Parameter inversion method based on Rydberg atom low-frequency alternating current electric field measurement

Abstract

The invention discloses a parameter inversion method based on Rydberg atom low-frequency alternating-current electric field measurement, and the method comprises the following steps: collecting a spectral signal, recognizing the oscillation frequency of the spectral signal, and inverting the frequency of a to-be-measured electric field according to the recognized oscillation frequency; collecting multiple groups of spectral signals, and averaging the collected spectral signals based on the oscillation frequency of the spectral signals to obtain an average spectral signal; measuring an amplitude peak value and an amplitude valley value of the average spectral signal, and inverting the amplitude value of the to-be-measured electric field according to a measurement result; and acquiring the moment and period of the first wave trough in the average spectral signal, and inverting the phase of the to-be-measured electric field according to the proportion of the moment and period of the first wave trough. According to the method, the influence of unstable power on the measurement precision is effectively reduced, meanwhile, a new electric field parameter extraction strategy is provided, the electric field characteristics can be recognized more accurately, and more reliable electric field measurement is achieved.

Description

Technical Field

[0001] The present invention relates to the field of electric field measurement, and in particular to a parameter inversion method for low-frequency alternating current electric field measurement based on Rydberg atoms. Background Art

[0002] At present, the application of electric field sensing technology based on Rydberg atoms has been gradually widespread. Rydberg atoms have special atomic properties, especially showing sensitivity and excellent self-calibration under an electric field. This means that it is extremely sensitive to external electric field changes and can accurately measure the intensity and changes of weak electric fields. In addition, Rydberg atoms are generally loaded in an atomic gas cell made of glass, which will not cause distortion to the measured electric field, and the requirements for multi-point electric field monitoring and imaging can be achieved through the miniaturization of the atomic gas cell. Therefore, quantum electric field measurement based on Rydberg atoms has gradually received attention and emphasis.

[0003] The low-frequency electric field acts on Rydberg atoms, generating the EIT and Stark effects and presenting corresponding characteristics in the spectrum. In terms of the measurement technical solution, the method of fixing the detection light frequency and scanning the coupling light frequency is generally adopted, and the measurement of the electric field amplitude is realized by detecting the frequency shift of the EIT spectrum. However, this method cannot obtain the frequency and phase of the electric field. The Rydberg atom electric field measurement method based on the double-lock scheme is not yet mature in the identification technology, especially there is no effective method for accurately identifying electric field parameters. The measurement of the double-lock scheme depends on the support of the steady-state power, but since the power often appears unstable in actual operation, the measurement result is affected by random fluctuations, further causing measurement errors. This problem seriously limits the application effect and reliability of this scheme in high-precision electric field measurement. Summary of the Invention

[0004] Aiming at the above deficiencies in the prior art, a parameter inversion method for low-frequency alternating current electric field measurement based on Rydberg atoms provided by the present invention solves the problems of low measurement accuracy and large error in the prior art.

[0005] In order to achieve the above invention purpose, the technical solution adopted by the present invention is: a parameter inversion method for low-frequency alternating current electric field measurement based on Rydberg atoms, comprising the following steps:

[0006] S1. Collect spectral signals, identify the oscillation frequency of the spectral signals, and invert the frequency of the electric field to be measured according to the identified oscillation frequency;

[0007] S2. Collect multiple groups of spectral signals, average the collected spectral signals based on the oscillation frequency of the spectral signals to obtain an average spectral signal;

[0008] S3. Measure the amplitude peak and amplitude valley of the average spectral signal, and invert the amplitude of the electric field to be measured according to the measurement result;

[0009] S4. Obtain the moment and period when the first wave trough appears in the average spectral signal, and invert the phase of the electric field to be measured according to the ratio of the moment when the first wave trough appears to the period.

[0010] The parameters of the electric field to be measured include amplitude, frequency and phase.

[0011] Further: The spectral signal is the EIT spectral signal in the electric field to be measured, that is, the EIT spectral signal formed by the interaction of the probe light and the coupling light with the Rydberg atoms.

[0012] Further: Step S1 is specifically as follows:

[0013] Calculate the oscillation period of the spectral signal according to the oscillation frequency of the spectral signal; multiply the oscillation period of the spectral signal by 2 to obtain the frequency of the electric field to be measured.

