyond the pseudocrossing. The pseudocrossing can be mapped out by changing the detuning of the coupled laser, which also interacts with the vapor of Rydberg atoms or molecules. Furthermore, the power of the RF local oscillator at the pseudocrossing can be used to determine one or both of the amplitude and detuning of the perturbed RF field. If the pseudocrossing is mapped out as a function of the local oscillator power and the coupled laser frequency, the power of the RF local oscillator can also be verified. In some implementations, signs of detuning of the RF local oscillator can be determined by detuning the RF local oscillator. In some implementations, the RF local oscillator is tuned (e.g., frequency, power, etc.), and detuning of the coupled laser is selected. In these implementations, the pseudocrossing in the energy spectrum can be mapped out.

[0008] The interaction between multiple RF fields and the Rydberg electronic states of Rydberg atom or molecule vapors is far more extensive than suggested by models that only consider simple mixtures of two or more RF fields (e.g., Rydberg atom mixer, heterodyne measurements). Such models do not support the use of Rydberg vapor-based sensors for self-calibration measurements. Furthermore, novel functionality with Rydberg vapor-based sensors can be realized using the physical properties of Rydberg atoms or molecules in a multicolor RF field (e.g., a dicolor field), rather than relying on simplified approximations that transform the system into something more than a mimicry of conventional RF systems. For example, in some cases, all properties of a perturbed RF field can be extracted by tuning the characteristics of the RF local oscillator and the frequency of the coupled laser. Such properties may be difficult (or impossible) to extract at small detunings where pseudocrossings are not induced. Moreover, at small detunings, the RF local oscillator may not be able to extract SI-traceable measurements.

[0009] "Pseudocrossing" is a quantum mechanical phenomenon that occurs, for example, when the energies of two different eigenstates of a system (e.g., stationary states) become close but cannot degenerate (and therefore the energy levels cannot cross). In some situations, the eigenstates are functions of parameters in the Hamiltonian that change the energy separation of the states. Examples of such Hamiltonians are described below in relation to Figures 6A-6D and Equation (1). For example, the states may be a combination of an RF field mode and an atomic or molecular energy level, e.g., two Rydberg electron levels used for sensing. If the RF field mode resonates with an atomic transition, a state with N photons of the RF1 field mode in a low atomic or molecular state will have the same energy as a state with N-1 photons of the excited RF1 field mode, so the RF1 field mode and the atomic or molecular energy state appear to be degenerate.

[0010] In some implementations, pseudocrossing can be described by models that correctly account for the interactions between states. Pseudocrossing may be, for example, due to the “non-crossing rule” representing a theorem of quantum mechanics. In these implementations, the actual eigenstates can be a mixture of atomic or molecular levels and RF field states, as further described below in relation to equation (2). These states have energy splitting at the Rabi frequency (Ω) of the RF1 field if the RF1 field is resonating with the transition. If the RF1 field is detuned (Δ) from the atomic or molecular transition, the minimum splitting is

[0011]

number

[0012] Second, third, or more RF fields (e.g., RF2, RF3, etc.) can generate even more pseudocrossings. For example, if the properties of the first RF field (RF1) can be controlled and used to determine both its own properties and those of other RF fields, then the power and detuning of each of these fields can be extracted. The determination of the former corresponds to the initial stage of Rydberg vapor-based sensing, and the determination of the latter corresponds to the subsequent stage of Rydberg vapor-based sensing, which is performed by mapping the pseudocrossings. In the physical image of a Rydberg atom or molecule, if there are two or more RF field modes, each field mode can be treated as a harmonic oscillator. The Rydberg atom or molecule acts as a medium (e.g., a photon) that exchanges excitations between field modes. In certain cases, the system of RF fields becomes a series of linearly coupled harmonic oscillators (e.g., for dipole transitions).

[0013] Figure 1 shows a schematic diagram of an embodiment system 100 for sensing a multicolor RF field. Embodiment system 100 includes an RF source 102 (e.g., a Tx antenna) configured to generate a reference RF field (RF1). Embodiment system 100 also includes a Rydberg vapor-based sensor 104a containing vapor of Rydberg atoms (e.g., Cs, Rb, etc.) or Rydberg molecules (e.g., H2, I2, etc.). The Rydberg vapor-based sensor 104a may be a vapor cell sensor such as those described in U.S. Patent No. 10,859,981, titled "Vapor Cells Having One or More Optical Windows Bonded to a Dielectric Body," and U.S. Patent No. 10,605,840, titled "Vapor Cells Having Reduced Scattering Cross-Sections and Their Methods of Manufacture." Embodiment system also includes a second RF source 106 configured to generate a perturbed RF field 108. In some implementations, as illustrated in Figure 1, the second RF source 106 is a device under test (DUT) capable of generating two or more perturbed RF fields (e.g., RF2, RF3, etc.). In these environments, combinations of RF fields (e.g., RF1, RF2, RF3, etc.) can define a multicolor RF field.

[0014] In some embodiments, the embodiment system 100 includes a laser system configured to generate multiple laser signals, including a probe laser signal and a coupled laser signal. The laser system can communicate optically with a Rydberg vapor-based sensor 104a (for example, via an optical fiber) so that the probe laser signal and the coupled laser signal can interact with the vapor of Rydberg atoms or molecules in the Rydberg vapor-based sensor 104a. Such interaction may enable the Rydberg vapor-based sensor 104a to generate an optical signal based on the probe laser signal and the coupled laser signal. The optical signal may represent the response of the vapor to a multicolor RF field, for example, by representing the transmittance of the probe laser signal through the vapor. In some embodiments, the embodiment system 100 includes a second Rydberg vapor-based sensor 104b adjacent to the first RF source 102. In these implementations, the laser system may also optically communicate with a second Rydberg steam-based sensor 104b, which may assist the first Rydberg steam-based sensor 104a in controlling the reference RF field (e.g., stabilizing the reference RF field, calibrating the reference RF field, etc.). In certain cases, this control may be performed in real time using a feedback loop. Figure 1 shows two Rydberg steam-based sensors 104, but other numbers and configurations of Rydberg steam-based sensors 104 (e.g., a pair of Rydberg steam-based sensors collectively defining a single scannable sensor) may be used.

[0015] In some embodiments, the embodiment system 100 includes a detector system configured to receive an optical signal from a Rydberg vapor-based sensor 104a and, in response, generate a detector signal representing a multicolor RF field. In some embodiments, the embodiment system 100 also includes a control system configured to receive the detector signal and, in response, generate data representing a multicolor RF field. The data may include, for example, first data representing the characteristics of a reference RF field (RF1), second data representing the characteristics of a first perturbed RF field (RF2), third data representing the characteristics of a second perturbed RF field (RF3), and so on. Embodiments of characteristics include the amplitude, frequency, phase, and polarity of the RF fields (e.g., RF1, RF2, RF3, etc.). In some embodiments, the characteristics include the detuning of the RF field with respect to the electronic transitions of the vapor (e.g., Δ1, Δ2, etc.). In some embodiments, the characteristics include the coupling strength of the RF field with respect to the electronic transitions of the vapor (e.g., Ω1, Ω2, etc.). In many embodiments, the control system is configured to generate data based on a model, which may be, for example, the Jaynes Cummings model. Possible examples of the model are further described in relation to Figures 6A to 6D.

[0016] In some implementations, the first RF source 102 may be integrated into a Rydberg steam-based sensor. For example, Figure 2 shows a schematic diagram of the embodiment system 100 of Figure 1, in which the Tx antenna is integrated into a second Rydberg steam-based sensor 104b. The second Rydberg steam-based sensor 104b may correspond to a steam cell sensor in which a slot waveguide defines part or all of the Tx antenna. An embodiment of a slot waveguide structure for a steam cell sensor is described in U.S. Patent No. 11,209,473, titled "Sensing Radio Frequency Electromagnetic Radiation". Alternatively, the second Rydberg steam-based sensor 104b may include a steam cell sensor coupled to a Rydberg steam-based maser. An embodiment of a configuration for a Rydberg steam-based maser is described in U.S. Patent No. 11,303,087, titled "Photonic Crystal Masers".

[0017] In some embodiments, the second RF source 106 is a device under test that generates a perturbed RF field 108 at multiple signal frequencies (e.g., spurs). Figure 3 is a schematic diagram of the embodiment system 100 of Figure 1, where the second RF source 106 generates a perturbed RF field 108 at two or more signal frequencies (e.g., spurs). Here, the first RF source 102 may be a Tx antenna that generates a reference RF field (RF1). The reference RF field may correspond to a primary RF output that functions as the control RF field of the embodiment system 100. The second RF source 106 (e.g., the device under test) may generate a perturbed RF field 108 (e.g., RF2, RF3, etc.) which is an undesirable or unknown secondary output that needs to be characterized. The perturbed RF field 108 may, in particular, correspond to spurs of the second RF source 106 at multiple signal frequencies. In some embodiments, the second RF source 106 is part of the environment of the embodiment system 100. In these implementations, the second RF source 106 may be local to the embodiment system 100. For example, the second RF source 106 may generate a perturbed RF field 108 in the environment, and the embodiment system 100 receives the perturbed RF field 108 from the environment.

[0018] In some implementations, the second RF source 106 is the device under test, and the embodiment system 100 includes a third RF source which is part of the environment of the embodiment system 100. Figure 4 is a schematic diagram of the embodiment system 100 of Figure 1, in which the perturbed RF field 108 is generated by the environment of the device under test and the embodiment system 100. In Figure 4, the device under test generates a first perturbed RF field 108a, and the environment includes one or more second perturbed RF fields 108b. In some cases, one or more second perturbed RF signals 108b are already present in the environment (e.g., generated by an unknown RF source). In some cases, one or more second perturbed RF signals 108b are generated in the environment (e.g., generated by a third RF source local to the embodiment system 100).

[0019] In some implementations, the characteristics of a target RF field (e.g., a perturbed RF field) can be determined using a Rydberg vapor-based sensor and a model such as the Jaynes Cummings model. Rydberg vapor-based sensors are essentially quantum mechanical types of RF sensors. These sensors can be configured to use an RF local oscillator to determine the characteristics of a target RF field. For example, the target RF field may be one of several RF fields that resonate approximately with the RF transitions of the vapor. Thus, a Rydberg vapor-based sensor can use vapor to sense the target RF field. This model can describe how multiple RF fields interact with Rydberg atoms or molecules within the Rydberg vapor-based sensor, as well as how perturbation signals and local oscillators affect measurements by the Rydberg vapor-based sensor. Conventional models may rely on simplified approximations of the interaction between the local oscillator and the target field, such as those using methods analogous to radio frequency heterodyne methods. More precise models, such as those described herein, can more accurately represent the physical properties of a Rydberg vapor-based sensor in two or more RF fields. A more accurate model may correspond, for example, to the multiple-dressed Jaynes-Cummings model. In such a model, Rydberg atoms or molecules in a Rydberg vapor-based sensor act as a medium for exchanging electromagnetic field excitations of field modes whose spectra are ladder-like. Using the Jaynes-Cummings states and their pseudo-crossings, the characteristics of two or more RF fields can be determined. As shown by the model, an improvement in RF field sensitivity to non-resonant radio frequencies is achieved, and under certain conditions, self-calibrated measurements can be recovered.

