Rydberg atomic gas microwave field precision measurement method based on hysteresis trajectory folding

Abstract

The invention discloses a microwave electric field high-sensitivity measurement method based on Rydberg atom hysteresis trajectory folding, and the method comprises the steps: preparing a high-density cold atom ensemble through a magneto-optical trap, and constructing a two-photon transition path to excite a Rydberg state; regulating and inducing quantum phase change through a microwave field to generate a hysteresis track with an intersection point; in combination with a noise suppression algorithm and a critical point tracking technology, extracting a nonlinear offset of a trajectory intersection point, and establishing a quantitative mapping relation between the nonlinear offset and the microwave field intensity; the atomic density is optimized to enhance the interaction between Rydberg atoms, and the SQL limitation is broken through. The quantum phase change critical behavior and the multi-body effect are combined, sub-nanovolt sensitivity, wide-frequency-band compatibility and high anti-interference capacity are achieved, and a new normal form is provided for high-precision microwave electric field measurement, quantum metering and basic physical research.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quantum precision measurement and sensing technology, and particularly relates to a Rydberg atom gas microwave field precision measurement method based on hysteresis trajectory folding. BACKGROUND

[0002] Magnetic optical trap (MOT) is a key technology for capturing and cooling neutral atoms. By combining magnetic field gradient and laser cooling technology, atoms are bound in a micron-scale spatial region and cooled to the order of microkelvin. The core process includes Doppler cooling and Zeeman cooling. Doppler cooling utilizes the Doppler effect of atoms and laser, and through tuning the 780nm laser frequency slightly lower than the Rb atom resonance frequency (red detuning 15MHz), the moving atoms are decelerated due to the absorption of photon momentum. Six beams of circularly polarized light (alternating between sigma and sigma) form a light trap along three-dimensional directions. 85 + - Zeeman cooling generates a magnetic field gradient with zero center and linearly increasing outward by an anti-Helmholtz coil, and combines polarization selection rules to make atoms absorb more photons at the edge of the magnetic field, generating a restoring force pointing to the center of the trap, further compressing the atom group. Cold atom preparation requires precise timing control. Through the ADwin system, the cooling light, the back-pumping light, the coupling light and the magnetic field are operated in stages (millisecond to second order), realizing atom cooling, trapping and detection.

[0003] Electromagnetic induced transparency (EIT) technology is the basis of Rydberg atom microwave sensing. By constructing a transmission window through the two-photon resonance of strong coupling light and weak probe light, the spectrum is obtained by scanning the two-photon detuning. However, the sensitivity of the traditional EIT scheme is limited by the spectral linewidth (about MHz order), and it needs to rely on complex external field disturbance detection mechanism. Existing technologies attempt to improve sensitivity through hysteresis trajectory analysis: for example, by exciting Rydberg states through two-photon transitions, using a triangular wave signal to modulate the intensity of the probe light, generating a hysteresis loop (separated rising and falling trajectories) of transmission rate changing with light intensity. Although this scheme can reflect the nonlinear response of atomic many-body interaction, the hysteresis trajectory form is single, the regulation range is limited, and the critical behavior is not explored, so the sensitivity improvement is limited.

[0004] ​​Further improved technology introduces microwave field regulation of hysteresis trajectory phase transition, induces system symmetry breaking by microwave coupling different Rydberg states, observes the phase transition process from clockwise rotation (W=-1) to counterclockwise rotation (W=1) of the trajectory, and is accompanied by trajectory crossing phenomenon. Although this method reveals the sensitivity enhancement potential of the phase transition region, it has significant limitations: first, the experimental parameters (such as microwave Rabi frequency, atomic density) need to be repeatedly optimized to match the critical condition, which is complex to operate; second, the crossing point tracking relies on empirical data processing, lacks quantitative algorithm support, and leads to unstable sensitivity measurement; third, the strong dipole interaction between Rydberg atoms is not fully utilized, and the system sensitivity is still constrained by the standard quantum limit (SQL), making it difficult to break through the sub-nanovolt level.

[0005] The above technical bottlenecks highlight the core challenge in the current field: how to extract high sensitivity features in nonlinear response while achieving parameter robustness and measurement stability. Traditional methods are limited by linear spectral analysis or single hysteresis trajectory observation, while microwave regulation phase transition technology touches the critical phenomenon, but does not establish an accurate mapping of crossing point shift and external field strength, and does not amplify nonlinear effects through atomic interactions. Therefore, a systematic solution that integrates critical point tracking, atomic density optimization, and anti-interference design is urgently needed to achieve sensitivity and practicality beyond existing technology. SUMMARY

[0006] The present application is directed to the defects of the prior art, and provides a Rydberg atom gas microwave field precision measurement method based on hysteresis trajectory folding.

