Weak electric field detection method and system based on cavity enhanced on-chip rydberg atom heterodyne spectrum

Abstract

The application provides a weak electric field detection method and system based on cavity-enhanced on-chip Rydberg atom superheterodyne spectrum, and relates to the fields of quantum precision measurement and microwave electric field sensing technology.The method comprises the following steps: comparing a transmission light intensity change rate sequence with a splitting spectrum line slope induced by a local microwave field driving adjacent Rydberg state transition point by point to obtain a linear working point position; performing orthogonal demodulation on a transmission light intensity time sequence at the linear working point position, and performing interval integration and accumulation calculation on the demodulated signal in a preset integration interval to obtain a low-frequency beat signal amplitude; and deriving a to-be-measured weak electric field amplitude according to the low-frequency beat signal amplitude and combining an effective electric field enhancement factor of a cylindrical high-frequency resonant cavity to output a high-frequency weak electric field detection result containing the to-be-measured weak electric field amplitude.The application can effectively characterize the stiffness time-varying degradation effect caused by the accumulation of saturated soft soil pore water pressure, and reasonably solve the problems of fatigue damage evaluation misalignment and lack of closed-loop iterative early warning capability.

Description

Technical Field

[0001] This invention relates to the fields of quantum precision measurement and microwave electric field sensing, and in particular to a weak electric field detection method and system based on the superheterodyne spectrum of Rydberg atoms on a cavity enhancement chip. Background Technology

[0002] As communication and sensing frequencies expand towards millimeter waves and Asia-Pacific Hertz, the electric fields to be measured often exhibit characteristics such as high frequency, weak amplitude, complex spatial distribution, and stringent requirements for phase and long-term stability. In recent years, electric field measurement techniques based on Rydberg atoms have attracted widespread attention due to their advantages such as self-calibration, traceability, wide bandwidth, and non-invasive readout. In particular, the Rydberg atom superheterodyne receiver scheme, which utilizes a strong local oscillator microwave field to convert the high-frequency, weak electric field to be measured into a low-frequency beat signal in an atomic medium, and then reads it out through electromagnetic induction transparent spectroscopy, has been proven to achieve extremely high sensitivity in electric field measurement.

[0003] However, when applying Rydberg atomic superheterodyne technology to the detection of high-frequency extremely weak electric fields, some existing methods have the following shortcomings: First, during the electromagnetic induction transparent spectral readout process of the Rydberg atomic vapor cell within the high-frequency resonant cavity, the variation in transmitted light intensity acquired by the photodetector with the probe light frequency is very slight. Existing technologies generally employ global static spectral line fitting to obtain spectral features, lacking the ability to locally resolve instantaneous changes in transmitted light intensity. This coarse-grained spectral processing method leads to deviations in the linear operating point positioning of the transmission spectrum under weak electric field conditions, resulting in a decrease in the conversion efficiency from high-frequency weak electric field to low-frequency beat frequency signals.

[0004] Second, in long-term measurement scenarios with high-frequency and weak electric fields, the signal-to-noise ratio of the measured signal is low and it is susceptible to environmental thermal drift interference. Existing signal processing methods mostly use arithmetic averaging after discrete point sampling, lacking a mechanism for accumulating continuous physical quantities of the transmitted light intensity time series output by the photodetector within a specific time interval. This discontinuous data processing method impairs the phase coherence of the low-frequency beat signal during long-term integration, and the equivalent noise floor is difficult to effectively reduce with the extension of integration time, limiting the measurement sensitivity and long-term stability.

[0005] Third, the wavelength of the high-frequency electric field to be measured is relatively short, and the field distribution varies significantly within millimeter or even sub-millimeter scales. Using a macroscopic atomic vapor cell introduces a spatial averaging effect, weakening the local signal intensity at the anti-node of the resonant enhancement structure; moreover, the integration design of the on-chip vapor cell and the high-frequency resonant enhancement structure is still insufficient, and the spatial matching problem between the sensing volume and the field distribution still needs to be improved. Summary of the Invention

[0006] This invention provides a weak electric field detection method and system based on Rydberg atom superheterodyne spectroscopy on cavity-enhanced sheets, which can effectively characterize the time-varying stiffness degradation effect caused by the accumulation of pore water pressure in saturated soft soil, and reasonably solve the problems of inaccurate fatigue damage assessment and lack of closed-loop iterative early warning capability.

[0007] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows: Firstly, a weak electric field detection method based on Rydberg atom superheterodyne spectra on cavity enhancement sheets, the method comprising: The weak electric field to be measured is injected into a cylindrical high-frequency resonant cavity, so that the weak electric field to be measured resonates and is enhanced at the anti-node of the electric field near the axis of the cylindrical high-frequency resonant cavity, thus obtaining an enhanced electric field inside the cavity. By placing the on-chip atomic vapor cell inside the cylindrical high-frequency resonant cavity, the effective detection area of ​​the on-chip atomic vapor cell, which is on the order of hundreds of micrometers, is located in the region of maximum enhanced electric field inside the cavity, thus obtaining a spatially matched sensing structure. The probe light and coupling light are injected into the spatial matching sensing structure through the optical aperture, causing the energy levels of alkali metal atoms to resonate two-photon, thus obtaining electromagnetically induced transparent transmitted light. The intensity of the electromagnetically induced transparent transmitted light is calculated point by point as the frequency of the probe light to obtain a sequence of the rate of change of transmitted light intensity. The position of the linear operating point is obtained by comparing the transmitted light intensity change rate sequence with the slope of the split spectral line induced by the transition of adjacent Rydberg states driven by the local oscillator microwave field point by point. The transmitted light intensity time series at the linear operating point is orthogonally demodulated, and the demodulated signal is integrated and accumulated within a preset integration interval to obtain the low-frequency beat frequency signal amplitude. The amplitude of the weak electric field to be measured is derived based on the amplitude of the low-frequency beat frequency signal and the effective electric field enhancement factor of the cylindrical high-frequency resonant cavity, and the high-frequency weak electric field detection result containing the amplitude of the weak electric field to be measured is output.

[0008] Secondly, a weak electric field detection system based on Rydberg atom superheterodyne spectroscopy on a cavity enhancement sheet includes: The acquisition module is used to inject the weak electric field to be measured into a cylindrical high-frequency resonant cavity, so that the weak electric field to be measured resonates and is enhanced at the anti-node of the electric field near the axis of the cylindrical high-frequency resonant cavity, thus obtaining an enhanced electric field inside the cavity; an on-chip atomic vapor cell is placed inside the cylindrical high-frequency resonant cavity, so that the effective detection area of ​​the on-chip atomic vapor cell on the order of hundreds of micrometers is located in the region of maximum enhanced electric field inside the cavity, thus obtaining a spatially matched sensing structure; the probe light and coupling light are injected into the spatially matched sensing structure through an optical aperture, so that the alkali metal atomic energy levels resonate with two photons, thus obtaining electromagnetically induced transparent transmitted light; The calculation module is used to calculate the change in light intensity of the electromagnetically induced transparent transmitted light with the frequency of the probe light point by point, and obtain the sequence of the rate of change of transmitted light intensity. The comparison module is used to compare the transmitted light intensity change rate sequence with the slope of the split spectral line induced by the transition of adjacent Rydberg states driven by the local oscillator microwave field point by point to obtain the position of the linear operating point. The demodulation module is used to perform orthogonal demodulation on the time series of transmitted light intensity at the linear operating point, and to perform interval integration and cumulative calculation on the demodulated signal within a preset integration interval to obtain the amplitude of the low-frequency beat frequency signal. The processing module is used to deduce the amplitude of the weak electric field to be measured based on the amplitude of the low-frequency beat frequency signal and the effective electric field enhancement factor of the cylindrical high-frequency resonant cavity, and output the high-frequency weak electric field detection result containing the amplitude of the weak electric field to be measured.

[0009] The above-described solution of the present invention has at least the following beneficial effects: By calculating the rate of change of electromagnetically induced transparent transmitted light intensity point by point and comparing the slope point by point, the precise location of the linear operating point of the transmission spectrum was achieved, overcoming the shortcomings of existing global static spectral line fitting methods, which suffer from large positioning deviations in the linear region under weak spectral variations. This improvement directly enhances the conversion efficiency from high-frequency weak electric fields to low-frequency beat frequency signals, resulting in more thorough signal extraction under weak electric field conditions. Theoretically, it can increase the system's response sensitivity to extremely weak electric fields by several times.

[0010] By employing orthogonal demodulation and a continuous integration accumulation mechanism within a preset integration interval, the phase coherence of low-frequency beat signals is effectively maintained during long-term observations. This solves the problems of phase noise accumulation caused by traditional discrete-point arithmetic averaging and the difficulty in reducing the equivalent noise floor with increasing integration time. As the integration time increases, the signal coherence accumulation leads to a continuous improvement in the signal-to-noise ratio, and the equivalent noise electric field strength can be reduced, ensuring the requirement for stable measurement over long periods.

[0011] By placing the on-chip atomic vapor cell at the anti-node of the electric field in the cylindrical high-frequency resonant cavity, the effective detection area on the order of hundreds of micrometers is highly matched with the spatial peak height of the enhanced electric field, greatly reducing the spatial field averaging effect and ensuring that the local enhanced electric field is fully sensed. At the same time, the on-chip integrated structure does not require large atomic beam or cold atom devices, the system is compact and highly stable, and is conducive to long-term unattended operation.