[0020] Referring here to Figure 5A, a schematic diagram of an embodiment system 500 for sensing an RF electromagnetic field is shown. The RF electromagnetic field may have frequencies ranging from 100 MHz to 1 THz in specific cases. Embodiment system 500 includes a vapor cell sensor 502 containing vapor 504 having an electronic state such as a Rydberg electronic state. The vapor 504 may include, for example, vapor of Rydberg atoms (e.g., Rb, Cs, etc.) and / or vapor of Rydberg molecules (e.g., H2, I2, etc.). In these cases, the vapor cell sensor 502 may be a Rydberg vapor-based sensor. Furthermore, the vapor cell sensor 502 may be analogous to the Rydberg vapor-based sensors described in relation to Figures 1 to 4.

[0021] In some implementations, the vapor 504 includes multiple electronic states that define an electronic state ladder. For example, Figure 5B shows a schematic diagram of an example set of electronic states 530 for the vapor of a Rb atom. The example set of electronic states 530 includes first and second electronic states 532a, 532b and first and second Rydberg electronic states 534a, 534b. These states are shown in Figure 5A using the spectroscopic notation applicable to the Rb atom, i.e., 5S 1 / 2 ,5P 3 / 2 ,53D 3 / 2 and 54P 3 / 2 Each is labeled using the following terms. The first electronic state 532a, the second electronic state 532b, and the first Rydberg electronic state 534a have progressively higher energies, defining an electronic state ladder. Furthermore, the second Rydberg electronic state 534b has a lower energy than the first Rydberg electronic state 534a. In some implementations, the second Rydberg electronic state 534b may have a higher energy than the first Rydberg electronic state 534a.

[0022] The set of examples of electronic states 530 defines electronic transitions of Rb atom vapor. For example, the energy gap between a first electronic state 532a and a second electronic state 532b defines a first photoelectron transition 536a. Similarly, the energy gap between a second electronic state 532b and a first Rydberg electronic state 534a defines a second photoelectron transition 536b. The first photoelectron transition 536a and the second photoelectron transition 536b may interact with (e.g., absorb) optical signals, such as laser signals from a laser system. In another example, the energy gap between a first Rydberg electronic state 534a and a second Rydberg electronic state 534b may define an RF transition 538 that interacts with (e.g., absorbs) an RF electromagnetic field. Examples of RF electromagnetic fields include electromagnetic fields from a reference antenna, the device under test, and the surrounding environment of the example system 500. Combinations of RF electromagnetic fields are also possible, such as two-color or multi-color RF electromagnetic fields.

[0023] In Figure 5B, an example set of electronic states 530 is shown having four electronic states, two of which are Rydberg electronic states. Other numbers and combinations of electronic states and Rydberg electronic states are also possible. For example, Figure 5C shows a schematic diagram of an example set of electronic states 550 for Cs atom vapor. The example set of electronic states 550 includes a third electronic state 532c, which causes the energies of the first electronic state 532a, the second electronic state 532b, the third electronic state 532c, and the first Rydberg electronic state 534a to gradually increase (e.g., define an electronic state ladder). The energy gap between the second electronic state 532b and the third electronic state 532c defines a third photoelectron transition 536c configured to interact with (e.g., absorb) an optical signal. In Figure 5C, the second Rydberg electronic state 534b has a higher energy than the first Rydberg electronic state 534a. However, in some implementations, the second Rydberg electronic state 534b may have a lower energy than the first Rydberg electronic state 534a.

[0024] Now, as shown by returning to Figure 5A, the embodiment system 500 also includes a laser system 506 optically coupled to the vapor cell sensor 502 via free space or an optical fiber assembly, etc. The laser system 506 is configured to generate a laser signal 508 transmitted to the vapor cell sensor 502. For example, the laser system 506 may generate a probe laser signal 508a and a coupled laser signal 508b, which are induced by the optical fiber 510 and interact with the vapor 504 of the vapor cell sensor 502. Figure 5A shows two laser signals 508 defined by the probe laser signal 508a and the coupled laser signal 508b, respectively. However, there can be other numbers of laser signals 508 (e.g., one probe laser signal and two coupled laser signals). Figure 5A also shows a laser signal 508 propagating in the reverse direction through the vapor 504 along the opposite optical path. However, other optical path configurations (e.g., parallel) including other numbers of optical paths are also possible. Examples of the configuration of laser signals and their interaction with Rydberg vapor are further described in U.S. Patent No. 10,509,065, entitled “Imaging of Electromagnetic Fields”.

[0025] In some implementations, the steam cell sensor 502 generates an optical signal 512 in response to the reception of a laser signal 508. The optical signal 512 may be defined by one or more laser signals 508 after they have interacted with the steam 504. For example, the optical signal 512 may be defined by a probe laser signal 508a after it has interacted with the steam 504 (and also while the coupled laser signal 508b is interacting with the steam 504). Thus, the optical signal 512 may be based on the transmittance of the probe laser signal 508a through the steam 504. In many implementations, the steam cell sensor 502 is configured to generate the optical signal 512 in response to a laser signal 508 and an RF electromagnetic field interacting with the steam 504 (e.g., a reference RF electromagnetic field 514a, a perturbed RF electromagnetic field 514b, or a combination thereof). In these implementations, the laser signal 508 interacts with the steam 504 to generate the optical signal 512, and the RF electromagnetic field may alter the optical signal 512 by interacting with the steam 504. If the optical signal 512 is defined by the probe laser signal 508a, the RF electromagnetic field can alter the optical properties of the probe laser signal 508a, such as its intensity, frequency, polarity, or phase. Combinations of altered optical properties are possible. Therefore, the optical signal 512 is obtained based on the transmittance of the probe laser signal 508a through the vapor 504, and may also represent the response of the vapor 504 to the RF electromagnetic field, if present.

[0026] In some embodiments, the embodiment system 500 includes an RF source 516 configured to generate a reference RF electromagnetic field 514a. The RF source 516 may be, for example, a reference RF antenna, a reference maser, or other type of local RF oscillator. Furthermore, the reference RF electromagnetic field 514a may match a target RF transition of the vapor 504, such as an RF transition of the vapor 504 in which the perturbed RF electromagnetic field is expected to interact (e.g., it may resonate or nearly resonate). In some embodiments, the RF source 516 is a reference RF antenna which is an integral part of the vapor cell sensor 502. For example, the vapor cell sensor 502 may include a slotted waveguide structure as described in U.S. Patent No. 11,209,473. In some embodiments, the RF source 516 is a Rydberg vapor-based maser coupled to the vapor cell sensor 502. The Rydberg vapor-based maser may, in certain cases, be an integral part of the vapor cell sensor 502. An embodiment of the Rydberg vapor-based maser is described in U.S. Patent No. 11,303,087.

[0027] In many implementations, the reference RF electromagnetic field 514a is part of a composite RF electromagnetic field 514 that includes the perturbed RF electromagnetic field 514b. For example, the embodiment system 500 may include a device under test (DUT) configured to generate the perturbed RF electromagnetic field 514b. In another embodiment, the perturbed RF electromagnetic field 514b may be received from the environment of the embodiment system 500, such as a known or unknown RF source in the environment. In these implementations, the perturbed RF electromagnetic field 514b may resonate or nearly resonate with the RF transitions of the vapor 504.

[0028] In some embodiments, the embodiment system 500 further includes a photodetection system 518 and a control system 520. The photodetection system 518 is optically coupled to the vapor cell sensor 502 and receives an optical signal 512 via free space or an optical fiber assembly, etc. The photodetection system 518 is configured to generate a signal 522 in response to the reception of the optical signal 512, and these signals 522 may represent one or more optical properties of the optical signal 512. For example, the photodetection system 518 may include a photodetector configured to generate an electrical signal in response to a measurement of the amplitude of the optical signal 512. However, other optical properties of the optical signal 512, such as frequency, polarity, and phase, are also possible. Combinations of optical properties are also possible.

[0029] The photodetection system 518 may include one or more optical elements (e.g., lenses, mirrors, polarizers, filters, gratings, beam splitters, etc.) that can be controlled to manipulate the optical signal 512. Such manipulation may enable the photodetection system 518 to measure the target optical properties of the optical signal 512 via a photodetector, etc. In some embodiments, the photodetection system 518 includes a photodetector configured to measure the target optical properties of the optical signal 512, such as the amplitude of the optical signal 512 at a specific frequency (or within a frequency range). In these embodiments, the photodetection system 518 may include multiple photodetectors, each photodetector configured to measure a different target property of the optical signal 512.

[0030] In some implementations, the control system 520 is configured to receive a signal 522 from the photodetection system 518, and upon receiving the signal 522, may include analog electronic equipment, digital electronic equipment, or both for processing the signal 522. The control system 520 may also be configured to generate data representing the vapor 504's response to the RF electromagnetic field 514. For example, the control system 520 may be configured to perform operations including adjusting a coupled laser signal 508b for the coupled optical transition of the vapor 504 and adjusting a reference RF electromagnetic field 514a for the RF transition of the vapor. These operations also include generating transmittance data based on the optical signal 512. The transmittance data represents the transmittance through the vapor 504 while the combined RF electromagnetic field 514 interacts with the vapor 504, with the coupled laser signal 508b and the reference RF electromagnetic field 514a being adjusted.

[0031] In some implementations, the operation also includes generating a value that represents the characteristics of the perturbed RF electromagnetic field 514b. The value is based on transmittance data and the pseudocrossing induced by the combined RF electromagnetic field 514 to the Rydberg electronic states of the vapor 504. Examples of the characteristics include the amplitude, frequency, phase, and polarity of the perturbed RF electromagnetic field 514b. In some implementations, the pseudocrossing is based on a pair of Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., the combined RF electromagnetic field 514). The pair of Rydberg electronic states may correspond, for example, to a first Rydberg electronic state 534a and a second Rydberg electronic state 534b, as described in relation to Figures 5B-5C. In some implementations, generating this value involves determining the pseudocrossing using the Jaynes Cummings model, which represents the response of the vapor 504 to the combined RF electromagnetic field 514.