[0007] In order to achieve the above application purpose, the technical scheme adopted by the present application is as follows:

[0008] A Rydberg atom gas microwave field precision measurement method based on hysteresis trajectory folding, characterized by comprising the following steps:

[0009] a. Capturing and cooling Rb atom gas using a three-dimensional magnetic optical trap (MOT) 85 to form a cold atom ensemble;

[0010] b. Using a two-photon transition scheme, constructing an electromagnetically induced transparency (EIT) effect by detecting light and coupling light to excite atoms from the ground state to the Rydberg state;

[0011] c. Coupling two different Rydberg states |r1> and |r2> by a microwave field, using a programmable signal generator to generate a triangular wave signal to drive an acousto-optic modulator, and performing periodic modulation of the Rabi frequency of the probe light in a linear increasing and decreasing manner to generate an upward scanning trajectory and a downward scanning trajectory of the probe light;

[0012] d. Real-time monitoring of the transmittance of the probe light by a photomultiplier tube (PMT) to obtain the hysteresis trajectory;

[0013] e、analysis of the intersection of the hysteresis trajectory, the position change of the trajectory intersection point is identified by moving average filtering, time reversal alignment and dichotomous criterion, and the intensity of the microwave field is reversed according to the intersection point offset, realizing high sensitivity measurement;

[0014] f、optimizing the atomic density N of the cold atomic ensemble, using the collective interaction between the Rydberg atoms to enhance the microwave field response, so that the sensitivity breaks through the standard quantum limit (SQL).

[0015] Further, in the step a, the magneto-optical trap is composed of a pair of gradient magnetic fields generated by anti-Helmholtz coils and six beams of orthogonal red-detuned lasers, the cooling light frequency detuning is 15MHz, the back-pumping light and the cooling light form a closed-loop transition, the atomic density is 3.5×10 11 cm -3 , and the atomic temperature is ≤20μK.

[0016] Further, in the step b, the intermediate state of the two-photon transition is 5P3 / 2F=4, the target Rydberg state is 50D5 / 2, and the microwave field frequency is 39.10GHz, which is used to couple the 50D5 / 2 state and the 48F7 / 2 state to form a four-level EIT structure.

[0017] Further, in the step c, the modulation period T s of the triangular wave signal is in the order of milliseconds to seconds, and the square of the probe light Rabi frequency Ω p increases linearly from 0MHz to 102.4MHz and then decreases symmetrically to 0MHz, which is realized by an acousto-optic modulator.

[0018] Further, in the step e, the identification of the intersection point of the hysteresis trajectory includes:

[0019] i、noise suppression and data alignment are performed on the rising and falling scan trajectories;

[0020] ii、the difference between the trajectories is quantified by a normalized parameter-log(Δ), Δ=|T up -T down |, T up and T down are the transmittances of the rising and falling processes, respectively;

[0021] iii、the mutation response of the intersection point is extracted near the critical region, and the sensitivity reaches 0.88nV·cm -1 ·Hz -1 / 2 .

[0022] In step f, the interatomic interaction of the Rydberg atom is enhanced by regulating the atomic number N, and when N is greater than or equal to a critical value, the sensitivity is exponentially increased with N, and exceeds the standard quantum limit (SQL).

[0023] Compared with the prior art, the present application has the advantages that:

[0024] 1. Breakthrough sensitivity improvement: the nonlinear response characteristics of the hysteresis trajectory in the critical region are utilized to improve the microwave electric field measurement sensitivity to the sub-nanovolt level, far exceeding the traditional linear spectroscopy method and the existing hysteresis trajectory technology, and breaking through the standard quantum limit restriction to realize the limit performance excavation of quantum resources.

[0025] 2. Strong robustness and anti-interference ability: through magnetic field shielding optimization and adaptive signal processing algorithm, the environmental noise and low-frequency interference are significantly suppressed to ensure the high stability of the measurement results in complex environment, and the sensitivity of the traditional scheme to parameter drift is overcome.

[0026] 3. Multi-body interaction enhancement effect: by regulating the cold atom density and the Rydberg state coupling strength, the response of the system to the external field is amplified by using the strong dipole interaction between atoms, and the scalability of the sensitivity with the scale of atomic resources is improved, providing a new paradigm for high-density quantum system sensing.