[0012] Employing a direct electric field amplitude detection mechanism, the electric field of the signal under test is approximately linearly amplified by the quality factor Q within the resonant cavity, making fuller use of the cavity's quality factor and achieving significant sensitivity gain across a wide frequency range from 10 GHz to 100 GHz. Combined with Rydberg atomic superheterodyne receiver technology, the system does not require the weak signal itself to cause resolvable spectral line splitting, further reducing the difficulty of optical readout and signal processing, and broadening its practical applications. Attached Figure Description

[0013] Figure 1 This is a schematic flowchart of a weak electric field detection method based on Rydberg atom superheterodyne spectroscopy on a cavity enhancement chip, provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of a weak electric field detection system based on Rydberg atom superheterodyne spectroscopy on a cavity enhancement chip, provided by an embodiment of the present invention. Figure 3 This is a schematic diagram of the atomic vapor chamber of the present invention being placed inside a resonant microwave cavity during the experiment.

[0014] Figure 4 This is a schematic diagram of the chip-level Rydberg atomic vapor chamber for optical readout of the present invention.

[0015] Figure 5 This is a schematic diagram of the energy levels of the superheterodyne detection scheme of the present invention.

[0016] Figure 6 This is a schematic diagram of the simulation results of electric field enhancement in a cylindrical cavity with a radius of 2.5 mm and a height of 3 mm according to the present invention. Detailed Implementation

[0017] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0018] This embodiment provides a weak electric field detection system and method for on-chip Rydberg atom superheterodyne spectroscopy with cavity enhancement. The system includes a high-frequency resonant cavity enhancement module, an on-chip Rydberg atom sensing module, an optical electromagnetic induction transparency (EIT) readout module, a local oscillator microwave module, a signal acquisition and processing module, and a frequency tuning and scanning module. The cooperative relationships between the modules are described below. Figure 2 A schematic diagram of the overall system structure is given. Figure 3 An experimental schematic diagram of placing an atomic vapor chamber within a resonant microwave cavity is given. Figure 4 A schematic diagram of a chip-scale Rydberg atomic vapor chamber for optical readout is provided. Figure 5 A schematic diagram of the energy levels for the superheterodyne detection scheme is given.

[0019] The high-frequency resonant cavity enhancement module is used to resonate and amplify the weak electric field under test. The core of this module is a millimeter-scale cylindrical microwave resonant cavity made of oxygen-free copper. The inner surface is precision-machined and chemically polished to reduce surface resistance loss caused by the microwave skin effect, with a surface roughness Ra controlled below 0.1 micrometers. A small optical through-hole, approximately 0.3 mm in diameter, is located on the cavity end face, allowing probe and coupling light to pass through the cavity and the atomic vapor cell. The optical through-hole is aligned with the cavity axis. A weakly coupled microwave port is located on the cavity sidewall for injecting the local oscillator microwave signal. The coupling structure adopts a coplanar waveguide-slot transition, allowing the coupling coefficient between the external microwave source and the cavity to be adjusted through the port's geometric parameters.

[0020] The on-chip Rydberg atom sensing module includes a chip-scale cesium atom vapor cell. This vapor cell is fabricated using a three-layer fused silica micromachining structure: the bottom layer is a transparent fused silica substrate approximately 0.5 mm thick; the middle layer is a square cavity approximately 0.2 mm deep, formed by wet etching; and the top layer is a transparent fused silica cover plate approximately 0.5 mm thick. The three layers are sealed under vacuum using anodizing bonding. The cavity is filled with cesium atom vapor and a suitable amount of buffer gas (such as neon). The buffer gas pressure is approximately 10 Torr to slow the diffusion rate of cesium atoms to the cavity walls and extend the effective coherence time. The overall dimensions of the vapor cell are approximately 2.5 mm × 2.5 mm × 2.5 mm, the effective dimensions of the middle vapor cavity are approximately 1.5 mm × 1.5 mm × 0.2 mm, and the internal effective atom detection area is approximately 200 μm × 200 μm × 200 μm. This vapor cell is positioned at the center of the axis of a cylindrical resonant cavity, placing the effective detection area at the anti-node of the cavity's electric field.

[0021] The optical EIT readout module includes a probe laser, a coupling laser, a frequency stabilization component, a beam shaping component, a polarization control component, an optical aperture coupling component, and a balanced differential photodetector. The probe laser outputs a laser beam with a wavelength of approximately 852 nm, corresponding to the transition from the ground state to the intermediate excited state of a cesium atom; the coupling laser outputs a laser beam with a wavelength of approximately 510 nm, corresponding to the transition from the intermediate excited state to the first Rydberg state of a cesium atom. The two laser beams are combined by a polarization beam splitter and then focused by a lens through an optical aperture and an atomic vapor cell on the cavity end face. The transmitted probe light is received by a balanced differential photodetector, which includes two matched silicon photodiodes and a low-noise differential amplifier with a common-mode rejection ratio better than 40 dB, used to suppress common-mode intensity noise of the probe laser.

[0022] The local oscillator microwave module includes a microwave frequency synthesizer, a power amplifier, an adjustable attenuator, and a microwave switch. The frequency synthesizer generates a frequency-stable, power-adjustable local oscillator microwave signal, which, after power amplification, reaches the field strength level required to drive Rydberg transitions. The local oscillator frequency is set near selected adjacent Rydberg state transition frequencies, and the local oscillator field strength is set to produce resolvable splitting in the EIT transmission spectrum, with splitting intervals typically ranging from 5 MHz to 50 MHz.

[0023] The signal acquisition and processing module includes a high-speed data acquisition card, a lock-in amplifier, and a signal processing computer. The data acquisition card has a sampling rate of no less than 10 megasamples per second and a resolution of no less than 16 bits. The lock-in amplifier is used to extract the low-frequency beat frequency component from the transmitted light intensity time series. The signal processing computer runs signal processing programs, including functional modules for calculating the rate of change of transmitted light intensity, linear operating point location, quadrature demodulation, interval integration and accumulation, field amplitude derivation, and frequency scanning control.

[0024] The frequency tuning and scanning module includes a cavity tuning mechanism, a magnetic field tuning coil, and a frequency control program. The cavity tuning mechanism contains a metal tuning rod that can be finely adjusted along the cavity's axis, regulating its native frequency by changing the effective length of the cavity. The magnetic field tuning coil, wound around the outside of the cavity, generates an axial static magnetic field from 0 to 50 Gauss, used to fine-tune the Rydberg level spacing via the Zeeman effect. The frequency control program coordinates cavity tuning, magnetic field tuning, local oscillator frequency scanning, and laser frequency locking.

[0025] The following combination Figure 1 The flowchart shown illustrates the detection method of this embodiment, providing a detailed explanation. The method includes: Step S1: Inject the weak electric field to be measured into the cylindrical high-frequency resonant cavity, so that the weak electric field to be measured resonates and is enhanced at the anti-node of the electric field near the axis of the cavity, thus obtaining the enhanced electric field inside the cavity.

[0026] In this embodiment, the radius is selected. Approximately 2.5 millimeters, length A cylindrical metal resonant cavity, approximately 3 mm in diameter. The cavity material is oxygen-free copper, and the inner surface is precision-machined and polished with a diamond tool to achieve a surface roughness of [missing information]. The diameter is controlled below 0.1 micrometers to reduce conductor loss caused by the microwave skin effect. An optical via with a diameter of approximately 0.3 mm is formed on each end face of the cavity, aligned with the cavity axis, allowing the probe light and coupling light to pass through. The via diameter is selected based on the principle of being as small as possible while ensuring the entire laser spot passes through, thereby minimizing the disturbance of the via to the electromagnetic field distribution of the cavity's microwave mode and the degradation of the quality factor. The quality factor degradation caused by the via has been pre-evaluated through electromagnetic simulation. In this embodiment, the presence of the via loads a quality factor on the cavity. Even when the quality factor drops from approximately 15,000 to the range of 8,000 to 10,000, this quality factor level can still produce a significant field enhancement effect.

[0027] Select the cavity working mode as follows: This mode is the axial electric field-dominated mode of the cylindrical resonant cavity, which has a significant and uniform axial electric field component near the cavity axis, and the electric field amplitude on the axis is close to the maximum value inside the cavity. mode resonant frequency With cavity radius The interval is determined in the following way: ; in The speed of light in a vacuum. For zero-order Bessel functions The third positive zero point has a value of approximately 8.654. ​​Substituting... Approximately 2.5 millimeters, can be obtained Approximately 165.2 gigahertz, this frequency falls within the Asia-Pacific Hertz band, suitable for searching for hidden photon dark matter in this band, as well as other high-frequency weak electric field detection scenarios. When the frequency of the weak electric field to be measured... With the cavity's intrinsic frequency When they are close, the absolute value of the frequency detuning is satisfied with the following: The ratio is not greater than the reciprocal of the quality factor (i.e., Under the condition of ), the weak electric field to be measured is effectively enhanced by resonance within the cavity.

[0028] Signal electric field amplitude in the atomically sampled region within the cavity Compared with the amplitude of the unenhanced weak electric field to be measured The relationship between them is: ; in, The effective electric field enhancement factor is determined by the loaded quality factor. and local field response factor Joint decision: ; for The mode is when the effective detection region of the atom is located near the center of the cavity axis. Approximately 1. In this embodiment, when loading the quality factor... Under the condition of approximately 8000 to 10000, the effective electric field enhancement factor Agreed to .

[0029] in, Indicates the radius of the cylindrical resonant cavity; Indicates the length of the cylindrical resonant cavity; Indicates cavity Mode eigenfrequency; Indicates the loading quality factor; Indicates the effective electric field enhancement factor; This represents the local field response factor.