[0032] In some embodiments, the embodiment system 500 includes a communication channel 524a between the control system 520 and the laser system 506. The communication channel 524a may be defined, for example, by a wired connection (e.g., an Ethernet connection) or a wireless connection (e.g., a WiFi connection). The embodiment system 500 may also include a power channel (e.g., a power cable) between the control system 520 and the laser system 506. In these embodiments, the control system 520 may be configured to control the laser system 506 so that the control system 520 can control one or more optical properties of the laser signal 508 produced by the laser system 506. Such control may include changing or maintaining the optical properties, and embodiments of optical properties include the amplitude (e.g., intensity), frequency, polarity, and phase of one or more laser signals 508. Combinations of optical properties are possible.

[0033] In an embodiment where the embodiment system 200 includes an RF source 516, the embodiment system 500 may include a communication channel between the control system 520 and the RF source 516. The communication channel may be defined, for example, by a wired connection (e.g., an Ethernet connection) or a wireless connection (e.g., a WiFi connection). The embodiment system 500 may also include a power channel (e.g., a power cable) between the control system 520 and the RF source 516. Furthermore, since the control system 520 may be configured to control the RF source 516, the control system 520 will be able to control the characteristics of the reference RF electromagnetic field 514a generated by the RF source 516. Such control may include changing or maintaining the characteristics, and embodiments of the characteristics may include the amplitude (e.g., intensity), frequency, polarity, and phase of the reference RF electromagnetic field 514a. Combinations of characteristics are possible. Such control may also allow the control system 520 to selectively match the reference RF electromagnetic field 514a to a target RF transition of the vapor 504, such as an RF transition of the vapor 504 in which the perturbed RF electromagnetic field 514b is expected to interact.

[0034] In some embodiments, the embodiment system 500 includes a communication channel 524b between the control system 220 and the photodetector system 518. The communication channel 524b may be defined, for example, by a wired connection (e.g., an Ethernet connection) or a wireless connection (e.g., a WiFi connection). The embodiment system 500 may also include a power channel (e.g., a power cable) between the control system 520 and the photodetector system 518. In these embodiments, the control system 220 may further be configured to control the photodetector system 518 so that the photodetector system 518 can measure one or more target characteristics of the optical signal 512. Such control may include controlling the optical elements of the photodetector system 518 to select the target optical characteristics of the optical signal 512. Such control may also include controlling one or more photodetectors, each photodetector configured to measure a different target optical characteristic.

[0035] In some embodiments, the control system 520 includes a computer that provides a user interface 526 for the embodiment system 500. Embodiments of the computer include desktop computers, workstations, servers, laptops, tablets, and mobile devices. The user interface 526 is configured to allow a user of the embodiment system 500 to view and manipulate data representing the characteristics of one or both of the reference RF electromagnetic field 514a and the perturbed RF electromagnetic field 514b. However, other functions are also possible, such as controlling the laser system 506, RF source 516, and photodetector system 518, and displaying information related to the laser system 506, RF source 516, and photodetector system 518. In some embodiments, the photodetector system 518 is configured to generate an analog signal, and the control system 520 is configured to convert the analog signal into a digital signal for processing. In these embodiments, the control system 520 may include circuitry for parallel processing of the digital signal (e.g., FPGA, ASIC, GPU, etc.).

[0036] During operation of the embodiment system 500, the probe laser signal 508a and the coupled laser signal 508b may interact with the vapor 504 of the vapor cell sensor 502. The combined RF electromagnetic field 514 also interacts with the vapor 504 of the vapor cell sensor 502. In response, the vapor cell sensor 502 generates an optical signal 512. For example, the probe laser signal 508a can be emitted from the vapor 504 after the probe laser signal 508a, the coupled laser signal 508b, and the combined RF electromagnetic field 514 have interacted with the electronic state of the vapor 504. Thus, the optical signal 514 may be based on the transmittance of the probe laser signal 508a through the vapor 504. In some cases, the electronic state of the vapor corresponds to that described in relation to Figure 5A. In some cases, the electronic state of the vapor corresponds to that described in relation to Figure 5B. Other electronic states are also possible.

[0037] During the operation of the embodiment system 500, the control system 520 may also adjust the coupled laser signal 508b with respect to the coupled optical transition of the vapor 504. In doing so, the control system 520 may change the difference between the frequency of the coupled laser signal 508b and the frequency of the coupled optical transition by instructing the laser system 506 to change the frequency of the coupled laser signal 508b. If the resulting difference is non-zero, the coupled laser signal 508b may be "detuned" with respect to the frequency of the coupled optical transition. In some embodiments, the coupled optical transition may correspond to the second photoelectron transition 536b described in relation to Figure 5A.

[0038] In addition, the control system 520 may adjust the reference RF electromagnetic field 514a for RF transitions of the steam 504. The RF transition may be, for example, a target RF transition of the steam 504 in which a perturbed RF electromagnetic field 514b is expected to interact. In some implementations, the RF transition corresponds to the RF transition 538 described in relation to Figures 5A and 5B.

[0039] When adjusting the reference RF field 514a, the control system 520 may instruct the RF source 516 to change one or more characteristics of the reference RF field 514a. For example, the control system 520 may change the first difference between the frequency of the reference RF field 514a and the frequency of the RF transition by instructing the RF source 516 to change the frequency of the reference RF field 514a. If the resulting frequency difference is non-zero, the reference RF field 514a may be "detuned" with respect to the frequency of the RF transition. In another embodiment, the control system 520 may instruct the RF source 516 to change the amplitude of the reference RF field 514a. In yet another embodiment, the control system 520 may change the second difference between the phase of the reference RF field 514a and the reference phase by instructing the RF source 516 to change the phase of the reference RF field 514a. The reference phase may, in certain cases, be generated by the reference clock of the embodiment system 500. In some implementations, the control system 520 adjusts the reference RF electromagnetic field 514a independently of the coupled laser signal 508b. However, in other implementations, the RF electromagnetic field 514 and the coupled laser signal 508b are adjusted simultaneously.

[0040] In addition, the control system 520 may generate transmittance data based on the optical signal 512. The transmittance data represents the transmittance of the probe laser signal 508a through the vapor 504 while the combined RF electromagnetic field 514 interacts with the vapor 504, with one or both of the coupled laser signal 508b and / or the RF electromagnetic field 514 being adjusted by the control system 520. In some implementations, the probe laser signal 508a has a frequency that matches (e.g., resonates or nearly resonates) the frequency of the probe optical transition of the vapor 504. In some implementations, the probe optical transition corresponds to a first photoelectron transition 536a described in relation to Figures 5A-5B.

[0041] The control system 520 may also generate values ​​representing the characteristics of the perturbed RF electromagnetic field 514b. These values ​​are based on transmittance data and the pseudo-crossings induced by the combined RF electromagnetic field 514 on the Rydberg electronic states of the vapor 504. Examples of the characteristics include the amplitude, frequency, polarity, and phase of the perturbed RF electromagnetic field 514b. In some implementations, the pseudo-crossings are based on a pair of Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., the combined RF electromagnetic field 514). The pair of Rydberg electronic states may correspond, for example, to a first Rydberg electronic state 534a and a second Rydberg electronic state 534b, as described in relation to Figures 5B-5C. In some implementations, generating the values ​​involves determining the pseudo-crossings using the Jaynes Cummings model, which represents the response of the vapor 504 to the combined RF electromagnetic field 514. Examples of the Jaynes Cummings model and its application to the dressed electronic states of Rydberg atoms or molecules are discussed further below.

[0042] In some implementations, the embodiment system 500 operates without the presence of a perturbed RF electromagnetic field 514b. In these implementations, the combined RF electromagnetic field 514 may include only a reference RF electromagnetic field 514a, and the operation of the control system 520 allows the embodiment system 500 to generate reference data representing the energy spectrum of the reference RF electromagnetic field 514a. The reference data may be based on values ​​generated by the control system 520 when one or both of the coupled laser signal 508b and the reference RF electromagnetic field 514a are adjusted. The control system 520 may then store the reference data so that the characteristics of the perturbed RF electromagnetic field (e.g., perturbed RF electromagnetic field 514b) can be determined at a later point in time.

[0043] In some implementations, the coupled laser signal 508b includes two or more components that interact with each coupled optical transition of the vapor 504. For example, the coupled laser signal 508b may include first and second coupled laser signals that interact with the vapor 504. In these cases, the vapor 504 (or its coupled optical transitions) may include first and second coupled optical transitions such as the second photoelectron transition 536b and the third photoelectron transition 536c described in relation to Figure 5C. Furthermore, the frequency of the first coupled laser signal may be matched to (e.g., resonant or nearly resonant) the frequency of the first coupled optical transition, and the frequency of the second coupled laser signal may be matched to (e.g., resonant or nearly resonant) the frequency of the second coupled optical transition.

[0044] In these implementations, the control system 520 may tune the first coupled laser signal with respect to the first coupled optical transition. By doing so, the control system 520 may change the difference between the frequency of the first coupled laser signal and the frequency of the first coupled optical transition by instructing the laser system 506 to change the frequency of the first coupled laser signal. If the resulting difference is non-zero, the first coupled laser signal may be “detuned” with respect to the frequency of the first coupled optical transition. In some implementations, the control system 520 may tune the second coupled optical laser signal, similar to the first coupled optical signal. Such tuning may be performed independently of or in conjunction with the tuning of the first coupled laser signal.

[0045] In some implementations, the perturbed RF electromagnetic field 514b may resonate or nearly resonate with the RF transition of the vapor 504. In some implementations, the reference RF electromagnetic field 514a and the perturbed RF electromagnetic field 514b each have different amplitudes. For example, the amplitude of the reference RF electromagnetic field 514a may be greater than that of the perturbed RF electromagnetic field 514b. Alternatively, the amplitude of the perturbed RF electromagnetic field 514b may be greater than that of the reference RF electromagnetic field 514a. Such amplitude differences may result in a change in the optical signal 514, which can help the control system 520 generate a value that represents the characteristics of the perturbed RF electromagnetic field 514b. For example, the optical signal 514 may include an EIT spectrum whose profile splits depending on the RF electromagnetic field interacting with the vapor 504. Such splitting may increase or decrease as the RF intensity (e.g., Rabi frequency) increases or decreases, respectively. Examples of amplitude differences and their effects are further described below.

[0046] In some implementations, the embodiment system 500 is used to determine the characteristics of multiple perturbed RF electromagnetic fields 514b (e.g., RF2, RF3, RF4, etc.). For example, the combined RF electromagnetic field 514 may include a second perturbed RF electromagnetic field. In these cases, the second perturbed RF electromagnetic field also interacts with the vapor 504, and its presence may alter the pseudocrossings and induce a second set of pseudocrossings for the Rydberg electronic states of the vapor 504. Thus, the original set of pseudocrossings may be associated only with the reference RF electromagnetic field 514a and the first perturbed RF electromagnetic field 514b, while the second set of pseudocrossings may be associated with the reference RF electromagnetic field 514a, the first perturbed RF electromagnetic field 514, and the second perturbed RF electromagnetic field. In some implementations, the second perturbed RF electromagnetic field resonates or nearly resonates with the RF transitions of the vapor.