[0027] 4. Wide frequency band compatibility and application flexibility: supporting dynamic adjustment of microwave field frequency, covering a wide range of measurement requirements from sub-GHz to terahertz frequency band, adapting to multiple application scenarios such as communication, radar, quantum information, etc., breaking through the frequency band limitation of traditional devices.

[0028] 5. Non-invasive high-resolution detection: based on the principle of optical non-contact measurement, avoiding the introduction of external electrode disturbance, and combining with micro-scale cold atom group and millisecond-level time sequence control, the spatial and temporal resolution is highly coordinated to provide a new means for micro-region transient field analysis.

[0029] 6. Theoretical innovation and technical inspiration: for the first time, a quantitative mapping model of hysteresis trajectory crossing point shift and external field strength is established, revealing the amplification mechanism of quantum critical behavior on sensing sensitivity, and opening up a new research direction for the application of multi-body quantum system in precision measurement field. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a numerical simulation diagram of the Rydberg atom energy level structure and hysteresis trajectory in the embodiment of the present application. Among them, (a) is an atomic energy level diagram, (b) is a schematic diagram, (c) is a layout difference of the numerical simulation upward scanning process and downward scanning process, and the inserted drawing is the trend of the trajectory crossing point with the change of the microwave field.

[0031] Figure 2These are experimental observations of the hysteresis loop phase transition and trajectory intersection points in an embodiment of the present invention. (a) is the phase diagram of the hysteresis loop, (b) is a trend diagram of the hysteresis loop trajectory intersection point as the microwave field changes, and (c) is the difference in the Rydberg state layout during the upward and downward sweep processes in the experiment.

[0032] Figure 3 This is an analysis of the effect of the number of atoms on the intersection of the hysteresis loop and the sensitivity of the embodiment of the present invention. (a) and (b) are the trend diagrams of the change of the intersection of the hysteresis loop trajectory with the microwave field under different atomic numbers, and (c) is the sensitivity under different atomic numbers.

[0033] Figure 4 The relationship between the microwave field amplitude and the signal response of the embodiment of the present invention is analyzed. Where (a) is the measured oscillation amplitude and the microwave field amplitude E mw (b) is the relationship diagram between the signal-to-noise ratio (SNR) and the microwave field amplitude obtained by Fourier transform (FFT) analysis. DETAILED DESCRIPTION

[0034] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0035] The present invention provides a Rydberg atomic gas microwave field precision measurement method based on hysteresis trajectory folding, comprising:

[0036] 1. Magneto-optical trap capture 85 Rb atomic group

[0037] The three-dimensional MOT consists of a magnetic trap formed by a pair of anti-Helmholtz coils and an optical trap formed by six orthogonal laser beams. The magnetic trap provides an inhomogeneous weak quadrupole magnetic field with a magnetic field strength of 0 at the center of the trap and linearly changing toward the edge. A pair of red detuned lasers with the same frequency but opposite circular polarization directions are used in three orthogonal directions to illuminate the center of the trap to form an optical trap. Laser cooling technology is used to decelerate atoms below a certain speed threshold and trap them in the central area of ​​the MOT, obtaining a cold atomic cluster with a lower temperature. The cooling light meets the 5S 1 / 2 (F=3) to 5P 3 / 2 (F=4) detuned 15MHz, return pump light meets 5S 1 / 2 (F=2) to 5P 3 / 2 (F=3) resonance. The role of the back pump light is to form a cyclic transition structure with the cooling light. The atoms form a closed loop under the excitation of the cooling light and the back pump light. The pulse width of the cooling light is smaller than the pulse width of the back pump light, so that the atoms are prepared in 5S 1 / 2 (F=3) energy level, the size of the prepared atomic cluster is 500 μm in diameter and the atomic density is 3.5×10 11 cm 3, and the atomic temperature is 20 μk. The period of the cooling light and the repumping light is 200 Hz.