[0030] The optical vias on the cavity end face and the microwave coupling ports on the sidewalls, while introducing a small amount of loss, also provide an optical path and an injection channel for the local oscillator microwave. The impact of the optical vias on the cavity's quality factor has been modeled and analyzed using electromagnetic simulation software, confirming that when the via diameter does not exceed 0.4 mm, the quality factor degradation does not exceed 40%. The microwave coupling ports employ a critical coupling or undercoupling design, allowing the energy from the external local oscillator source to be effectively injected into the cavity without excessively altering the cavity's resonant characteristics.

[0031] Step S2: Place the on-chip atomic vapor cell inside a cylindrical high-frequency resonant cavity, so that the effective detection area of ​​the on-chip atomic vapor cell, which is on the order of hundreds of micrometers, is located in the region of maximum enhanced electric field inside the cavity, thus obtaining a spatially matched sensing structure.

[0032] The fabrication process of the on-chip cesium atom vapor cell is as follows. On three fused silica wafers, each approximately 0.5 mm thick, a square cavity with a depth of approximately 0.2 mm and a side length of approximately 1.5 mm is formed on the middle wafer using photolithography and wet etching processes. This cavity forms the main structure of the vapor cell. A relaxation-resistant coating (such as a paraffin coating or an OTS self-assembled monolayer) with a thickness of approximately 50 nanometers is deposited on the inner surfaces of the bottom and top wafers to extend the spin coherence lifetime after cesium atoms collide with the cavity walls. Under conditions of vacuum superior to... Inside the vacuum chamber of the Torr, three wafers are aligned and anoly bonded. Before bonding, cesium atom vapor is introduced into the vapor chamber by heating a cesium release agent (such as the thermal decomposition reaction of alkali metal silicides), and neon gas at approximately 10 Torr is introduced as a buffer gas. The bonded vapor chamber is then removed from the vacuum chamber and formed into independent chip-level vapor chamber units through dicing and packaging.

[0033] The steam tank has an external dimension of approximately 2.5 mm. 2.5 mm 2.5 mm, with the effective size of its intermediate steam chamber being approximately 1.5 mm. 1.5 mm 0.2 mm. Considering the spot diameters of the probe and coupling beams (approximately 50 to 100 micrometers after focusing by the lens), the overlapping area of ​​the two laser beams within the vapor cavity constitutes the effective atom detection region, with a size of approximately 200 micrometers. 200 micrometers 200 micrometers. The size of this effective detection region is much smaller than the radius of the cylindrical resonant cavity (2.5 millimeters). Therefore, the spatial distribution of the high-frequency electric field in this region is approximately uniform, and the spatial averaging effect caused by the non-uniform field distribution can be ignored.

[0034] The steam pool is fixed at the center of the cavity axis using precision mechanical clamps or UV-cured optical adhesive, ensuring the effective detection area is aligned with the cavity. The regions of maximum axial electric field values ​​in the mode coincide. The electric field amplitude at the cavity axis is the maximum value within the cavity, and the electric field direction is parallel to the cavity axis. The direction of the electric dipole moment of the Rydberg transition of cesium atoms should be as consistent as possible with the direction of the electric field within the cavity. In this embodiment, this is achieved by selecting... Towards The transition (selection) of (Transition), which orients the electric dipole moment along the cavity axis, thereby maximizing the coupling strength between the atom and the enhanced electric field inside the cavity.

[0035] Thermal management between the steam pool and the cavity is a practical engineering issue that needs to be addressed in this embodiment. The cesium atom steam pool typically needs to be heated to 60 to 120 degrees Celsius to obtain sufficient atomic number density, while the cavity temperature needs to be kept stable to maintain its intrinsic frequency. In this embodiment, a miniature ceramic heating element is placed on each side of the steam pool, and the steam pool temperature is stabilized at approximately 80 degrees Celsius through closed-loop thermocouple temperature control. The temperature is maintained at 0.1 degrees Celsius, while water-cooled pipes or semiconductor cooling chips are installed on the outer wall of the cavity to maintain the cavity temperature at approximately 25 degrees Celsius. At 0.1 degrees Celsius, thermal isolation between the two is achieved through a silicon nitride ceramic support with low thermal conductivity. A microporous aerogel insulation layer is filled between the heating element of the steam tank and the cavity wall to further reduce heat conduction.

[0036] Step S2: Place the on-chip atomic vapor cell inside a cylindrical high-frequency resonant cavity, so that the effective detection area of ​​the on-chip atomic vapor cell, which is on the order of hundreds of micrometers, is located in the region of maximum enhanced electric field inside the cavity, thus obtaining a spatially matched sensing structure.

[0037] The fabrication process of the on-chip cesium atom vapor cell is as follows. On three fused silica wafers, each approximately 0.5 mm thick, a square cavity with a depth of approximately 0.2 mm and a side length of approximately 1.5 mm is formed on the middle wafer using photolithography and wet etching processes. This cavity forms the main structure of the vapor cell. A relaxation-resistant coating (such as a paraffin coating or an OTS self-assembled monolayer) with a thickness of approximately 50 nanometers is deposited on the inner surfaces of the bottom and top wafers to extend the spin coherence lifetime after cesium atoms collide with the cavity walls. Under conditions of vacuum superior to... Inside the vacuum chamber of the Torr, three wafers are aligned and anoly bonded. Before bonding, cesium atom vapor is introduced into the vapor chamber by heating a cesium release agent (such as the thermal decomposition reaction of alkali metal silicides), and neon gas at approximately 10 Torr is introduced as a buffer gas. The bonded vapor chamber is then removed from the vacuum chamber and formed into independent chip-level vapor chamber units through dicing and packaging.

[0038] The vapor chamber has external dimensions of approximately 2.5 mm × 2.5 mm × 2.5 mm, with the effective dimensions of the central vapor cavity being approximately 1.5 mm × 1.5 mm × 0.2 mm. Considering the spot diameters of the probe and coupling beams (approximately 50 to 100 micrometers after focusing by the lens), the overlapping area of ​​the two laser beams within the vapor cavity constitutes the effective atomic detection region, with dimensions of approximately 200 micrometers × 200 micrometers × 200 micrometers. This effective detection region is much smaller than the radius of the cylindrical resonant cavity (2.5 mm), therefore the spatial distribution of the high-frequency electric field within this region is approximately uniform, and the spatial averaging effect caused by non-uniform field distribution can be neglected.

[0039] The steam pool is fixed at the center of the cavity axis using precision mechanical clamps or UV-cured optical adhesive, ensuring the effective detection area is aligned with the cavity. The regions of maximum axial electric field values ​​in the mode coincide. The electric field amplitude at the cavity axis is the maximum value within the cavity, and the electric field direction is parallel to the cavity axis. The direction of the electric dipole moment of the Rydberg transition of cesium atoms should be as consistent as possible with the direction of the electric field within the cavity. In this embodiment, this is achieved by selecting... Towards The transition (selection) of (Transition), which orients the electric dipole moment along the cavity axis, thereby maximizing the coupling strength between the atom and the enhanced electric field inside the cavity.

[0040] Thermal management between the steam pool and the cavity is a practical engineering issue that needs to be addressed in this embodiment. Cesium atom steam pools typically need to be heated to 60°C to 120°C to obtain sufficient atomic number density, while the cavity temperature needs to be kept stable to maintain its intrinsic frequency. In this embodiment, a micro-ceramic heating element is placed on each side of the steam pool. A closed-loop thermocouple temperature control system stabilizes the steam pool temperature at approximately 80°C ± 0.1°C. Simultaneously, water-cooled pipes or semiconductor cooling chips are installed on the outer wall of the cavity to maintain the cavity temperature at approximately 25°C ± 0.1°C. Thermal isolation between the two is achieved using a silicon nitride ceramic support with low thermal conductivity. A microporous aerogel insulation layer is filled between the heating element of the steam pool and the cavity wall to further reduce heat conduction.

[0041] Step S3: Inject the probe light and coupling light through the optical aperture into the space-matching sensing structure to induce two-photon resonance in the energy levels of alkali metal atoms, thereby obtaining electromagnetically induced transparent transmitted light.

[0042] This embodiment uses a four-level cesium atom system as an example for illustration. The ground state is selected. Corresponding cesium atom Energy level, intermediate excited state correspond Energy level, first Rydberg state correspond Energy level, second Rydberg state correspond or Energy level. Principal quantum number Select based on the target measurement frequency: for example, for an electric field to be measured at approximately 165 GHz, you can select... The principal quantum number is approximately between 58 and 62, making and The transition frequency between the cavity The modes and frequencies match. Different The transition frequency corresponding to the value can be precisely calculated using the quantum defect parameters of the cesium atom.

[0043] The probe laser is an external cavity semiconductor laser (ECDL) with a free-running linewidth of less than 1 MHz. It is locked to the cross-resonance peak of the transition from the ground state to the intermediate excited state of cesium atoms using saturable absorption spectroscopy frequency stabilization technology, achieving a frequency stability better than 1 MHz per hour. The probe light power is approximately 10 to 100 microwatts before entering the vapor cell, and the spot diameter is focused by a lens to approximately 80 micrometers. The coupling laser is a frequency-doubled semiconductor laser or a Ti:sapphire laser, with a wavelength around 510 nanometers (the specific wavelength depends on the selected wavelength). The frequency is stabilized by the Fabry-Perot etalon, and the linewidth is less than 1 MHz. The coupled light power is approximately 1 mW to 10 mW before incident on the vapor cell, and the spot diameter is focused to approximately 100 micrometers.