[0047] In these implementations, the control system 520 generates a second value representing the characteristics of a second perturbed RF electromagnetic field. The second value is based on transmittance data and a second set of pseudocrossings. In some implementations, the second set of pseudocrossings is based on pairs of Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., a combined RF electromagnetic field 514). The pairs of Rydberg electronic states may correspond, for example, to a first Rydberg electronic state 534a and a second Rydberg electronic state 534b, as described in relation to Figures 5B-5C. In some implementations, generating the second value involves determining the second set of pseudocrossings using the Jaynes Cummings model, which represents the response of vapor 504 to the combined RF electromagnetic field 514.

[0048] Rydberg vapor-based sensors are attracting increasing interest in various applications of metrology and radio frequency (RF) field sensing. Their access to transition frequencies from sub-GHz to sub-THz makes these sensors suitable for calibration-free measurements across a wide range of RF frequencies. For example, the characteristics of an unknown RF field resonating with a pair of Rydberg states can be estimated by observing Outler-Townes (AT) splitting. A slightly detuned second RF field can then be applied to the Rydberg vapor-based sensor to correspond to the same pair of Rydberg states. The stronger of the two fields acts as the symmetric field, and the weaker one acts as the perturbing RF field (e.g., the interfering RF field). However, in certain situations, the symmetric field can become the control field, and the weaker field can become the symmetric field. Given the previous situation, the symmetric field splits the EIT function into two AT peaks. The perturbing RF field can generate additional peaks and splittings for varying detuning and field strengths. The emergence of these additional spectral characteristics is a result of harmonic and subharmonic resonances, which can be explained by the double-dressed Jaynes-Cummings model. Atoms or molecules act as a medium for exchanging RF excitations between two RF fields.

[0049] In some implementations, the Jayne Cummings model can provide an understanding of RF dressing that allows for self-calibration recovery when measuring RF fields, including measurements of out-of-resonance perturbed RF fields. Out-of-resonance sensing can be achieved by other means, in certain cases, for example, by tuning the transition frequency using a DC field, but in these cases, SI traceability is not demonstrated. Using the Jayne Cummings model, perturbed signals and target signals can be measured with SI traceability.

[0050] Studies have been conducted on two-level atoms interacting with two optical fields, starting from the ground state. However, these studies may not adequately address the understanding of perturbed RF fields in Rydberg vapor-based sensors. While studies have been made on Rydberg atoms in two RF fields for sensing applications, these cases focus on treating the two fields as analogous to a conventional RF mixer. Although these approaches are valid for specific parameter ranges, the general response of Rydberg vapor-based sensors to two-color fields is more complex. Therefore, the models derived from (or described in) these studies do not support the use of Rydberg vapor-based sensors for self-calibration measurements of two-color fields.

[0051] To understand Rydberg sensors in a two-color RF field, experiments can be conducted and the results compared with numerical calculations of a Rydberg EIT system coupled to two RF fields. The experimental data, analytical formulas, and numerical calculations demonstrate RF sensing without the need for calibration of the target and perturbation fields. Understanding of the results is achieved by employing a multi-dressed Jaynes-Cummings model. The results are not limited to two fields but can be generalized to multiple RF fields via a multimode Jaynes-Cummings model.

[0052] Figure 6A shows a schematic diagram of the Example 4 level system of electronic transitions. The Example 4 level system can experience two-color RF electromagnetic fields (e.g., RF1 and RF2). The Example 4 level system, which can correspond to a four-level EIT scheme, includes four RF-dressed electronic states in progressively increasing energy levels. The four RF-dressed electronic states define two optical transitions and an RF transition. For example, the Example 4 level system has a probe optical transition (ω) defined by electronic states |1> and |2>. p ) and coupled optical transitions (ω) defined by electronic states |2> and |3> c ) may include. The Example 4 level system also includes two RF electromagnetic fields (RF1 and RF2) that interact with the RF transitions defined by the electronic states |3> and |4>. In Figure 6A, the electronic states |3> and |4> are Rydberg electronic states. Figure 6A shows that the electronic state |4> has a higher energy than the electronic state |3>. However, in certain cases, the electronic state |4> has a lower energy than the electronic state |3>. Figure 6B is a schematic diagram of the Example Single Dressed System showing only the single-photon Jaynes Cummings states for the electronic states |3> and |4> in Figure 6A. In Figure 6B, the energy levels of the electronic states |3> and |4> are represented by dashed lines. Furthermore, in Figure 6B ω 34 This corresponds to the frequency (e.g., energy difference) between electronic states |3> and |4>.

[0053] Figure 6C is a schematic diagram of the example double-dressed system based on the Example 4 level system of Figure 6A. The example double-dressed system is based on the ground state of the electronic state described in the following formula (6)

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[0061] In FIGS. 6A - 6D, a probe beam (p) and a coupling beam (c) are configured for Rubidium EIT. The energy interval between two Rubidium states |3> and |4> is in the RF range. By corresponding two Rubidium levels to two near - resonant RF fields, a two - color field can be realized. One of the RF fields, the in - band field RF1, is maintained at resonance, while the other field, the out - of - band field RF2, is maintained tens of MHz away from resonance. The total Hamiltonian governing the four - level system is H = H A +H RF1 +H RF2 and is described as H A represents the bare atomic Hamiltonian interacting with the probe and coupling beams. H RF1 and H RF2 describe two RF fields interacting with the atom. The coupling strengths of the transitions are Ω p , Ω c , Ω1, and Ω2, and the detunings are Δ p =ω 12 -ω p , Δ c =ω 23 -ω c , Δ1 = ω 34 -ω RF1 , and Δ2 = ω 34 -ω RF2 .

[0062] In some implementations, the total Hamiltonian governing the four - level system interacting with the probe, coupling, RF1, and RF2 fields can be represented by Equation (1).

[0063]

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[0064] The dynamics of the system are given by the Liouville equation.

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[0066] The example experimental setup includes a Cs vapor cell with a probe laser beam and a coupled laser beam propagating in opposite directions. In this setup, the probe beam is D2 transition, λ p The coupled laser is tuned to λ = 852nm. c = 56D at 509nm 5 / 2 It is adjusted to accommodate the transition. The RF field is incident on the vapor cell from an orthogonal direction, and Cs 56D 5 / 2 From page 57 3 / 2 This corresponds to the transition to . RF1 and RF2 are emitted from the same antenna to maximize field overlap. The polarities of the two laser beams and RF sources are linear and aligned in parallel. Often, when only RF1 is present, the transition from D to P can split without residual uncoupled transition probability. If the coupled laser is detuned beyond resonance, two probe transmittance peaks are observed.

[0067] The calculation results show good agreement with the experimental data from the example experimental setup illustrated in Figures 7A to 7D. The out-of-band power Ω2 varies depending on different out-of-band detuning Δ2. Small deviations from the calculation data can arise from the DC and RF fields of non-uniform stray electricity. Figures 7A to 7D show graphs of example transmittance data (solid lines) and calculations (dashed lines) for various Ω2 scans. In Figure 7A, Ω2 = -1 MHz, and in Figure 7B, Ω2 = -30 MHz. Figure 7C shows a contour graph of experimental data for Δ2 scanning at Ω1 = 74.5 MHz, and Figure 7D shows a contour graph of calculated data for Δ2 scanning at Ω1 = 74.5 MHz. When Δ2 matches the harmonic and subharmonic conditions, multiple pseudocrossings occur. In Figures 7C and 7D, the horizontal dashed lines represent n, and Δ2 = Ω1 / n. The vertical dashed line indicates Rabi splitting ±Ω¹ / ² in a single dressed state.

[0068] The spectrum can be understood using a dressed-state model in which two Rydberg states |3> and |4> are dressed by an RF field. The Rydberg states are ω RF1 =ω 34 As shown, the resonant RF1 can be the first to be dressed. Next, the RF1-dressed state is dressed by RF2. The double-dressed model can reveal the conditions for harmonic and subharmonic resonances.

[0069] A single dressed state is given by equation (2) below.

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[0072] The addition of RF2 allows for the modification of the RF1 Jaynes Cumming Ladder. For M excitations in RF2, the uncoupled double-dressed states are |N±,M>, and their energies are:

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[0075] In certain cases, the two states are contracted, i.e., E + =E - In these cases, the states intersect when Δ2 = Ω1 / n, and n = m - m' is a non-zero integer. This equation shows that for a fixed n, |+> and |-> intersect as functions of Δ2 and Ω1. Redefining the states by substituting m' = mn can be useful in forming a basis shown by equation (6) below.

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[0077] The coupling between RF2 and the single dressed state can be captured by treating the interaction perturbatively. When |n|=1, the solution is straightforward. The interaction involves avoidance energy level crossing with energy splitting.

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[0081] In Rydberg vapor-based RF field sensing, as demonstrated by experimental and computational data, the minimum splitting of the double-dressed state is invariant for the in-band RF1 field and depends only on the resonant Rabi frequency of the perturbed field. The double-term intra-splitting at resonance is

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[0083] In some implementations, when RF2 is applied, Δ c As a function of Ω2, different sets of transmittance peaks appear. If Γ is the EIT linewidth, then for Δ2≦Γ, the two-color EIT signal can broaden with increasing RF2 power, as shown in Figure 7A. The sum of the two fields oscillates at the mean frequency and produces an effective field with a slowly pulsating amplitude. For small detuning, the beat rate can reach a steady state. The total amplitude swings between the sum and difference of the two field amplitudes. When the two powers are equal, as can be seen in Figure 7A, minimum splitting reaches 0 MHz when Ω2 is approximately 74.5 MHz. When RF2 is large, the detuning dynamics can be different. In this case, the atoms appear as two different frequency components at any given time. To grasp the overall situation, a complete Hamiltonian containing the two RF components is needed, as shown in Figure 7B. When RF2 is large, there is an interaction between the RF1 Rabi frequency and the RF2 detuning. When Δ2=Ω1 / n, subharmonic resonances can occur. Figures 7C and 7D show a comparison between experimental and calculated results. Pseudocrossing occurs under resonance conditions, for example, when n = -1, -2, -3. Slight discrepancies between data and calculations can be attributed to broadening or shifts due to RF field inhomogeneities, stray fields, etc.

[0084] A detailed analysis can be performed on the pseudo-crossing characteristics near the first harmonic where n=-1. Figures 8A and 8C show contour maps of the example spectrum as functions of Δ2 and Ω1, respectively. In Figure 8A, the contour map is a function of Δ2, with Ω1=70.6MHz and Ω2=19.8MHz. In Figure 8C, the contour map is a function of Ω1, with Δ2=-70.0MHz and Ω2=12.5MHz. The peak positions in Figures 8A and 8C are plotted in Figures 8B and 8D, respectively, and the amplitude is represented by a color depth scale. The circles in Figures 8B and 8D are peak values ​​obtained from the data. The lines superimpose a pseudo-crossing model that considers only the first harmonic resonance.