[0038] II. Preparation of Rydberg state and construction of EIT

[0039] The 85 Rb atoms are trapped in a three-dimensional magneto-optical trap (MOT) and optically pumped to prepare the atoms in the ground state |g> = |5S 1 / 2 , F = 3> by a two-photon excitation scheme. The atomic state is coherently transferred from the ground state to the Rydberg state |r1> = |50D 85 > by a two-photon excitation scheme. The energy level diagram is shown in Fig. Figure 1 (a). The detailed process is as follows: the probe light (wavelength ω p ≈ 10 μm) drives the atoms from the ground state |g> to the intermediate excited state |e> = |5P p , F = 4> with the Rabi frequency Ω 3 / 2 and the detuning Δ1; the coupling light (wavelength ω c ≈ 20 μm) then drives the atoms from the state |e> to the Rydberg state |r1> = |50D c > with the Rabi frequency Ω 5 / 2 and the detuning Δ2. A resonant microwave field (ω w = 2π × 39.10 GHz) generated by a radio frequency source and a horn antenna couples two different Rydberg states |r1> and |r2> = |48F 7 / 2 >. The two laser beams are focused into the atomic ensemble, and the electromagnetically induced transparency (EIT) spectrum is obtained by monitoring the transmission of the probe light with a photomultiplier tube (PMT).

[0040] III. Microwave control

[0041] A resonant microwave field controlled by a signal source is emitted to the center of the MOT through a horn antenna, and the microwave frequency is controlled by a digital signal generator to achieve the coupling between the Rydberg states. At this time, the model diagram is a four-level system as shown in Fig. Figure 1 (a). The frequency of the probe field Ω p is dynamically controlled by an acousto-optic modulator using a programmable signal generator (RIGOL DG4102). By programming, the instrument generates a precisely configured triangular waveform, and in each scanning period Ts, two distinct light intensity modulation stages are established: a linearly increasing slope modulation followed by a symmetric decreasing slope modulation. The transmission spectrum during the change is detected by the PMT. p

[0042] IV. Physical mechanism of enhanced sensing

[0043] ​This example analyzes the electromagnetically induced transparency (EIT) spectrum by comparing the signal differences between the rising and falling scanning phases. At different microwave frequencies, the hysteresis trajectory of the observed system undergoes symmetry breaking and phase transition. During the phase transition, the system response exhibits intermediate state characteristics ( Figure 1 (b)), the transmission trajectory folds and forms a crossover point. The characteristics of this crossover point indicate that the system enters a critical state - e.g. Figure 1 As shown in (c), its dynamic behavior is synchronized with the external field, and this feature can be used for microwave field sensing. Figure 1 (b) The physical mechanism of the sensing enhancement effect in the Rydberg atomic system is elucidated: as the microwave field Ω w The complex interaction of the multi-body system will induce the system to undergo a phase transition from the hysteresis trajectory winding number -1 to 1. During this phase transition, the system will present Ω p The intermediate state process in which the upward scanning trajectory and the downward scanning trajectory fold over each other. In this mechanism, the system experiences a competition between absorption and transmission, resulting in the intersection of the hysteresis loops. This trajectory intersection is regarded as a high-resolution observation indicator, and its position is related to the microwave Rabi frequency Ω. w One-to-one correspondence, such as Figure 1 As shown in (c), this enables the method of this embodiment to achieve enhanced sensing. The transition from non-crossing tracks to crossing tracks has critical behavior characteristics, which can significantly improve the measurement sensitivity of the system.

[0044] To obtain the track intersection point, this embodiment calculates the transmittance difference Δρ between the up-scan and down-scan tracks. rr In the trajectory folding area, in addition to the starting point and the end point, the intersection of the two trajectories also satisfies Δρ rr = 0. Here, the starting point and the ending point are ignored in this embodiment, and the microwave field strength Ω w Under these conditions, the corresponding Rabi frequency of the detection field can be obtained by Δρ rr =0 point confirmed, such as Figure 1 As shown in (c), when the microwave frequencies are set to A and B, the transmission spectrum at the intersection of the trajectories has a very high degree of recognition.

[0045] 5. Tracking the intersection of hysteresis trajectories

[0046] This example analyzes electromagnetically induced transparency (EIT) spectra by comparing the signal differences between the ascending and descending scanning phases. The specific processing method is as follows: The probe light transmittance data is first preprocessed using a moving average filter to suppress high-frequency noise. The descending phase data is then time-reversed and aligned with the ascending phase trajectory to eliminate scanning direction effects. Finally, the relative intensity of the two aligned curves is evaluated, and a binary criterion is used to identify intersection points.