[0044] The probe light and coupling light propagate through the steam pool in opposite directions, and the two beams spatially overlap in the central region of the steam chamber. When the probe light frequency meets... Towards The single-photon resonance condition is met, and the difference between the probe light frequency and the coupling light frequency satisfies... Towards Under two-photon resonance conditions, quantum interference occurs between the three energy levels, producing a narrow-linewidth transparent window in the absorption spectrum, known as the electromagnetically induced transparency (EIT) transmission peak. The transmitted probe light exits through an optical aperture at the other end of the cavity and is received by a balanced differential photodetector. The balanced differential detector differentially amplifies the signal beam and a reference beam, effectively suppressing common-mode intensity noise of the probe laser and improving the photoelectric detection signal-to-noise ratio by approximately 10 to 20 dB.

[0045] The probe light frequency is scanned in steps of approximately 0.1 MHz near the resonance frequency from the ground state to the intermediate excited state, while the transmission light intensity is recorded as a function of probe light frequency detuning, yielding the EIT transmission spectrum. Without an applied local oscillator microwave field, the EIT transmission peak exhibits a single, narrow-linewidth transparent window, the amplitude and linewidth of which depend on the Rabi frequency of the probe light, the Rabi frequency of the coupling light, and the atomic coherent dephasing rate. In this embodiment, the full width at half maximum (FWHM) of the EIT transparent window is approximately 5 MHz to 10 MHz.

[0046] Step S4: Calculate the change in intensity of electromagnetically induced transparent transmitted light with the frequency of the probe light point by point to obtain the sequence of transmission light intensity change rate. This step includes the following sub-steps.

[0047] Step S41 (Obtaining the discrete sequence of transmitted light intensity): During the probe light frequency scanning process, a fixed frequency step size is used. Collect each probe light frequency point sequentially The corresponding transmitted light intensity value This yields a discrete sequence of transmitted light intensity. Frequency step size. The selection must satisfy the Nyquist sampling condition, i.e. It should be less than half the full width at half maximum (FWHM) of the EIT transparent window. In this embodiment, the full width at half maximum (FWHM) of the EIT transparent window is approximately 5 MHz to 10 MHz, therefore... The frequency is set to approximately 0.1 MHz, and the total number of sampling points is [number missing]. The range is approximately 500 to 1000, covering a frequency range of about 50 MHz to 100 MHz. At each frequency point, the data acquisition card collects the transmitted light intensity signal at a sampling rate of about 1 mega-samples per second. After each acquisition, the average value is taken as the light intensity value at that frequency point after about 1 millisecond, in order to suppress high-frequency random noise.

[0048] Step S42 (Calculate the rate of change point by point): The difference between adjacent light intensity values ​​in the discrete sequence of transmitted light intensity. Interval with corresponding probe light frequency The ratios are calculated point by point to obtain the sequence of transmitted light intensity change rates.

[0049] Step S421 (Extracting adjacent light intensity differences): For the first value in the discrete sequence of transmitted light intensity... Frequency points ( The corresponding light intensity value Extract the light intensity value and the previous frequency point. The corresponding light intensity value The difference between them, i.e. For the first frequency point ( Since there is no previous frequency point, its rate of change can be approximated by the rate of change of the second frequency point.

[0050] Step S422 (calculate the ratio to obtain the rate of change sequence), for each satisfying The frequency point will be the difference between adjacent light intensities. As the dividend, the frequency interval As a divisor, calculate the ratio. , to obtain at the frequency point The rate of change of transmitted light intensity at each frequency point is used as a characterizing quantity. The above calculation steps are performed sequentially at each frequency point to obtain the result containing... The sequence of transmission light intensity variation rates for each element. This sequence reflects the local slope distribution characteristics of the EIT transmission spectral lines along the probe light frequency scanning direction. Its absolute value reaches a local maximum near the rising and falling edges of the EIT transparent window, and approaches zero near the center of the transparent window.

[0051] It should be noted that the rate of change in the above operation is the ratio of the light intensity difference between two adjacent points to the frequency interval between those two points, performed on a discrete frequency point sequence. The result is used as a local slope characterization of the EIT transmission spectrum at different frequency positions, and is used for the precise positioning of the subsequent linear working point.

[0052] Step S5: Compare the transmitted light intensity change rate sequence with the slope of the split spectral line induced by the transition of adjacent Rydberg states driven by the local oscillator microwave field point by point to obtain the position of the linear operating point.

[0053] Based on establishing EIT optical readout and obtaining the transmitted light intensity change rate sequence, this step locates the linear operating point by injecting a strong local oscillator microwave field and utilizing the spectral line splitting induced by it.

[0054] Turn on the local oscillator microwave source. Local oscillator frequency. Settings Towards transition frequency Near the frequency deviation The absolute value is controlled within 1 MHz. The local oscillator field, after being amplified by a power amplifier, is injected into the cavity through a microwave coupling port on the cavity sidewall. The Rabi frequency of the local oscillator field within the cavity... It is controlled by adjusting the attenuation of the adjustable attenuator.

[0055] Local oscillator frequency The selection principle is: This causes a clearly discernible split in the EIT transmission spectrum, i.e. It should be at least 3 to 5 times the full width and half-height of the EIT transparent window. In this embodiment... Agreed megahertz to Megahertz. When When the width at half maximum (FWHM) of the EIT transparent window is significantly larger than the full width at half maximum (FWHM), the original single-peak EIT transmission window splits into two windows with a spacing of approximately [missing information] in the direction of the probe light frequency scan. The sub-transmission peaks, and the region between the two sub-peaks corresponds to the frequency range between the two adorned states. Figure 5 The energy level structure and splitting spectral morphology of the superheterodyne detection scheme are schematically shown.

[0056] Under the condition of applying a local oscillator microwave field, the same frequency step size is used again. The frequency of the probe light is scanned within the scanning range, and the transmitted light intensity sequence after the local oscillator field is applied is collected. The transmission light intensity change rate sequence after the local oscillator field is applied is calculated in the same way as S41 to S422 in step S4.

[0057] The rate of change sequence before and after applying the local oscillator field is compared point-by-point across the same set of frequencies. Specifically, for each frequency point... Calculate the difference between corresponding elements in two rate of change sequences. This yields a sequence of rate of change differences. In this sequence, the frequency points with larger absolute values ​​of the differences correspond to the locations where the local oscillator has a greater influence on the slope of the EIT spectral line. These locations are usually situated on the outer slopes of the two sub-peaks after the splitting.

[0058] In this specific implementation, the top 10% of frequency points with the highest absolute values ​​of the rate of change difference are selected as the candidate operating point set. The local linearity of the transmitted light intensity to the probe light frequency response at each of these candidate points is examined: Within a neighborhood of ±1 MHz centered on the candidate point, the absolute value of the Pearson correlation coefficient between the transmitted light intensity and frequency mistuning is calculated. If this absolute value is greater than 0.95, the candidate point is considered to meet the linear response condition. Among the candidate points that meet the linear response condition, the frequency point with the largest absolute value of the rate of change difference is selected as the linear operating point, and its corresponding probe light frequency is denoted as . At the linear operating point At this point, the detector frequency is locked at this value, and all subsequent time series measurements are performed at this frequency.

[0059] At the linear operating point At this point, a tiny change in the Rydberg level, caused by the coherent mixing between the weak electric field being measured and the local oscillator field, can be approximately linearly converted into a change in the intensity of the transmitted probe light. This approximately linear relationship holds under the condition that the Rabi frequency corresponding to the weak electric field being measured... Much smaller than the local oscillator Rabi frequency (typically) Under these conditions, the residual of the linear approximation is less than one percent.

[0060] Step S6: Perform orthogonal demodulation on the time series of transmitted light intensity at the linear operating point, and perform interval integration and cumulative calculation on the demodulated signal within the preset integration interval to obtain the amplitude of the low-frequency beat frequency signal.

[0061] Determining the linear operating point Then, the probe light frequency was locked at this operating point, and the time series of transmitted light intensity was continuously acquired. This step extracts the amplitude of the low-frequency beat frequency component from the transmitted light intensity time series through orthogonal demodulation processing.

[0062] Step S61 (generating a local oscillator reference signal and performing quadrature mixing): In the signal processing computer, two frequencies equal to the expected low-frequency beat frequency are generated. (i.e., the frequency of the weak electric field to be measured) With local oscillator frequency The absolute value of the difference: The digital reference signal is ( ). The in-phase reference signal is ( ). The orthogonal reference signal is The collected transmitted light intensity time series Multiply by the in-phase reference signal and the quadrature reference signal respectively, that is, multiply by each sampling point at each sampling time. calculate and This yields in-phase and quadrature mixing signal sequences. In this embodiment, the sampling rate of the data acquisition card is set to 1 megasamples per second. Typical settings range from 1 kHz to 100 kHz, ensuring at least 10 sampling points are available for resolving the signal waveform within each beat cycle.