[0085] In Figures 8A to 8D, two independent experiments are performed. First, Δ2 is scanned near Ω1 / n, as shown in Figures 8A and 8B. Second, Ω1 is scanned near Δ2, as shown in Figures 8C and 8D. These two cases generate the harmonic resonance condition by representing the scanning of detuning δ above 0 MHz in equation (7). The transmittance peaks exhibit pseudo-crossing features. The minimum splitting between transmittance peaks is equal to Ω2 / 2, as if RF2 were resonating. This condition maintains SI traceability. In addition, Ω1 and Δ2 are estimated in the two cases, respectively.

[0086] Subharmonic resonance can be used to improve the amplitude sensitivity of the out-of-resonance field by resonating the energy levels of the dressed state. When Δ2 matches the harmonic resonance condition, improvements in the sensitivity of Ω1, Ω2, and Δ2 are observed. For example, RF2 detuning can be set to -73 MHz, close to the RF1 Rabi frequency. As shown in Figures 9A to 9D, even low RF powers of -20 dBm can be detected, although outside the resonance, detection may be limited to -8 dBm. The spectral resolution of the pair of peaks split by RF2 is plotted in Figure 9D. This resolution is,

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[0089] Figures 9A to 9C show contour graphs of the example Ω2 scan at various magnitudes of Δ2 when Ω1 = 72.9 MHz. The magnitudes of Δ2 in Figures 9A to 9C are -65 MHz, -73 MHz, and -40 MHz, respectively. Figure 9D shows the average resolution R for each of the doublet pairs shown in Figures 9A to 9C. For these example Ω2 scans, the condition Δ2 = -73.0 MHz produces the best detectable peak, which corresponds to an improvement in sensitivity of approximately 12 dB compared to the non-resonant condition. The RF1 field is approximately 11 mV / cm, while the lowest detected RF2 field is approximately 1.1 mV / cm. c The double peak near 0MHz appears with Δ2 being approximately Ω1 / n when n=-2.

[0090] In many implementations, the appearance of equally spaced doublets helps to demonstrate double Rydberg state dressing. Figures 9A and 9B correspond to the condition n is approximately -1. As shown in Figure 9C, Δ c The appearance of a doublet in the center of the main AT peak at =0MHz satisfies the condition that n is approximately -2. When Ω2 < Ω1, doublet splitting increases with Ω2. When Ω2 / Ω1 > 1, doublet splitting begins to decrease. This effect is a result of the reversal of the roles of the dressing fields. Since Ω2 / Ω1 > 1, the system of energy levels can be dressed first by RF2 and then by RF1. In the absence of RF1, the AT peak becomes asymmetric, as shown in Figures 9A and 9B, Δ c approximately 50MHz and Δ cA peak appears at approximately -100MHz, and AT splitting occurs at approximately 150MHz. RF1 is shifted by +73MHz from RF2, satisfying the subharmonic condition where n is approximately +2. Therefore, Δ is approximately -50MHz. c A double peak appears in the vicinity of Ω. A similar situation can be observed in Figure 9C, where Δ1 is shifted 40 MHz from RF2. Ω c Around 100 MHz, the subharmonic condition is met when n is approximately +3, and therefore, two doublet peaks appear during the splitting of the main AT peak. If RF1 and RF2 have equal power, the combined field is sin((ω 34 It oscillates according to -Ω²(t). Since the mean frequency can be shifted to the center of the two bands, the observed AT doublet exhibits an asymmetrical peak height.

[0091] In some implementations, Δ2 can be scanned while maintaining Ω1 = 70.56 MHz and Ω2 = 19.84 MHz. The corresponding peak transmittance frequencies can be obtained by fitting a double Gaussian model to the scan data. Figure 10A shows Δ2 and Δ when Ω1 = 70.56 MHz and Ω2 = 19.84 MHz. c Figure 10B shows a contour graph of the example transmittance map generated by scanning the data. Figure 10B shows a graph of peak transmittance frequencies from the example transmittance map in Figure 10A. In Figure 10B, a pseudo-crossing model is plotted against the peak transmittance data and is represented by a dashed line.

[0092] In some implementations, Ω2 can be scanned while maintaining Ω1 = 72.9 MHz. Peak positions can be obtained by fitting a double Gaussian model to the transmittance map data. Equally spaced doublets can indicate the energy of the double-dressed state and the reversal of roles due to RF2 becoming stronger than RF1. Figure 11A shows a graph of the peak transmittance positions of an implementation of the double-dressed state when Ω1 = 72.9 MHz and Δ2 = -40 MHz. Figure 11B shows a graph of the peak transmittance positions of an implementation of the double-dressed state when Ω1 = 72.9 MHz and Δ2 = -73 MHz.

[0093] In some implementations, Ω2 can be scanned while maintaining Ω1 = -60 MHz. Peak positions can be obtained by fitting a double Gaussian model to the transmittance map data. Figures 12A, 12C, and 12E represent the respective contour maps of the RF1 Rabi frequency scanning measurements of the implementations near Δ2 = Ω1 / n for n = -1 and Ω1 = -60 MHz, for Ω2 = 7.1 MHz, 8.9 MHz, and 12.5 MHz, respectively. The corresponding peak transmittance positions in Figures 12B, 12D, and 12F are plotted with amplitudes shown on a color depth scale for the same parameters as the contour maps. The circles in these figures represent peak values ​​obtained from experimental scanning measurement data. The double-dressed state is,

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[0098] Experimental and computational data demonstrate the suitability of the double-dressed Jaynes-Cummings model to represent a Rydberg state coupled to two near-resonant RF fields. The data show that the exchange of excitations between the two fields plays a crucial role in revealing the spectral characteristics. Furthermore, the double-dressing feature allows for the recovery of SI-traceable RF-based sensing, and the Jaynes-Cummings model is utilized as an approach for measuring multiple RF fields through pseudo-crossing mapping. The modulated RF field contains multiple frequency components, and the model provides a method for obtaining information associated with each frequency component of the modulated signal. This model may also enable increased sensitivity of Rydberg atom-based sensors to non-resonant RF fields.

[0099] In some implementations, the estimation of the unknown field RF2 is performed by controlling a local RF field RF1, which is set to resonate with atomic Rydberg transitions. The atomic Rydberg states coupled to RF1 are

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[0103] In the second approach to estimating Ω2 and Δ2, a fixed Δ c While maintaining this, a transmittance map is generated as a function of Ω1 and Δ1. First, as shown in Figure 16A, Δ c By setting =0MHz, Δ2 is estimated. The effect of RF2 on the probe transmittance at Δ1=40MHz is clearly visible. As a result of interference between the two fields, a decrease in transmittance occurs when Δ1=Δ2. Further extending this approach, multiple out-of-band frequency components can be detected simultaneously, as shown in Figure 16B. This approach provides a method for simultaneously detecting multiple RF components in total light. The effect of relative phase will be discussed further below.

[0104] RF-dressed atomic images can further be used to estimate Δ2. As Ω1 increases, the energy levels of the dressed states begin to diverge. To observe these states, Δ c It is set to a non-zero detuning. As Ω1 increases, the energy level of the dressed state changes to Δ cIt intersects with Δ. This is an alternative process for observing atomic spectra, c The Ω1 is fixed, and the energy levels are scanned. The transmittance profile is plotted in Figure 17A, where Ω1 and Δ1 are equal to Δ c Scanned at 20MHz. The transmittance peak is Δ c This occurs when the value is E±, where

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[0106] When Ω2 > 0, at a specific Δ1 and Ω1, the single dressed energy level coincides with RF2 detuning Δ2. As a result, the energy state splits into a doublet, as shown in Figures 17B to 17D. If pseudocrossing occurs, Δ2, Δ c , and the relationship between Δ1, that is,

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[0110] The RF2 field strength Ω2 can be estimated by setting Δ1=Δ2. When Δ1 is scanned near Δ2, the interference between the two fields generates a vector sum of the RF fields. As shown in Figures 18A to 18D, the transmittance signals show the deviation of the signal from the case where Ω2=0MHz. For a stationary (or slowly fluctuating) RF2 phase, the amplitude and phase of RF2 can be accurately estimated. In Figure 18E, the transmittance signals for different phases at Δ1=Δ2=40MHz are calculated. The variation in the peak position of the transmittance is a result of the interference between RF1 and RF2. As shown in Figure 18F, the difference between the transmittances at Φ=π and Φ=0 shows a peak and a dip, and their frequency difference corresponds to Ω2. Therefore, Ω2 can be estimated by measuring the frequency difference.

[0111] Furthermore, as shown in Figures 19A to 19F, due to the different relative phases, Δ1 is near 40 MHz, i.e., Δ1 is at approximately Δ2. c The transmittance at 0MHz is investigated. The data shows the signal transmittance fluctuating at the matching frequency as a result of interference. It is clear that the sum of the RF fields is added when Φ=0 and subtracted when Φ=π. Figure 19F shows the transmittance profile at Δ1=Δ2 as a function of Ω1 for various relative phases Φ. At Φ=π, the peak appears at the maximum Ω1. Phase-dependent transmittance profiles can be used to estimate the relative phase between two RF fields.

[0112] When Φ=π and Δ1=Δ2=40MHz, scanning Ω1 reveals a transmittance peak as shown in Figures 20A and 20B. This peak is symmetrical and centered at Ω1=Ω2. The peak is flat but has sharp edges. The center frequency can be determined by measuring the entire profile. Figure 20B demonstrates the linearity between Ω2 and the corresponding Ω1, where a peak is observed. The relative phase between RF1 and RF2 can also be determined here.

[0113] Figure 21 shows a flowchart of the example measurement process for obtaining Δ2 and Ω2 by scanning Δ1 and Ω1. The example measurement process is Δ c This process involves determining the out-of-band RF fields Δ2 and Ω2 by scanning Δ1 and Ω1 for a fixed magnitude. In this process, Δ1 and Ω1 are scanned to generate a probe laser transmittance map. If pseudo-crossing occurs within the probe laser transmittance map, other frequencies (e.g., RF2, RF3, etc.) are present. Δ2 can be determined by the location of the level crossing. c =Δ2 / 2, and when Δ1 is scanned, the intersection and RF2 frequency can be confirmed. By adjusting RF1, the detuning of RF1 and RF2 (Δ1 and Δ2) is set to be equal, and the detuning of the coupled laser is half the detuning of RF2 (Δ c By setting it to (Δ2 / 2), the RF2 Rabi frequency can be determined. The example measurement process allows the parameters of the RF2 field to be determined based on the calibration of the RF1 field, which uses the principle of Rydberg vapor-based electrometric methods (such as Rydberg atom-based electrometric methods) and detuning (Δ) of the coupled laser and RF1. c This can be done by measuring Δ1).