[0047] Precision measurement experiment of Rydberg atomic gas based on trajectory overlap—sensitivity reaches 0.88nV cm -1 Hz -1 / 2

[0048] Rb 85 The cold atomic gas is confined in a three-dimensional magneto-optical trap (MOT). The MOT is shielded by a double-layer magnetic shield. This setup effectively shields the system from external magnetic fields and reduces the internal magnetic field to below 10 milligauss. This structure avoids dephasing of the Earth's magnetic field. 1 / 2 ,F=3>, through the two-photon EIT scheme, the ground state atoms are excited to the Rydberg state|50D 5 / 2 >, a resonant microwave field (ω m =2π×39.10GHz) is transmitted through the horn antenna to realize the Rydberg state|50D 5 / 2 >With Rydberg State|48F 7 / 2 > coupling. The probe beam and coupling beam are focused into the cold atom ensemble, and the intensity of the probe beam is detected by a photomultiplier tube to obtain the transmittance of EIT. The triangular waveform generated by the signal generator (RIGOL DG4102) is loaded onto the acousto-optic modulator. The function form of the triangular wave signal is V(τ) = 6(1 / 2-|τ / T s -1 / 2|, where T s Indicates the cycle time of a scan cycle, 0<τ <T s In this way, (Ω p / 2π) 2 From 0MHz to 102.4MHz (upward process) and (Ω p / 2π) 2 The process of decreasing from 102.4 MHz to 0 MHz (downward process).

[0049] In order to study this effect, this example measures the phase diagram of the evolution trajectory in a two-dimensional parameter space, such as Figure 2 (a) The horizontal axis of the coordinate axis represents the transmittance data obtained by the oscilloscope, which is represented by an index from small to large. The other axis corresponds to the microwave field amplitude E mw In the figure, red indicates that the transmittance of upward scanning is greater than that of downward scanning, and blue indicates that the transmittance of upward scanning is less than that of downward scanning. The boundary between red and blue is Figure 1 (b) The intersection points described by the upper plane. The intersection points of these folding trajectories were further extracted to explore their relationship with the microwave field amplitude E. mw A crucial observation is that the intersection of the trajectories changes continuously with the change of the microwave amplitude. In this example, a sudden jump in the position of the intersection is observed, showing obvious critical behavior. This sudden change shows that the system is sensitive to Emw The extreme sensitivity to changes in the ions demonstrates its potential for high-precision microwave sensing.

[0050] By monitoring the evolution path and tracking the mutations at the intersection, small changes in the microwave amplitude E can be accurately detected. mw , using the quantum criticality of the system to improve sensitivity. To quantitatively analyze this key enhancement, this example tracks the system evolution at points A, B, and C near the critical region, where the intersection index exhibits a significant nonlinear response. The spectral characteristics of the critical region are normalized by the parameter -log(Δ) (Δ =

[0051] |T up -T down |) further capture (T up Representative (Ω p / 2π) 2 The transmittance during the process of increasing from 0MHz to 102.4MHz, T down Representative (Ω p / 2π) 2 The transmittance decreases from 102.4 MHz to 0 MHz), which shows quantum criticality in sensitivity enhancement, such as Figure 2 (c) By analyzing the experimental data at points B and C, even a small change in the microwave amplitude can lead to a significant change in the intersection position, and the sensitivity is extracted as S = 4.12nV cm -1 Hz -1 / 2 In addition, by adjusting the number of atoms N to control the interaction strength, it was found that the interaction strength plays a crucial role in the measurement sensitivity. Figure 3 As N increases, the system becomes highly sensitive to the microwave amplitude and exhibits a more dramatic response. Figure 3 (a) Sensitivity S = 11.1 nV cm -1 Hz -1 / 2 , and in Figure 3 (b) Sensitivity S = 0.88 nV cm -1 Hz -1 / 2 . Figure 3 (c) shows the extracted sensitivity S as a function of N, indicating a clear sensitivity enhancement at higher atomic numbers N. The increase in sensitivity at high N is due to the enhanced collective interactions between Rydberg atoms, which amplifies the system's response to small perturbations in the microwave field. In addition, the dependence of the standard quantum limit (SQL) on the atomic number is plotted as Figure 3 The orange line in (c) shows that when the atomic number N reaches a sufficiently high level, the system exceeds the SQL, highlighting the key difference between enhanced sensing by tracking the intersection of hysteresis trajectories and conventional sensing.