[0063] Step S62 (accumulate numerical integration within a preset integration interval), within the preset integration interval Within the sequence, the product of each sampled value of the in-phase mixer signal sequence and the sampling time interval is accumulated point by point to obtain the in-phase integral value. The summation iterates through all sampling times within the integration interval. This is the time interval between adjacent sampling points (i.e., the reciprocal of the sampling period). Perform the same operation on the quadrature mixing signal sequence to obtain the quadrature integral value. The process of accumulating these values ​​is physically equivalent to applying a low-pass filter to the mixing signal: the frequency in the mixing signal is twice that of the mixing signal. The high-frequency components (sum frequency components) are averaged to near zero due to oscillations within the integration interval, while the DC component (difference frequency component) with zero frequency increases linearly with the accumulation time. (Preset integration interval) The selection depends on the characteristics of the signal to be measured: for narrowband signals with long coherence times, A larger value can be chosen to narrow the equivalent noise bandwidth, as shown in this embodiment. Typically, this ranges from 0.1 seconds to 10 seconds; for transient signals with finite coherence time, It should not exceed the coherence time of the signal.

[0064] Step S63 (Calculate the low-frequency beat frequency signal amplitude based on the in-phase integral value and the quadrature integral value): Calculate the square root of the sum of the squares of the in-phase integral value and the squares of the quadrature integral value, i.e., for... The square of and The square root of the sum of the squares is used as the amplitude of the low-frequency beat frequency signal, denoted as . The advantage of this calculation method is that its results are not affected by the relative phase difference between the measured signal and the reference signal. When there is a constant phase shift between the measured signal and the local oscillator reference signal, the in-phase integral value and the quadrature integral value will change with the phase shift, but their sum of squares depends only on the amplitude of the measured signal and is independent of the phase shift.

[0065] Low frequency beat frequency signal amplitude Rabi frequency corresponding to the weak electric field to be measured Slope conversion coefficient of EIT spectral line at the operating point and the length of the integration interval The qualitative relationship between them is: Proportional to and The product of then multiplied by .in, Indicates at the linear operating point The change in transmitted light intensity caused by a unit change in Rabi frequency is expressed in volts per second (radians per second). The specific values ​​were determined through subsequent calibration steps using a calibration microwave field of known intensity.

[0066] Step S7: Based on the low-frequency beat frequency signal amplitude and the effective electric field enhancement factor of the cylindrical high-frequency resonant cavity, derive the amplitude of the weak electric field to be measured, and output the high-frequency weak electric field detection result containing the amplitude of the weak electric field to be measured. This step converts the low-frequency beat frequency signal amplitude obtained in step S6 into the amplitude of the weak electric field to be measured, specifically including the following steps: Step S71 (Obtain System Response Parameters): Retrieve two key system response parameters from the system calibration database. The first parameter is the cylindrical high-frequency resonant cavity's response at the current operating frequency. Effective electric field enhancement factor This parameter was determined by measuring the cavity scattering parameters using a vector network analyzer and combining them with electromagnetic simulation. The first parameter is a dimensionless quantity, defined as the ratio of the electric field amplitude at the atomic sampling region inside the cavity to the amplitude of the electric field being measured outside the cavity. The second parameter is the Rydberg atom microwave electric field sensitivity. This parameter was determined through calibration experiments and is defined as the beat frequency signal amplitude generated at the end of the S6 processing flow (i.e., after quadrature demodulation and integration accumulation) after EIT optical readout and photoelectric detection when a unit intensity microwave electric field is applied to the atomic sampling region. Its dimension is volt-meter per volt. It encompasses the entire link conversion efficiency from electric field-atomic coupling, EIT transmission light intensity modulation, photoelectric conversion to orthogonal demodulation.

[0067] Step S72 (deriving the amplitude of the weak electric field to be measured based on system response parameters) involves two stages. The first stage derives the equivalent electric field inside the cavity: the amplitude of the low-frequency beat signal obtained in step S63 is... Divide by the microwave electric field sensitivity of the Rydberg atom and the length of the integration interval The product of these two values ​​yields the equivalent amplitude of the enhanced signal electric field actually sensed by the atom within the cavity. The second-level derivation is the electric field to be measured outside the cavity: the amplitude of the equivalent electric field inside the cavity is... Divide by the effective electric field enhancement factor The amplitude of the weak electric field under test is restored to the value when there is no external reinforcement. In each step of the above two-level derivation, the intermediate and final quantities retain their physical dimensions and uncertainties.

[0068] In practical applications, the limitations of system noise on the measurement results must also be considered. First, the system's performance within the integration interval is calculated. The root mean square value of noise within It can be achieved through the shooting frequency Within a frequency band of approximately 1 kHz on both the left and right (excluding) The signal-to-noise ratio (SNR) is obtained by processing the same orthogonal demodulation and integral accumulation process (itself). and with the preset detection threshold A comparison is made. In this embodiment... A value of 5 corresponds to approximately a 95% confidence level (under the assumption of pure Gaussian noise). When At that time, the amplitude of the electric field to be measured is output. and its uncertainty (Synthesized from signal-to-noise ratio and system calibration uncertainty according to error propagation relationship); when At that time, the elimination sensitivity at that frequency point is calculated based on the system noise floor and integration time. .

[0069] Excluding sensitivity The derivation process is as follows: Under the assumption that only system noise exists, the standard deviation of the noise in the integration interval is... Take the detection threshold. If the value is 5, then the minimum detectable intracavity equivalent electric field amplitude is 5. Divide by the effective electric field enhancement factor Afterwards, the sensitivity was excluded. The physical meaning of excluding sensitivity is: at approximately a 95% confidence level, if the true amplitude of the weak electric field being measured is greater than... If the signal is within the specified range, the system can detect it with a signal-to-noise ratio exceeding the threshold under the current conditions; if the actual amplitude is less than the specified value... If so, the system cannot reliably distinguish the signal from the noise under the current conditions.

[0070] The final output of the high-frequency weak electric field detection results includes the following: the frequency of the weak electric field to be measured. (Based on the local oscillator frequency) and shooting frequency Estimation: or (The sign of the signal needs to be determined by changing the direction of the local oscillator frequency) and the amplitude of the weak electric field to be measured. (Given only if a signal is detected) Relative phase of the weak electric field to be measured (Determined by the arctangent of the in-phase integral and the orthogonal integral:) Measurement uncertainty of the amplitude of the weak electric field to be measured When no signal exceeding the threshold is detected, the exclusion sensitivity at that frequency point is output. For dark matter search applications, the exclusion sensitivity of all scanned frequency points is summarized into an exclusion sensitivity spectrum output.

[0071] Before formally measuring the weak electric field to be measured, the entire detection system needs to be fully calibrated, and multiple sets of background data under reference conditions need to be collected. The calibration work is divided into the following four parts.

[0072] Frequency calibration is performed using a microwave frequency counter calibrated with rubidium or cesium atom frequency standards to calibrate the absolute value of the output frequency of the local oscillator microwave frequency synthesizer. The frequency measurement accuracy is better than [previous standard]. Simultaneously, the transmission coefficient of the cavity was measured using a vector network analyzer. The curve determines the cavity's intrinsic frequency by identifying the frequency position corresponding to the resonance peak. The loading quality factor of the cavity was calculated using the 3 dB bandwidth method of the resonance peak. ,in for The frequency width at which the peak of the curve drops by 3 dB. Frequency calibration should be performed after the cavity has reached thermal equilibrium (usually requiring preheating for more than 30 minutes), and recalibrated at regular intervals (e.g., every 24 hours) to track long-term drift.

[0073] Field enhancement factor calibration: The effective electric field enhancement factor is determined by combining the perturbation method with electromagnetic simulation. The specific operation is as follows: Under the condition of known input microwave power, a miniature electric field probe (such as an electro-optic crystal probe or a small-sized dipole antenna probe) is moved point by point along the cavity axis with a fixed step size (such as 0.1 mm), and the relative amplitude of the electric field at each spatial position is measured. The electric field amplitude at the atom sampling position on the cavity axis (i.e., the location of the effective detection area of ​​the vapor pool) is compared with the electric field amplitude at a reference position outside the cavity far away from the cavity. The ratio of the two is the measured effective electric field enhancement factor. The measured values ​​are cross-validated with the predicted values ​​from the electromagnetic simulation software; the deviation between the two should typically be within 10%. In this embodiment, within the cavity... Under typical operating conditions of approximately 9000, actual measurements Approximately .

[0074] Atomic sensitivity calibration is performed under the condition that the cavity is in a detuned state (i.e., the cavity's intrinsic frequency deviates from the measured frequency by at least 5 resonant linewidths by inserting a dielectric tuning rod or changing the cavity temperature, at which point the field enhancement effect is negligible). A series of calibration microwave fields with known frequencies and amplitudes are injected into the cavity through the microwave coupling port. The frequency of the calibration microwave field is set to the target measurement frequency, and the amplitude is calculated using a calibrated microwave power meter and the transmission coefficient of the coupling port. Following the complete processing flow from steps S3 to S6, the corresponding low-frequency beat frequency signal amplitude for each calibration field amplitude is recorded. The relationship between the calibration electric field amplitude and the beat frequency signal amplitude is fitted using linear regression. The slope of the fitted line is the microwave electric field sensitivity of the Rydberg atom. The calibration process should be repeated at no fewer than 10 frequency points (uniformly covering the target frequency range) and no fewer than 5 sets of calibration field strengths (covering more than two orders of magnitude of the expected dynamic range of the test field strength) to evaluate... Frequency dependence and linear response range.

[0075] Background data acquisition and system pseudo-signal diagnosis: A set of data was collected under each of the following four reference conditions to identify and quantify possible sources of system pseudo-signals.

[0076] Condition 1 (Local Oscillator Off): Turn off the local oscillator microwave field output, keep the other conditions unchanged, collect the transmitted light intensity time series, and obtain the background noise level under this condition according to the processing flow of step S6. This noise mainly comes from the detection laser intensity noise and the dark current noise of the photodetector.