[0114] In the embodiments described herein, coupled laser detuning Δ cRF1 detuning Δ1, RF1 amplitude Ω1, and RF1 phase are used as control parameters to measure the characteristics of RF2. Multiple fields (e.g., RF3, RF4, etc.) can also be measured. Once the Jaynes Cummings model is understood, pseudocrossings can also be mapped using other combinations of scanned parameters. The model reveals analytical equations about where crossings occur and how energy splitting evolves as a function of parameters. By fitting the region around the pseudocrossing, it becomes possible to extract (e.g., estimate) characteristics of the RF field, such as power, frequency, and phase. Understanding the Jaynes Cummings model and the derivation of the equations describing pseudocrossings allows for the restoration of SI traceability of the measurements.

[0115] In some aspects of what is described, the system may be described by the following embodiments. The system may be configured to sense RF electromagnetic fields, such as electromagnetic fields associated with radio frequency (RF) electromagnetic waves. In certain cases, the RF electromagnetic field refers to a composite RF electromagnetic field that is multicolored. Example 1. A system for sensing radio frequency (RF) electromagnetic fields, A laser system configured to generate a probe laser signal and a coupled laser signal, An RF source configured to generate a reference RF electromagnetic field, A vapor cell sensor configured to generate an optical signal in response to a probe laser signal, a coupled laser signal, and a composite RF electromagnetic field interacting with the vapor of the vapor cell sensor, The optical signal is based on the transmittance of the probe laser signal through the vapor. The combined RF electromagnetic field includes a reference RF electromagnetic field and a perturbed RF electromagnetic field, and a vapor cell sensor, A control system, Adjusting the coupled laser signal for coupled optical transitions of vapor, Adjusting the reference RF electromagnetic field for the RF transition of vapor, The process involves generating transmittance data based on an optical signal, and the transmittance data is: Either the coupled laser signal or the reference RF electromagnetic field, or both, are adjusted by the control system. This represents the transmission rate of the probe laser signal through vapor when a composite RF electromagnetic field interacts with vapor, and the generation of the signal. The purpose is to generate a value that represents the characteristics of a perturbed RF electromagnetic field, and the value is Transmittance data and, The system comprises a control system configured to perform operations that include generating and generating pseudocrossings induced by a composite RF electromagnetic field on the Rydberg electronic states of vapor. Example 2. In the system of Example 1, adjusting the coupled laser signal involves changing the difference between the frequency of the coupled laser signal and the frequency of the coupled optical transition by changing the frequency of the coupled laser signal. Example 3. The system of Example 1 or 2, wherein the reference RF electromagnetic field is adjusted. By changing the frequency of the reference RF electromagnetic field, the first difference between the frequency of the reference RF electromagnetic field and the frequency of the RF transition is changed. By changing the amplitude of the reference RF electromagnetic field, or The method includes changing the phase of the reference RF electromagnetic field, thereby changing the second difference between the phase of the reference RF electromagnetic field and a reference phase (for example, from the system's reference clock). Example 4. The system of Example 1 or any one of Examples 2-3, wherein the perturbed RF electromagnetic field resonates or nearly resonates with the RF transition of the vapor. Example 5. The system of Example 1 or any one of Examples 2 to 4, wherein the characteristics of the perturbed RF electromagnetic field are: Amplitude of the perturbed RF electromagnetic field, Frequency of perturbed RF electromagnetic field, The phase of the perturbed RF electromagnetic field, or It possesses the polarity of a perturbed RF electromagnetic field. Example 6. The system of Example 1 or any one of Examples 2 to 5, wherein the probe laser signal has a frequency that matches the frequency of the probe light transition of the vapor. Example 7. The system of Example 1 or any one of Examples 2 to 6, wherein generating a value comprises determining pseudocrossing using the Jaynes Cummings model, which represents the response of vapor to a composite RF electromagnetic field. Example 8. The system of Example 1 or any one of Examples 2-7, wherein the steam is The first and second electronic states, It has an electronic state comprising a first and a second Rydberg electronic state, which are part of the Rydberg electronic state of the vapor, The first electronic state, the second electronic state, and the first Rydberg electronic state have progressively higher energies. The coupled optical transition is determined by the second electronic state and the first Rydberg electronic state. The RF transition is defined by the first and second Rydberg electronic states. Example 9. The system of Example 8, The probe laser signal has a frequency that matches the frequency of the probe light transition of the vapor. The probe light transition is determined by the first and second electronic states of the vapor. Example 10. The system of Example 8 or 9, wherein the second Rydberg electronic state has a higher energy than the first Rydberg electronic state. Example 11. The system of Example 8 or 9, wherein the second Rydberg electronic state has lower energy than the first Rydberg electronic state. Example 12. A system of Example 8 or any one of Examples 9-11, in which the pseudocrossing is based on first and second Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., a combined RF electromagnetic field). Example 13. The system of Example 1 or any one of the systems of Examples 2 to 12, The system includes a device under test (DUT) configured to generate a perturbed RF electromagnetic field. Example 14. The system of Example 1 or any one of Examples 2-12, wherein the perturbed RF electromagnetic field is received from the system environment. Example 15. The system of Example 13 or 14, wherein the amplitude of the reference RF electromagnetic field is greater than the amplitude of the perturbed RF electromagnetic field. Example 16. The system of Example 13 or 14, wherein the amplitude of the perturbed RF electromagnetic field is greater than the amplitude of the reference RF electromagnetic field. Example 17. The system of Example 1, The combined laser signal comprises a first and a second combined laser signal. The coupled phototransition comprises a first and a second coupled phototransition, Adjusting the coupled laser signal is Adjusting the first coupled laser signal for the first coupled optical transition of the vapor, This comprises either or both of the following: adjusting a second coupled laser signal for a second coupled optical transition of vapor. Example 18. The system of Example 17, Adjusting the first coupled laser signal involves changing the frequency of the first coupled laser signal, thereby changing the difference between the frequency of the first coupled laser signal and the frequency of the first coupled optical transition. Adjusting the second coupled laser signal involves changing the frequency of the second coupled laser signal, thereby changing the difference between the frequency of the second coupled laser signal and the frequency of the second coupled optical transition. Example 19. The system of Example 17 or 18, wherein the reference RF electromagnetic field is adjusted. By changing the frequency of the reference RF electromagnetic field, the first difference between the frequency of the reference RF electromagnetic field and the frequency of the RF transition is changed. By changing the amplitude of the reference RF electromagnetic field, or The method includes changing the phase of the reference RF electromagnetic field, thereby changing the second difference between the phase of the reference RF electromagnetic field and a reference phase (for example, from the system's reference clock). Example 20. The system of Example 17 or any one of Examples 18-19, wherein the perturbed RF electromagnetic field resonates or nearly resonates with the RF transition of the vapor. Example 21. The system of Example 17 or any one of Examples 18-20, wherein the characteristics of the perturbed RF electromagnetic field are: Amplitude of the perturbed RF electromagnetic field, Frequency of perturbed RF electromagnetic field, The phase of the perturbed RF electromagnetic field, or It possesses the polarity of a perturbed RF electromagnetic field. Example 22. The system of Example 17 or any one of Examples 18-21, wherein the probe laser signal has a frequency that matches the frequency of the probe light transition of the vapor. Example 23. A system of Example 17 or any one of Examples 18-22, wherein generating a value comprises determining pseudocrossing using the Jaynes Cummings model, which represents the response of vapor to a composite RF electromagnetic field. Example 24. The system of Example 17 or any one of the systems of Examples 18-23, wherein the steam is It has an electronic state comprising a first, second, and third electronic state, and the first and second Rydberg electronic states which are part of the Rydberg electronic state of vapor, The first electronic state, the second electronic state, the third electronic state, and the first Rydberg electronic state have progressively higher energies. The first coupled optical transition is determined by the second and third electronic states, The second coupled optical transition is determined by the third electronic state and the first Rydberg electronic state, The RF transition is defined by the first and second Rydberg electronic states. Example 25. The system of Example 24, The probe laser signal has a frequency that matches the frequency of the probe light transition of the vapor. The probe light transition is determined by the first and second electronic states of the vapor. Example 26. The system of Example 24 or 25, wherein the second Rydberg electronic state has a higher energy than the first Rydberg electronic state. Example 27. The system of Example 24 or 25, wherein the second Rydberg electronic state has lower energy than the first Rydberg electronic state. Example 28. The system of Example 24 or any one of Examples 25-27, wherein the pseudocrossing is based on first and second Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., combined RF electromagnetic fields). Example 29. The system of Example 1 or any one of the systems of Examples 2 to 28, The perturbed RF electromagnetic field is the first perturbed RF electromagnetic field, the value is the first value, and the pseudocrossing is the first set of pseudocrossings associated with the reference RF electromagnetic field and the first perturbed RF electromagnetic field. The combined RF electromagnetic field includes a second perturbed RF electromagnetic field. The operation of the control system comprises generating a second value that represents the characteristics of the second perturbed RF electromagnetic field, the second value being, Transmittance data and, Based on a second set of pseudo-crossings induced by a composite RF electromagnetic field on the Rydberg electronic states of vapor, The second set of pseudo-intersections is associated with the reference RF electromagnetic field, the first perturbed RF electromagnetic field, and the second perturbed RF electromagnetic field. Example 30. The system of Example 29, wherein the second perturbed RF electromagnetic field resonates or nearly resonates with the RF transition of the vapor. Example 31. A system of Example 29 or 30, wherein generating a second value comprises determining a second set of pseudo-crossings using the Jaynes Cummings model, which represents the response of vapor to a composite RF electromagnetic field. Example 32. The system of Example 29 or any one of the systems of Examples 30 to 31, The Rydberg electronic states of the vapor consist of a first and a second Rydberg electronic state, A second set of pseudo-intersections is based on the first and second Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., a combined RF electromagnetic field). Example 33. The system of Example 29 or any one of the systems of Examples 30 to 32, The system includes a device under test (DUT) configured to generate a first perturbed RF electromagnetic field, The second perturbed RF electromagnetic field is received from the system environment. Example 34. A system of either Example 29 or any one of Examples 30-32, wherein the first and second perturbed RF electromagnetic fields are received from the system environment.