[0052] Heterodyne detection provides an effective measurement method by converting weak microwave fields into detectable optical signals. Figure 4 (a) is the measured oscillation amplitude and microwave field amplitude E mw The data points align well with the red dashed line fit, indicating a stable and predictable response of the system to the microwave field. Figure 4 (b) shows the relationship between the signal-to-noise ratio (SNR) and the microwave field amplitude obtained by fast Fourier transform (FFT) analysis. The system sensitivity is estimated to be 2300nV / cm -1 Hz -1 / 2 , with the threshold signal-to-noise ratio SNR=2 (red dashed line) as a reference for sensitivity estimation. A fundamental limitation of heterodyne detection is its dependence on atomic population, which places strict requirements on the atomic density for optimal performance. More importantly, this method is ultimately limited by the standard quantum limit (SQL), which restricts its sensitivity improvement. In contrast, the method of this embodiment is not constrained by the SQL and benefits from the enhanced interaction effect, thereby achieving higher detection sensitivity. This advantage emphasizes the potential of this embodiment in high-precision microwave sensing, surpassing the limitations of traditional heterodyne technology.

[0053] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation methods of the present invention, and it should be understood that the scope of protection of the present invention is not limited to such specific descriptions and embodiments. Those skilled in the art can make various other specific variations and combinations based on the technical teachings disclosed in the present invention without departing from the essence of the present invention, and such variations and combinations are still within the scope of protection of the present invention.

Claims

1. A method for precise measurement of microwave fields of Rydberg atomic gas based on hysteresis trajectory folding, characterized in that: The following steps are involved: a. Capture and cool using a three-dimensional magneto-optical trap (MOT) 85 Rb atomic gas, forming a cold atomic ensemble; b. Using a two-photon transition scheme, the electromagnetically induced transparency (EIT) effect is constructed by using probe light and coupled light to excite atoms from the ground state to the Rydberg state; c. Using a microwave field to couple two different Rydberg states |r1> and |r2>, a programmable signal generator is used to generate a triangular wave signal to drive an acousto-optic modulator. This modulates the Rabi frequency of the probe light in a linearly increasing and decreasing manner, generating rising and falling scanning trajectories of the probe light. d. Monitor the transmittance of the detection light in real time through the photomultiplier tube (PMT) to obtain the hysteresis trajectory; e. Analyze the intersection points of the hysteresis trajectory, identify the position changes of the trajectory intersection points through moving average filtering, time reversal alignment and binary criterion, and invert the intensity of the microwave field based on the intersection point offset to achieve high-sensitivity measurement; f. Optimize the atomic density N of the cold atomic ensemble and utilize the collective interaction between Rydberg atoms to enhance the microwave field response, so that the sensitivity exceeds the standard quantum limit SQL.

2. The Rydberg atomic gas microwave field precision measurement method according to claim 1, characterized in that: In step a, the magneto-optical trap is composed of a gradient magnetic field generated by a pair of anti-Helmholtz coils and six orthogonal red detuned lasers. The frequency detuning amount of the cooling light is 15 MHz. The return pump light and the cooling light form a closed-loop transition. The atomic density is 3.5×10 11 cm -3 , atomic temperature ≤20μK.

3. The Rydberg atomic gas microwave field precision measurement method according to claim 1, characterized in that: In the step b, the intermediate state of the two-photon transition is 5P3 / 2F=4, the target Rydberg state is 50D5 / 2, and the microwave field frequency is 39.10 GHz, which is used to couple the 50D5 / 2 state and the 48F7 / 2 state to form a four-level EIT structure.

4. The Rydberg atomic gas microwave field precision measurement method according to claim 1, characterized in that: In step c, the modulation period T of the triangular wave signal s The detection light Rabi frequency is in the order of milliseconds to seconds. p The square of the frequency increases linearly from 0 MHz to 102.4 MHz and then decreases symmetrically to 0 MHz, and dynamic regulation is achieved through an acousto-optic modulator.

5. The Rydberg atomic gas microwave field precision measurement method according to claim 1, characterized in that: In the step e, the identification of the intersection of the hysteresis trajectory includes: i. Noise suppression and data alignment for ascending and descending scan traces; ii. Quantify the trajectory difference by normalizing the parameter -log(Δ), Δ = |T up -T down |, T up and T down are the transmittances during the rising and falling processes, respectively; iii. Extracting the sudden change response of the intersection near the critical region with a sensitivity of 0.88nV·cm -1 ·Hz -1 / 2 .

6. The Rydberg atomic gas microwave field precision measurement method according to claim 1, characterized in that: In step f, the Rydberg interatomic interaction is enhanced by regulating the number of atoms N. When N ≥ the critical value, the sensitivity increases exponentially with the increase of N and exceeds the standard quantum limit SQL.

Images