[0077] Condition 2 (probe light detuning): The frequency of the probe light is adjusted at least 50 MHz away from the center of the EIT transparent window so that the probe light no longer resonates with the atomic energy level. All other conditions remain unchanged. The collected data is used to evaluate the time-varying characteristics of non-resonant background absorption and scattered light.

[0078] Condition 3 (Cavity Detuning): The cavity's intrinsic frequency is tuned away from the frequency to be measured by at least 100 MHz using a mechanical tuning mechanism, so that the cavity no longer significantly enhances the electric field in the frequency band to be measured. All other conditions remain unchanged, and the collected data is used to separate the cavity thermal drift effect and the influence of environmental electromagnetic interference.

[0079] Condition 4 (Laser off then on): Alternately turn the detection laser and the coupling laser on and off, and record the dark noise level of the photodetector under no-light conditions for comparison and analysis with the noise spectrum under light conditions.

[0080] For weak electric field signals with extremely low amplitudes (such as electric fields induced by hidden photons and dark matter), the signal-to-noise ratio of a single short-duration measurement is far below the detectable level. Therefore, long-term integration and statistical analysis methods are necessary to accumulate the signal and suppress noise. This embodiment employs segmented coherent processing and power spectrum superposition to achieve long-term integration.

[0081] Determine the duration of a single time segment. , The selection of the phase noise is limited by the effective coherence time of the system, which is mainly determined by the phase noise of the local oscillator microwave frequency synthesizer. When using a low-phase-noise microwave frequency synthesizer with a phase noise better than -120 dB / Hz at a 1 kHz offset frequency, the effective coherence time of the local oscillator field can reach more than 10 milliseconds. In this embodiment, A conservative estimate of 1 millisecond corresponds to a frequency resolution of approximately 1 kilohertz, which is sufficient to distinguish beat frequencies. (Its typical value is in the kilohertz range).

[0082] Segmented processing, the total measurement time for each frequency tuning point (Typically, 2 hours, or approximately 7200 seconds) is divided into In this embodiment, there are time segments of equal length. Approximately For the transmitted light intensity time series within each segment, the orthogonal demodulation and integration accumulation operations of steps S61 to S63 are performed independently to obtain the low-frequency beat frequency signal amplitude corresponding to that segment. ,in From 1 to .

[0083] Power spectrum superposition, for The power spectrum of each signal segment is superimposed. For each segment... Calculate its beat frequency Signal power at Meanwhile, in terms of shooting frequency Within a frequency band shifted approximately 1 kHz to the left and right (the total width of this frequency band is taken as the beat frequency) About 20%, but excluding (It is located in a narrow frequency band), and follows the same processing procedure as the signal channel (i.e., it generates signals at the same frequency). The reference signal, also performs quadrature demodulation and has the same length (Integral accumulation) to calculate the power of the noise reference channel. The same procedure described above, performed on a narrow frequency band without a real signal, ensures that the signal channel and the noise reference channel experience exactly the same system gain and filtering characteristics, making their statistical distributions comparable.

[0084] Statistical judgment, The signal power and noise reference power of each segment are averaged to obtain the average signal power. and average noise power Under the pure noise assumption (i.e., the amplitude of the electric field being measured is zero), the statistic... asymptotic obedience has degrees of freedom The chi-square distribution. Based on this distribution, the probability of a false alarm (e.g., ...) can be calculated. The detection threshold is set below ) and any value exceeding this threshold is considered valid. This is considered a candidate signal.

[0085] To evaluate the sensitivity level of this embodiment under typical conditions, the following estimates are given. Referring to the reported Rydberg atom superheterodyne scheme, the equivalent noise electric field spectral density under cavity-free enhancement conditions is approximately 55 nanovolts per centimeter per root hertz. In this embodiment, the effective electric field enhancement factor... Approximately After field enhancement, the equivalent noise electric field spectral density of the system is reduced to approximately Volts per centimeter per root-number hertz. After integration over 2 hours (approximately 7200 seconds), the equivalent noise bandwidth is approximately Hertz, minimum detectable electric field amplitude Approximately Divide by volt per centimeter Then multiply by the signal-to-noise ratio factor corresponding to the detection threshold, and finally... The typical value is approximately volts per centimeter.

[0086] To cover different target electric field frequencies, this embodiment uses a combination of various tuning methods to achieve frequency tuning and scanning.

[0087] Table 1 shows the combination of various tuning methods to achieve frequency tuning and scanning.

[0088] In frequency scanning mode, the dwell time at each frequency tuning point is determined by the preset total scan time budget and the number of frequency points to be covered. Taking a typical scanning task as an example: the total scan time budget is 30 days (approximately...). The system requires approximately 556 frequency points to be covered, with a frequency range of 10 GHz and a single cavity bandwidth of approximately 18 MHz. The average integration time for each frequency point is approximately 4700 seconds (about 1.3 hours). The actual scanning strategy employs non-uniform time allocation across different sub-intervals of the target frequency band: longer integration times are allocated to frequency bands physically more likely to contain signals (such as preferred mass intervals predicted by specific dark matter mass models) to achieve lower exclusion sensitivity; for frequency bands with higher background noise, the integration time can be appropriately shortened to save on the overall time budget. After the measurement process is completed, the system outputs a measurement report based on the detection results.

[0089] For typical high-frequency weak electric field measurement applications: If at the expected beat rate The signal-to-noise ratio was detected to exceed the preset threshold. If the signal peak is high, the following four pieces of information will be output: Frequency of the electric field to be measured From the local oscillator frequency and shooting frequency Calculation ( The ambiguity of the positive and negative signs is eliminated by observing the direction of the beat frequency change after changing the local oscillator frequency by a known small amount.

[0090] Amplitude of the electric field to be measured This is obtained from the calculation process in step S72.

[0091] Relative phase of the electric field to be measured It is calculated from the arctangent of the in-phase integral and the orthogonal integral.

[0092] Measurement uncertainty, the standard deviation or expanded uncertainty of each of the above physical quantities (the inclusion factor must be specified), is given by combining the signal-to-noise ratio and the calibration uncertainty of each link according to the error propagation rule.

[0093] For dark matter search applications: If the signal-to-noise ratio does not exceed the threshold at a certain frequency tuning point The candidate signal is then combined with the effective electric field enhancement factor at that frequency. Integral Time Atomic microwave electric field sensitivity Based on the measured noise floor, and following the elimination sensitivity calculation method given in step S7, output the elimination sensitivity at that frequency point. Summarize the exclusion sensitivities of all frequency tuning points that have been scanned, and plot the exclusion sensitivity spectrum with frequency on the x-axis and exclusion sensitivity on the y-axis. The frequency points corresponding to the local minima in the exclusion sensitivity spectrum are the frequency coverage blind spots of the system (usually caused by cavity mode cross-interference, environmental electromagnetic interference, or laser frequency instability), and the local maxima correspond to the strongest detection depth that the system can achieve in that frequency band.

[0094] Candidate signal confirmation process: If the signal-to-noise ratio exceeds a threshold at a certain frequency point Candidate signals cannot be directly identified as real signals. Remeasurement must be performed with at least two independent measurement conditions changed to eliminate internal spurious signals and external electromagnetic interference. The measurement conditions to be changed include, but are not limited to, at least two of the following five: Switching the cavity working mode: such as from Switch mode to Mode. If it is a real external electric field signal, the frequency remains unchanged while the field enhancement factor changes, and the signal amplitude will change according to the ratio of the field enhancement factor of the new mode to that of the old mode.

[0095] Replace the Rydberg state combination: such as from Switch to The actual signal frequency remains unchanged, but the atomic response sensitivity will change.

[0096] Change the local oscillator frequency: to adjust the beat frequency A known change occurs (e.g., from 10 kHz to 15 kHz). The beat frequency peak of the real signal should shift accordingly in the spectrum, while spurious signals within the system (e.g., local oscillator leakage harmonics) remain in place or shift according to different patterns.

[0097] Changing the Zeeman magnetic field strength shifts the atomic transition frequency by a known amount. The actual signal should behave in accordance with the known response of atomic transitions to the magnetic field.

[0098] Changing the cavity temperature causes the cavity's intrinsic frequency to shift by a known amount. The intensity change of the actual signal should conform to the Lorentz curve of the cavity resonance curve.

[0099] A candidate signal is reported as a true signal to be confirmed only if all of the following conditions are met: the signal can be reproduced in at least two verifications under different measurement conditions, and the behavior of the signal’s frequency and amplitude as a function of the conditions is consistent with the expected physical laws within the measurement uncertainty range.

[0100] Comparative Example 1: Measurement method without using resonant cavity enhancement Without using a high-frequency resonant cavity, the weak electric field to be measured acts directly on the on-chip atomic vapor cell. In this case, the actual signal field amplitude experienced by the atoms is the same as the amplitude of the unenhanced electric field to be measured. No effective electric field enhancement factor The contribution of this invention is significant. Atoms can still be superheterodyne detected via EIT optical readout and local oscillator microwave field, acquiring and demodulating low-frequency beat signals according to the complete process of steps S3 to S6. Compared to this invention, the comparative example lacks a factor in step S7 when deriving the amplitude of the electric field to be measured. Division operation (because) (No field enhancement). Under the same measured electric field amplitude... Under these conditions, the amplitude of the beat frequency signal Reduced times (when) about At that time, the signal amplitude decreased by approximately (times). To achieve the same signal-to-noise ratio as this invention, the integration time needs to be extended. The square of that, that is, from about 2 hours to about Hours (approximately) (Year), which is impractical in practice. Alternatively, for the same integration time (2 hours), the minimum detectable electric field for this comparison is... Compared with the present invention higher than times (i.e., about twice as high) The detection sensitivity for extremely weak signals is significantly degraded (by a factor of 1), because this invention amplifies the originally extremely weak electric field to be measured in the atomic sampling region by approximately 10 times through the field enhancement effect of the resonant cavity. This multiplier, resulting in an approximately 10 times improvement in the signal-to-noise ratio within the same integration time. times.