[0116] In some aspects of the described content, the method may be described by the following embodiments. The method may be used to sense RF electromagnetic fields, such as those associated with radio frequency (RF) electromagnetic waves. In particular cases, the RF electromagnetic field refers to a composite RF electromagnetic field that is multicolored. Example 35. A method for sensing a radio frequency (RF) electromagnetic field, The probe laser signal and the coupled laser signal are to be interacted with the vapor of a vapor cell sensor, wherein the probe laser signal and the coupled laser signal are generated by the laser system, and the interaction is to be performed. The method involves interacting a composite RF electromagnetic field with the vapor of a vapor cell sensor, wherein the composite RF electromagnetic field comprises a reference RF electromagnetic field and a perturbed RF electromagnetic field, and the reference RF electromagnetic field is generated by an RF source, and the interaction is performed accordingly. The operation of the vapor cell sensor generates an optical signal in response to a probe laser signal, a coupled laser signal, and a composite RF electromagnetic field interacting with the vapor in the vapor cell sensor, wherein the optical signal is generated based on the transmittance of the probe laser signal through the vapor. The operation of the control system that communicates with the laser system and RF source, Adjusting the coupled laser signal for coupled optical transitions of vapor, Adjusting the reference RF electromagnetic field for the RF transition of vapor, This involves generating transmittance data based on an optical signal. The transmittance data is generated, representing the transmittance of the probe laser signal through the vapor when one or both of the coupled laser signal and the reference RF electromagnetic field are adjusted by the control system and the combined RF electromagnetic field interacts with the vapor. The method involves generating a value that represents the characteristics of a perturbed RF electromagnetic field, the value being generated based on transmittance data and pseudo-crossings induced by the combined RF electromagnetic field on the Rydberg electronic states of vapor. Example 36. The method of Example 35, wherein adjusting the coupled laser signal comprises changing the difference between the frequency of the coupled laser signal and the frequency of the coupled optical transition by changing the frequency of the coupled laser signal. Example 37. The method of Example 35 or 36, wherein the reference RF electromagnetic field is adjusted. By changing the frequency of the reference RF electromagnetic field, the first difference between the frequency of the reference RF electromagnetic field and the frequency of the RF transition is changed. By changing the amplitude of the reference RF electromagnetic field, or The method includes changing the phase of the reference RF electromagnetic field, thereby changing a second difference between the phase of the reference RF electromagnetic field and a reference phase (for example, from the system's reference clock). Example 38. The method of Example 35 or any one of Examples 36-37, wherein the perturbed RF electromagnetic field resonates or nearly resonates with the RF transition of the vapor. Example 39. The method of Example 35 or any one of Examples 36-38, wherein the characteristics of the perturbed RF electromagnetic field are: Amplitude of the perturbed RF electromagnetic field, Frequency of perturbed RF electromagnetic field, The phase of the perturbed RF electromagnetic field, or It possesses the polarity of a perturbed RF electromagnetic field. Example 40. The method of Example 35 or any one of Examples 36-39, wherein the probe laser signal has a frequency that matches the frequency of the probe light transition of the vapor. Example 41. The method of Example 35 or any one of Examples 36-40, wherein generating a value comprises determining pseudocrossing using the Jaynes Cummings model, which represents the response of vapor to a composite RF electromagnetic field. Example 42. The method of Example 35 or any one of Examples 36 to 41, Steam, The first and second electronic states, It has an electronic state comprising a first and a second Rydberg electronic state, which are part of the Rydberg electronic state of the vapor, The first electronic state, the second electronic state, and the first Rydberg electronic state have progressively higher energies. The coupled optical transition is determined by the second electronic state and the first Rydberg electronic state. The RF transition is defined by the first and second Rydberg electronic states. Example 43. The method of Example 42, The probe laser signal has a frequency that matches the frequency of the probe light transition of the vapor. The probe light transition is determined by the first and second electronic states of the vapor. Example 44. The method of Example 42 or 43, wherein the second Rydberg electronic state has a higher energy than the first Rydberg electronic state. Example 45. The method of Example 42 or 43, wherein the second Rydberg electronic state has lower energy than the first Rydberg electronic state. Example 46. The method of Example 42 or any one of Examples 43-45, wherein the pseudocrossing is based on first and second Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., combined RF electromagnetic fields). Example 47. The method of Example 35 or any one of Examples 36 to 46, The system includes generating a perturbed RF electromagnetic field through the operation of the device under test (DUT). Example 48. The method of Example 35 or any one of Examples 36 to 46, The laser system, RF source, vapor cell sensor, and control unit are part of the sensing system. The method involves receiving a perturbed RF electromagnetic field from the environment of the sensing system. Example 49. The method of Example 47 or 48, wherein the amplitude of the reference RF electromagnetic field is greater than the amplitude of the perturbed RF electromagnetic field. Example 50. The method of Example 47 or 48, wherein the amplitude of the perturbed RF electromagnetic field is greater than the amplitude of the reference RF electromagnetic field. Example 51. The method of Example 35, The combined laser signal comprises a first and a second combined laser signal. Interacting the probe laser signal and the coupled laser signal involves interacting the first and second coupled laser signals with the vapor of the vapor cell sensor. The coupled phototransition comprises a first and a second coupled phototransition, Adjusting the coupled laser signal is The first coupled laser signal is adjusted to the first coupled optical transition of the vapor, The method comprises either or both of the following: adjusting the second coupled laser signal to the second coupled optical transition of the vapor. Example 52. The method of Example 51, Adjusting the first coupled laser signal involves changing the frequency of the first coupled laser signal, thereby changing the difference between the frequency of the first coupled laser signal and the frequency of the first coupled optical transition. Adjusting the second coupled laser signal involves changing the frequency of the second coupled laser signal, thereby changing the difference between the frequency of the second coupled laser signal and the frequency of the second coupled optical transition. Example 53. The method of Example 51 or 52, Adjusting the reference RF electromagnetic field is By changing the frequency of the reference RF electromagnetic field, the first difference between the frequency of the reference RF electromagnetic field and the frequency of the RF transition is changed. By changing the amplitude of the reference RF electromagnetic field, or The method includes changing the phase of the reference RF electromagnetic field, thereby changing a second difference between the phase of the reference RF electromagnetic field and a reference phase (for example, from the system's reference clock). Example 54. The method of Example 51 or any one of Examples 52-53, wherein the perturbed RF electromagnetic field resonates or nearly resonates with the RF transition of the vapor. Example 55. The method of Example 51 or any one of Examples 52-54, wherein the characteristics of the perturbed RF electromagnetic field are: Amplitude of the perturbed RF electromagnetic field, Frequency of perturbed RF electromagnetic field, The phase of the perturbed RF electromagnetic field, or It possesses the polarity of a perturbed RF electromagnetic field. Example 56. The method of Example 51 or any one of Examples 52 to 55, wherein the probe laser signal has a frequency that matches the frequency of the probe light transition of the vapor. Example 57. The method of Example 51 or any one of Examples 52-56, wherein generating a value comprises determining pseudocrossing using the Jaynes Cummings model, which represents the response of vapor to a composite RF electromagnetic field. Example 58. The method of Example 51 or any one of Examples 52 to 57, Steam, The first, second, and third electronic states, It has an electronic state comprising a first and a second Rydberg electronic state, which are part of the Rydberg electronic state of the vapor, The first electronic state, the second electronic state, the third electronic state, and the first Rydberg electronic state have progressively higher energies. The first coupled optical transition is determined by the second and third electronic states, The second coupled optical transition is determined by the third electronic state and the first Rydberg electronic state, The RF transition is defined by the first and second Rydberg electronic states. Example 59. The method of Example 58, The probe laser signal has a frequency that matches the frequency of the probe light transition of the vapor. The probe light transition is determined by the first and second electronic states of the vapor. Example 60. The method of Example 58 or 59, wherein the second Rydberg electronic state has a higher energy than the first Rydberg electronic state. Example 61. The method of Example 58 or 59, wherein the second Rydberg electronic state has lower energy than the first Rydberg electronic state. Example 62. The method of Example 58 or any one of Examples 59-61, wherein the pseudocrossing is based on first and second Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., combined RF electromagnetic fields). Example 63. The method of Example 35 or any one of Examples 36 to 62, The perturbed RF electromagnetic field is the first perturbed RF electromagnetic field, the value is the first value, and the pseudocrossing is the first set of pseudocrossings associated with the reference RF electromagnetic field and the first perturbed RF electromagnetic field. The combined RF electromagnetic field includes a second perturbed RF electromagnetic field. The method is, The control system is configured to generate a second value representing the characteristics of the second perturbed RF electromagnetic field, wherein the second value is Transmittance data and, Based on a second set of pseudocrossings induced in the Rydberg electronic state of vapor by a combined RF electromagnetic field, the second set of pseudocrossings is associated with the reference RF electromagnetic field, the first perturbed RF electromagnetic field, and the second perturbed RF electromagnetic field. Example 64. The method of Example 63, wherein the second perturbed RF electromagnetic field resonates or nearly resonates with the RF transition of the vapor. Example 65. The method of Example 63 or 64, wherein generating a second value comprises determining a second set of pseudo-crossings using the Jaynes Cummings model, which represents the response of vapor to a composite RF electromagnetic field. Example 66. The method of Example 63 or any one of Examples 64-65, The Rydberg electronic states of the vapor consist of a first and a second Rydberg electronic state, A second set of pseudo-intersections is based on the first and second Rydberg electronic states when dressed by two or more RF electromagnetic fields (e.g., a combined RF electromagnetic field). Example 67. The method of Example 63 or any one of Examples 64-66, The system includes a device under test (DUT) configured to generate a first perturbed RF electromagnetic field, The second perturbed RF electromagnetic field is received from the system environment. Example 68. The method of Example 63 or any one of Examples 64-67, wherein the first and second perturbed RF electromagnetic fields are received from the system environment.

[0117] This specification contains many details, but these should not be understood as limitations on the scope of claims, but rather as descriptions of features specific to particular embodiments. Certain features described in this specification or shown in the drawings in the context of separate embodiments can be combined. Conversely, various features described or illustrated in the context of a single embodiment can be implemented individually or in any suitable partial combination in multiple embodiments.

[0118] Similarly, while the diagrams show operations in a specific order, this should not be understood as requiring that such operations be performed in a specific illustrated or sequential order, or that all illustrated operations be performed, in order to achieve the desired result. In certain situations, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system components in the above implementations should not be understood as requiring such separation in all implementations, and the described program components and systems should be understood as generally being able to be integrated into a single product or packaged into multiple products.

[0119] Many embodiments have been described. However, it will be understood that various modifications are possible. Therefore, other embodiments are also within the scope of the following claims.