[0101] Comparative Example 2: Conventional EIT-AT Measurement Method Without Using Local Oscillator Microwave Field Without applying a strong local oscillator microwave field, the weak electric field to be measured needs to induce resolvable spectral line changes (Autler-Townes splitting or measurable AC Stark shift) at its atomic energy levels in order to achieve amplitude readout via static EIT spectroscopy. Specifically, based on the EIT optical readout established in step S3, the local oscillator microwave field injection operation in step S5 is not performed; instead, the weak electric field to be measured is directly coupled to... Towards At the Rydberg transition, the amplitude of the electric field to be measured is inferred by observing whether splitting or spectral shift induced by the electric field appears in the EIT transmission spectrum. The fundamental limitation of this method is that when the amplitude of the electric field to be measured is extremely low, its corresponding Rabi frequency... Much smaller than the full width at half maximum (FWHM) of the EIT transparent window (approximately 5 MHz to 10 MHz). For example, the typical electric field amplitude corresponding to a sensitivity level with an equivalent noise electric field spectral density of approximately 55 nanovolts per centimeter per root hertz (approximately... (volts per centimeter), its Rabi frequency is only The magnitude is approximately 1 Hz, far smaller than the EIT linewidth of several megahertz. Under these conditions, the spectral line splitting caused by the electric field under test (equal to...) Only about 1 / 3 of the spectral linewidth The signal is completely submerged in the noise background and cannot be resolved in a single static spectral scan. In contrast, this invention, through the injection of a strong local oscillator in step S5 and the orthogonal demodulation in step S6, downconverts the information of the high-frequency weak electric field from the high-frequency carrier to a low-frequency beat frequency signal. It does not require the electric field under test to generate resolvable spectral line splitting itself, but rather encodes the amplitude and phase information of the field under test into a low-frequency intensity modulation through coherent mixing of the local oscillator and the field under test, resulting in a Rabi frequency of only [value missing]. Even extremely weak signals on the order of 1 Hz can be gradually accumulated and detected by extending the integration time.

[0102] Comparative Example 3: Measurement using a macroscopic atomic vapor cell If a conventional glass atomic vapor cell (e.g., 1 cm × 1 cm × 1 cm) is used instead of the chip-level on-chip vapor cell of this invention, and it is placed in a cylindrical high-frequency resonant cavity of the same frequency for measurement, the spatial matching conditions will be significantly worsened. The first problem faced by this comparative example is the incompatibility of physical dimensions: the external dimensions of a conventional glass vapor cell (1 cm) are much larger than the radius of the cavity in this embodiment (2.5 mm), making it physically impossible to place a macroscopic vapor cell within a millimeter-scale resonant cavity. Even if the cavity size is proportionally enlarged to accommodate the macroscopic vapor cell (e.g., increasing the cavity radius from 2.5 mm to 15 mm, correspondingly...) (The mode frequency decreased from 165.2 GHz to about 27.5 GHz), but the spatial averaging effect caused by the non-uniform spatial distribution of the high-frequency electric field in the amplified cavity is still not negligible. The axial electric field amplitude distribution of the mode in the radial direction is determined by the zeroth-order Bessel function. Description, in which It is the radial distance from the axis. Where is the radius of the cavity. The electric field amplitude reaches its maximum value along the cavity axis; On the sidewalls of the cavity, the electric field amplitude drops to zero. Within the magnified cavity, the atoms in the macroscopic vapor pool are distributed... Within a radial range from 0 to several millimeters, the magnitude of the electric field enhancement experienced by atoms at different radial positions varies: at the axis ( )for The maximum value is 1.5 mm off the axis (corresponding to the area near the edge within the macroscopic steam pool). The field enhancement amplitude drops to approximately 79% at the axis. After the response of atoms at all locations within the entire vapor cell is spatially averaged, the overall effective field enhancement factor will be lower than the maximum value at the axis, and the actual effect of field enhancement is weakened. In comparison, the effective detection area of ​​the on-chip vapor cell of this invention is only about 200 micrometers × 200 micrometers × 200 micrometers, even in an unmagnified millimeter-scale cavity ( Within a range of millimeters, the radial position difference within the effective detection area is only about 0.2 millimeters, corresponding to... With a function value difference of less than 2%, the spatial average effect is negligible, and the maximum field enhancement at the cavity axis can be fully utilized.

[0103] The following describes the module composition of the detection system in this embodiment and the connection relationship between each module. The module division of the system corresponds one-to-one with the steps of the detection method described above.

[0104] A high-frequency resonant cavity enhancement module is used to perform the operation of injecting the weak electric field to be measured into the cavity and causing it to resonate and enhance at the anti-node of the electric field, thereby obtaining an enhanced electric field within the cavity. This module includes a cylindrical metal resonant cavity (approximately 2.5 mm in radius and 3 mm in length, made of oxygen-free copper with a precision-polished inner surface), an optical through-hole assembly (with a through-hole diameter of approximately 0.3 mm, located at the center of both end faces of the cavity), and a microwave coupling port (located on the sidewall of the cavity, using a coplanar waveguide-slot line transition coupling structure). This module interacts with the on-chip atom sensing module via spatial electromagnetic coupling, and the enhanced electric field within the cavity directly acts on the cesium atomic vapor in the atomic vapor pool located at the center of the cavity axis.

[0105] The on-chip atomic sensing module performs the operation of placing the chip-scale atomic vapor cell within the cavity in the region of maximum electric field to obtain a spatially matched sensing structure. This module includes a chip-scale cesium atomic vapor cell (approximately 2.5 mm × 2.5 mm × 2.5 mm in size, with an effective detection area of ​​approximately 200 μm × 200 μm × 200 μm, fabricated as described above), a micro-ceramic heating element (for heating the vapor cell to approximately 80 degrees Celsius), a platinum resistance temperature sensor (for feedback signals for temperature closed-loop control), and a low thermal conductivity silicon nitride ceramic support (for achieving thermal isolation between the vapor cell and the cavity). This module is fixed to the center of the cavity axis using precision mechanical clamps and is located inside the high-frequency resonant cavity enhancement module.

[0106] The optical EIT readout module is used to perform the operation of injecting probe light and coupling light into a spatially matched sensing structure to obtain EIT transmitted light, and the calculation operation of the transmitted light intensity change rate sequence. This module includes: a probe laser (external cavity semiconductor laser, center wavelength approximately 852 nm, linewidth less than 1 MHz, frequency stabilized by saturated absorption spectroscopy), a coupling laser (frequency-doubled semiconductor laser, center wavelength approximately 510 nm, linewidth less than 1 MHz, frequency stabilized by Fabry-Perot etalon), probe light frequency stabilization components and coupling light frequency stabilization components, a beam-shaping lens group (including collimating lens and focusing lens), a polarization beam splitter (for combining probe light and coupling light), two mirrors (for aligning the optical path), and a balanced differential photodetector (containing two matched silicon photodiodes and a low-noise differential amplifier, with a common-mode rejection ratio better than 40 dB). The outputs of the probe laser and the coupling laser are beam-shaped and then combined by a polarization beam splitter. The combined laser beam passes through an optical aperture and an atomic vapor cell on the front face of the cavity. The transmitted probe light exits from the optical aperture on the rear face of the cavity and enters the signal input terminal of the balanced differential photodetector. The electrical output terminal of the balanced differential photodetector is connected to the input terminal of the high-speed data acquisition card of the signal acquisition and processing module.

[0107] The local oscillator microwave module is used to perform the injection operation of the local oscillator microwave field, enabling... and The transition between two adjacent Rydberg states is driven by a strong local oscillator field, producing resolvable split spectral lines. The module includes: a microwave frequency synthesizer (frequency resolution better than 1 Hz, phase noise better than -120 dB / Hz at a 1 kHz offset), a microwave power amplifier (gain approximately 30 dB, output power up to 100 milliwatts), an adjustable microwave attenuator (attenuation range 0 to 60 dB, in 0.1 dB steps), and a microwave isolating switch (for rapidly shutting off the local oscillator field during calibration). The RF output of the microwave frequency synthesizer is connected to the input of the power amplifier, and the output of the power amplifier, via the adjustable attenuator and isolating switch, is connected to a microwave coupling port on the cavity sidewall via a microwave coaxial cable. The local oscillator microwave field generated by this module is injected into the cavity through the coupling port, establishing a spatial distribution within the cavity that is consistent with... Local oscillator standing wave field with consistent mode.