Claims

1. A system for sensing radio frequency (RF) electromagnetic fields, A laser system configured to generate a probe laser signal and a coupled laser signal, An RF source configured to generate a reference RF electromagnetic field, A steam cell sensor configured to generate an optical signal in response to the probe laser signal, the coupled laser signal, and a composite RF electromagnetic field interacting with the steam of the steam cell sensor, The optical signal is determined based on the transmittance of the probe laser signal through the vapor. The composite RF electromagnetic field comprises a steam cell sensor with the reference RF electromagnetic field and the perturbed RF electromagnetic field, A control system, The coupled laser signal is adjusted with respect to the coupled optical transition of the vapor, The aforementioned reference RF electromagnetic field is adjusted with respect to the RF transition of the vapor, The process involves generating transmittance data based on the aforementioned optical signal, wherein the transmittance data is The coupled laser signal and the reference RF electromagnetic field, or either one or both, are adjusted by the control system. The transmission rate of the probe laser signal through the vapor when the composite RF electromagnetic field interacts with the vapor is represented and generated. The purpose is to generate a value that represents the characteristics of a perturbed RF electromagnetic field, wherein the value is The aforementioned transmittance data and, A system comprising a control system configured to perform an operation comprising generating a pseudo-crossover induced by the composite RF electromagnetic field on the Rydberg electronic state of the vapor.

2. The system according to claim 1, wherein adjusting the coupled laser signal involves changing the frequency of the coupled laser signal, thereby changing the difference between the frequency of the coupled laser signal and the frequency of the coupled optical transition.

3. Adjusting the aforementioned reference RF electromagnetic field means By changing the frequency of the reference RF electromagnetic field, the first difference between the frequency of the reference RF electromagnetic field and the frequency of the RF transition is changed. Changing the amplitude of the aforementioned reference RF electromagnetic field, or The system according to claim 1, further comprising changing the phase of the reference RF electromagnetic field to change a second difference between the phase of the reference RF electromagnetic field and a reference phase from the reference clock of the system.

4. The system according to claim 1, wherein the perturbed RF electromagnetic field resonates or substantially resonates with the RF transition of the vapor.

5. The characteristics of the perturbed RF electromagnetic field are, The amplitude of the perturbed RF electromagnetic field, The frequency of the aforementioned perturbed RF electromagnetic field, The phase of the perturbed RF electromagnetic field, or The system according to claim 1, comprising the polarity of the perturbed RF electromagnetic field.

6. The system according to any one of claims 1 to 6, wherein generating the value comprises determining the pseudo-crossing using the Jaynes Cummings model, which represents the response of the vapor to the combined RF electromagnetic field.

7. The aforementioned steam is The first and second electronic states, The vapor has an electronic state comprising a first and a second Rydberg electronic state which are part of the Rydberg electronic state of the vapor, The first electronic state, the second electronic state, and the first Rydberg electronic state gradually increase in energy. The coupled optical transition is defined by the second electronic state and the first Rydberg electronic state, The system according to any one of claims 1 to 6, wherein the RF transition is defined by the first and second Rydberg electronic states.

8. The system according to claim 7, wherein the pseudo-crossover is dressed by two or more RF electromagnetic fields, based on the first and second Rydberg electronic states.

9. The system according to any one of claims 1 to 6, comprising a device under test (DUT) configured to generate the aforementioned perturbed RF electromagnetic field.

10. The perturbed RF electromagnetic field is received from the environment of the system, according to any one of claims 1 to 6.

11. The combined laser signal comprises a first and a second combined laser signal, The coupled light transition comprises a first and a second coupled light transition, Adjusting the aforementioned coupled laser signal is Adjusting the first coupled laser signal for the first coupled optical transition of the vapor, The system according to claim 1, comprising one or both of the following: adjusting the second coupled laser signal for the second coupled optical transition of the vapor.

12. The aforementioned steam is The first, second, and third electronic states, The vapor has an electronic state comprising a first and a second Rydberg electronic state which are part of the Rydberg electronic state of the vapor, The first electronic state, the second electronic state, the third electronic state, and the first Rydberg electronic state have progressively higher energies. The first coupled phototransition is determined by the second and third electronic states, The second coupled optical transition is defined by the third electronic state and the first Rydberg electronic state, The system according to claim 11, wherein the RF transition is defined by the first and second Rydberg electronic states.

13. The aforementioned perturbed RF electromagnetic field is a first perturbed RF electromagnetic field, The aforementioned value is the first value, The pseudocrossing is a first set of pseudocrossings associated with the reference RF electromagnetic field and the first perturbed RF electromagnetic field, The aforementioned composite RF electromagnetic field comprises a second perturbed RF electromagnetic field, The operation of the control system comprises generating a second value representing the characteristics of the second perturbed RF electromagnetic field, The second value is, The aforementioned transmittance data and, Based on a second set of pseudocrossings induced by the composite RF electromagnetic field to the Rydberg electronic states of the vapor, The system according to any one of claims 1 to 6, wherein the second set of pseudo-intersections is associated with the reference RF electromagnetic field, the first perturbed RF electromagnetic field, and the second perturbed RF electromagnetic field.

14. The system according to claim 13, wherein generating the second value comprises determining the second set of pseudo-crossings using a Jaynes Cummings model representing the response of the vapor to the combined RF electromagnetic field.

15. The system according to claim 13, wherein the first and second perturbed RF electromagnetic fields are received from the environment of the system.

16. A method for sensing radio frequency (RF) electromagnetic fields, The method involves interacting a probe laser signal and a coupled laser signal with the vapor of a vapor cell sensor, wherein the probe laser signal and the coupled laser signal are generated by a laser system, and the interaction is performed accordingly. The method involves interacting a composite RF electromagnetic field with the vapor of the vapor cell sensor, wherein the composite RF electromagnetic field comprises a reference RF electromagnetic field and a perturbed RF electromagnetic field, and the reference RF electromagnetic field is generated by an RF source, and the interaction is performed accordingly. The operation of the vapor cell sensor generates an optical signal in response to the probe laser signal, the coupled laser signal, and the combined RF electromagnetic field interacting with the vapor of the vapor cell sensor, wherein the optical signal is generated based on the transmittance of the probe laser signal through the vapor. The operation of the control system that communicates with the laser system and the RF source, The coupled laser signal is adjusted with respect to the coupled optical transition of the vapor, The aforementioned reference RF electromagnetic field is adjusted with respect to the RF transition of the vapor, The process involves generating transmittance data based on the aforementioned optical signal, wherein the transmittance data is The coupled laser signal and one or both of the reference RF electromagnetic field are adjusted by the control system. The transmission rate of the probe laser signal through the vapor when the composite RF electromagnetic field interacts with the vapor is represented and generated. To generate a value that represents the characteristics of the perturbed RF electromagnetic field, wherein the value is The aforementioned transmittance data and, A method comprising generating based on pseudocrossings induced by the composite RF electromagnetic field to the Rydberg electronic states of the vapor.

17. The method according to claim 16, wherein adjusting the coupled laser signal involves changing the frequency of the coupled laser signal, thereby changing the difference between the frequency of the coupled laser signal and the frequency of the coupled optical transition.

18. Adjusting the aforementioned reference RF electromagnetic field means By changing the frequency of the reference RF electromagnetic field, the first difference between the frequency of the reference RF electromagnetic field and the frequency of the RF transition is changed. Changing the amplitude of the aforementioned reference RF electromagnetic field, or The method according to claim 16, further comprising changing the phase of the reference RF electromagnetic field to change a second difference between the phase of the reference RF electromagnetic field and a reference phase from a reference clock.

19. The method according to claim 16, wherein the perturbed RF electromagnetic field resonates or substantially resonates with the RF transition of the vapor.

20. The characteristics of the perturbed RF electromagnetic field are, The amplitude of the perturbed RF electromagnetic field, The frequency of the aforementioned perturbed RF electromagnetic field, The phase of the perturbed RF electromagnetic field, or The method according to claim 16, wherein the polarity of the perturbed RF electromagnetic field is provided.

21. The method according to any one of claims 16 to 20, wherein generating the value comprises determining the pseudo-crossing using a Jaynes Cummings model representing the response of the vapor to the combined RF electromagnetic field.

22. The aforementioned steam is The first and second electronic states, The vapor has an electronic state comprising a first and a second Rydberg electronic state which are part of the Rydberg electronic state of the vapor, The first electronic state, the second electronic state, and the first Rydberg electronic state gradually increase in energy. The coupled optical transition is defined by the second electronic state and the first Rydberg electronic state, The method according to any one of claims 16 to 20, wherein the RF transition is defined by the first and second Rydberg electronic states.

23. The method according to claim 22, wherein the pseudocrossing is dressed by two or more RF electromagnetic fields, and is based on the first and second Rydberg electronic states.

24. The method according to any one of claims 16 to 20, comprising generating the perturbed RF electromagnetic field by the operation of a device under test (DUT).

25. The laser system, the RF source, the vapor cell sensor, and the control unit are part of the sensing system. The method according to any one of claims 16 to 20, further comprising receiving the perturbed RF electromagnetic field from the environment of the sensing system.

26. The combined laser signal comprises a first and a second combined laser signal, Interacting the probe laser signal and the coupled laser signal involves interacting the first and second coupled laser signals with the vapor of the vapor cell sensor. The coupled light transition comprises a first and a second coupled light transition, Adjusting the aforementioned coupled laser signal is The first coupled laser signal is adjusted with respect to the first coupled optical transition of the vapor, The method according to claim 16, comprising either or both of the following: adjusting the second coupled laser signal with respect to the second coupled optical transition of the vapor.

27. The aforementioned steam is The first, second, and third electronic states, The vapor has an electronic state comprising a first and a second Rydberg electronic state which are part of the Rydberg electronic state of the vapor, The first electronic state, the second electronic state, the third electronic state, and the first Rydberg electronic state have progressively higher energies. The first coupled phototransition is determined by the second and third electronic states, The second coupled optical transition is defined by the third electronic state and the first Rydberg electronic state, The method according to claim 26, wherein the RF transition is defined by the first and second Rydberg electronic states.

28. The perturbed RF electromagnetic field is a first perturbed RF electromagnetic field, the value is a first value, and the pseudocrossing is a first set of pseudocrossings associated with the reference RF electromagnetic field and the first perturbed RF electromagnetic field. The aforementioned composite RF electromagnetic field comprises a second perturbed RF electromagnetic field, The aforementioned method, According to the operation of the control system, The system comprises generating a second value representing the characteristics of the second perturbed RF electromagnetic field, wherein the second value is Transmittance data and, Based on the combined RF electromagnetic field and a second set of pseudocrossings induced in the Rydberg electronic state of the vapor, The method according to any one of claims 16 to 20, wherein the second set of pseudo-intersections is associated with the reference RF electromagnetic field, the first perturbed RF electromagnetic field, and the second perturbed RF electromagnetic field.

29. The method of claim 28, wherein generating the second value comprises determining the second set of pseudo-crossings using a Jaynes Cummings model representing the response of the vapor to the combined RF electromagnetic field.

30. The method according to claim 28, wherein the first and second perturbed RF electromagnetic fields are received from the environment of the system.

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