[0108] The signal acquisition and processing module is used to perform point-by-point calculation of the transmitted light intensity change rate sequence, point-by-point comparison of the change rate sequence with the slope of the split spectral line and determination of the linear operating point, orthogonal demodulation and interval integration accumulation calculation, as well as the derivation of the amplitude of the weak electric field to be measured and the output of results. This module includes: a high-speed data acquisition card (analog bandwidth not less than 50 MHz, sampling rate of 10 mega-samples per second, 16-bit resolution, supporting continuous streaming acquisition mode), a digital lock-in amplifier (using FPGA or DSP as the processing core to realize real-time processing of orthogonal demodulation, low-pass filtering and integration accumulation), and a signal processing computer (running data acquisition control software, transmitted light intensity change rate calculation program, linear operating point location program, orthogonal demodulation program, integration accumulation program, field amplitude derivation program, and frequency scanning control program). The analog output terminal of the balanced differential photodetector is connected to the analog input channel of the data acquisition card via a BNC coaxial cable, and the data acquisition card is connected to the signal processing computer via a PCIe bus. The various programs running on the signal processing computer exchange data through shared memory or inter-process communication, realizing the fully automated processing from the original transmitted light intensity data to the final measured electric field amplitude.

[0109] The frequency tuning and scanning module is used to change the effective operating frequency of the system to cover different target frequencies. This module includes: a cavity mechanical tuning mechanism (containing a piezoelectric actuator, a metal tuning disk, and a drive amplifier; the piezoelectric actuator's stroke resolution is better than 10 nanometers), a Zeeman magnetic field tuning assembly (containing a solenoid coil wound on the outer wall of the cavity, a precision DC current source, and a Hall probe for magnetic field calibration), and a frequency scanning control program (running on a signal processing computer, coordinating the timing of cavity tuning, magnetic field tuning, local oscillator frequency setting, and data acquisition). The metal tuning disk of the cavity mechanical tuning mechanism is mounted on the outside of one end face of the cavity, with the plane of the tuning disk parallel to the cavity end face; the distance between them is precisely adjusted by the piezoelectric actuator. The solenoid coil of the Zeeman magnetic field tuning assembly is sleeved outside the cavity, with the coil axis coinciding with the cavity axis. The frequency scanning control program communicates with the piezoelectric actuator driver and precision current source via a serial interface (such as USB or GPIB) and with the microwave frequency synthesizer via an Ethernet or USB interface, enabling coordinated control and automatic scanning of multiple devices.

[0110] It should be noted that this system is a system corresponding to the above method. All implementation methods in the above method embodiments are applicable to this embodiment and can achieve the same technical effect.

[0111] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A weak electric field detection method based on Rydberg atom superheterodyne spectroscopy on a cavity enhancement sheet, characterized in that, The method includes: The weak electric field to be measured is injected into a cylindrical high-frequency resonant cavity, so that the weak electric field to be measured resonates and is enhanced at the anti-node of the electric field near the axis of the cylindrical high-frequency resonant cavity, thus obtaining the enhanced electric field inside the cavity. By placing the on-chip atomic vapor cell inside a cylindrical high-frequency resonant cavity, the effective detection area of ​​the on-chip atomic vapor cell, which is on the order of hundreds of micrometers, is located in the region of maximum enhanced electric field inside the cavity, thus obtaining a spatially matched sensing structure. The probe light and coupling light are injected into the space-matching sensing structure through the optical aperture, causing the energy levels of alkali metal atoms to resonate two-photon, thus obtaining electromagnetically induced transparent transmitted light. The intensity of electromagnetically induced transparent transmitted light is calculated point by point as a function of the probe light frequency to obtain a sequence of the rate of change of transmitted light intensity. The position of the linear operating point is obtained by comparing the sequence of transmitted light intensity change rate with the slope of the split spectral line induced by the transition of adjacent Rydberg states driven by the local oscillator microwave field point by point. The transmitted light intensity time series at the linear operating point is orthogonally demodulated, and the demodulated signal is integrated and accumulated within a preset integration interval to obtain the low-frequency beat frequency signal amplitude. The amplitude of the weak electric field to be measured is derived by combining the amplitude of the low-frequency beat frequency signal with the effective electric field enhancement factor of the cylindrical high-frequency resonant cavity, and the high-frequency weak electric field detection result containing the amplitude of the weak electric field to be measured is output.

2. The method according to claim 1, characterized in that, The intensity of the electromagnetically induced transparent transmitted light was calculated point-by-point as a function of the probe light frequency to obtain a sequence of transmitted light intensity change rates, including: The intensity values ​​of the electromagnetically induced transparent transmitted light at adjacent probe light frequency points are obtained to obtain a discrete sequence of transmitted light intensity. The ratio of the difference between adjacent light intensity values ​​in the discrete sequence of transmitted light intensity to the corresponding frequency interval of the probe light is calculated point by point to obtain the sequence of the rate of change of transmitted light intensity.

3. The method according to claim 2, characterized in that, The ratio of the difference between adjacent light intensity values ​​in the discrete sequence of transmitted light intensity to the corresponding frequency interval of the probe light is calculated point by point to obtain the sequence of transmitted light intensity change rates, including: Extract the light intensity value at the current detection light frequency point and the light intensity value at the previous detection light frequency point from the discrete sequence of transmitted light intensity to obtain the adjacent light intensity difference; The frequency interval between the current probe light frequency point and the previous probe light frequency point is calculated point by point to obtain the sequence of transmission light intensity change rate.

4. The method according to claim 3, characterized in that, The transmission light intensity change rate sequence is obtained by calculating the frequency interval between the current and previous probe light frequency points point by point using the adjacent light intensity difference values. This sequence includes: Using the adjacent light intensity difference as the numerator and the frequency interval between the current and previous light frequency points as the denominator, we obtain the frequency interval denominator. The transmission light intensity change rate sequence is obtained by calculating the adjacent light intensity difference and the frequency interval denominator point by point.

5. The method according to claim 4, characterized in that, The transmitted light intensity time series at the linear operating point is orthogonally demodulated, and the demodulated signal is integrated and accumulated within a preset integration interval to obtain the low-frequency beat frequency signal amplitude, including: A local oscillator reference signal with a frequency equal to the low-frequency beat frequency is generated. The transmitted light intensity time series is multiplied by the in-phase reference signal and the quadrature reference signal, respectively, to obtain the in-phase mixing signal and the quadrature mixing signal. Within the preset integration interval, the in-phase mixing signal is numerically integrated and accumulated to obtain the in-phase integral value, and the quadrature mixing signal is numerically integrated and accumulated to obtain the quadrature integral value. The amplitude of the low-frequency beat frequency signal is calculated based on the in-phase integral value and the quadrature integral value.

6. The method according to claim 5, characterized in that, The in-phase reference signal is a sinusoidal signal with a frequency equal to the low-frequency beat frequency, and the quadrature reference signal is a cosine signal with a frequency equal to the low-frequency beat frequency.

7. The method according to claim 6, characterized in that, The amplitude of the low-frequency beat frequency signal is calculated based on the in-phase integral value and the quadrature integral value, including: Calculate the square root of the sum of the squares of the in-phase integral and the squares of the quadrature integral, and use the result as the amplitude of the low-frequency beat frequency signal.

8. The method according to claim 7, characterized in that, The amplitude of the weak electric field to be measured is derived based on the amplitude of the low-frequency beat frequency signal and the effective electric field enhancement factor of the cylindrical high-frequency resonant cavity, including: The effective electric field enhancement factor and the Rydberg atom microwave electric field sensitivity of the cylindrical high-frequency resonant cavity are obtained to obtain the system response parameters. The amplitude of the low-frequency beat signal is combined with the system response parameters to derive the amplitude of the weak electric field to be measured.

9. The method according to claim 8, characterized in that, The amplitude of the low-frequency beat signal is combined with the system response parameters to derive the amplitude of the weak electric field to be measured, including: The amplitude of the low-frequency beat frequency signal and the sensitivity of the Rydberg atom microwave electric field are calculated point by point to obtain the intermediate electric field value; The amplitude of the weak electric field to be measured is obtained by calculating the intermediate electric field value and the effective electric field enhancement factor point by point.

10. A weak electric field detection system based on Rydberg atom superheterodyne spectroscopy on a cavity enhancement sheet, wherein the system implements the method as described in any one of claims 1 to 7, characterized in that, include: The acquisition module is used to inject the weak electric field to be measured into the cylindrical high-frequency resonant cavity, so that the weak electric field to be measured will resonate and be enhanced at the anti-node of the electric field near the axis of the cylindrical high-frequency resonant cavity, thus obtaining the enhanced electric field inside the cavity. An on-chip atomic vapor cell is placed inside a cylindrical high-frequency resonant cavity, so that the effective detection area of ​​the on-chip atomic vapor cell, which is on the order of hundreds of micrometers, is located in the region of maximum enhanced electric field inside the cavity, thus obtaining a spatially matched sensing structure. The probe light and coupling light are injected into the spatially matched sensing structure through an optical aperture, causing the energy levels of alkali metal atoms to undergo two-photon resonance, thus obtaining electromagnetically induced transparent transmitted light. The calculation module is used to calculate the change in the intensity of electromagnetically induced transparent transmitted light with the frequency of the probe light point by point, and obtain the sequence of the rate of change of transmitted light intensity. The comparison module is used to compare the transmitted light intensity change rate sequence with the slope of the split spectral line induced by the transition of adjacent Rydberg states driven by the local oscillator microwave field point by point to obtain the position of the linear operating point. The demodulation module is used to perform orthogonal demodulation on the time series of transmitted light intensity at the linear operating point, and to perform interval integration and cumulative calculation on the demodulated signal within a preset integration interval to obtain the amplitude of the low-frequency beat frequency signal. The processing module is used to derive the amplitude of the weak electric field to be measured based on the amplitude of the low-frequency beat frequency signal and the effective electric field enhancement factor of the cylindrical high-frequency resonant cavity, and output the high-frequency weak electric field detection result containing the amplitude of the weak electric field to be measured.

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