[0014] Further: Step S3 is specifically as follows:

[0015] Perform peak detection on the average spectral signal to obtain the amplitude peak of the average spectral signal; take the negative of the average spectral signal, perform peak detection on the averaged spectral signal after taking the negative to obtain the amplitude trough of the average spectral signal; invert the amplitude of the electric field to be measured based on the peak of the average spectral signal and the trough of the average spectral signal to obtain the amplitude of the electric field to be measured.

[0016] Further: The specific method for inverting the amplitude of the electric field to be measured based on the amplitude peak of the average spectral signal and the amplitude trough of the average spectral signal to obtain the amplitude of the electric field to be measured is as follows:

[0017] Load multiple groups of known electric field measurement data and the corresponding light intensity data, and substitute the known electric field measurement data and the corresponding light intensity data into the equivalent expression of I p to calculate the values of the fitting constants a, b, and c;

[0018] Let the value of I p be equal to the amplitude peak of the average spectral signal, and according to the equivalent expression of I p obtain the amplitude trough of the electric field to be measured;

[0019] Let the value of I p be equal to the amplitude trough of the average spectral signal, and according to the equivalent expression of I p obtain the amplitude peak of the electric field to be measured;

[0020] Subtract the amplitude peak of the electric field to be measured from the amplitude trough of the electric field to be measured to obtain the amplitude of the electric field to be measured;

[0021] where the equivalent expression of I p is:

[0022]

[0023] Among them, a, b, and c respectively represent fitting constants, n is a positive integer, E represents the electric field strength, and I p is the light intensity.

[0024] Furthermore: Step S4 is specifically as follows:

[0025] Identify the trough of the average spectral signal, and obtain the position where the first trough appears; according to the relationship between the position where the first trough appears and the oscillation period of the average spectral signal, calculate the phase of the first trough to obtain the phase of the electric field to be measured.

[0026] The beneficial effects of the present invention are as follows: The present invention calculates the mean value through multiple samplings to offset the influence of power drift, thereby significantly improving the stability and reliability of the signal. It not only effectively reduces the error caused by unstable power, but also provides a new method for extracting electric field parameters, enabling more accurate identification and determination of electric field parameters in electric field measurement. This improvement provides strong support for high-precision electric field measurement, and improves the adaptability and accuracy of the Rydberg atom electric field measurement method in practical applications. Description of the Drawings

[0027] Figure 1 is the flow chart of the method proposed by the present invention;

[0028] Figure 2 is the optoelectronic output waveform diagram after averaging the spectral signal twice;

[0029] Figure 3 is the optoelectronic output waveform diagram after averaging the spectral signal four times;

[0030] Figure 4 is the optoelectronic output waveform diagram after averaging the spectral signal eight times;

[0031] Figure 5 is the optoelectronic output waveform diagram after averaging the spectral signal sixteen times;

[0032] Figure 6 is the optoelectronic output waveform diagram after averaging the spectral signal thirty-two times;

[0033] Figure 7 is the optoelectronic output waveform diagram after averaging the spectral signal sixty-four times. Detailed Embodiments

[0034] The following describes the specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions created using the concept of the present invention are within the scope of protection.

[0035] In one embodiment of the present invention, as Figure 1 shown, the present invention provides a parameter inversion method based on the measurement of a low-frequency alternating electric field of Rydberg atoms. The electric field parameters to be measured include amplitude, frequency, and phase.

[0036] Specifically, it includes the following steps:

[0037] S1. Collect spectral signals, identify the oscillation frequency of the spectral signals, and calculate the oscillation period of the spectral signals according to the oscillation frequency of the spectral signals; multiply the oscillation period of the spectral signals by 2 to obtain the frequency of the electric field to be measured.

[0038] S2. Collect multiple groups of spectral signals, and average the collected multiple groups of spectral signals based on the oscillation frequency of the spectral signals to obtain an average spectral signal; set the number of acquisitions before collecting the spectral signals, simulate or actually collect multiple groups of spectral signal data, accumulate the data collected each time into a matrix, and after reaching the number of acquisitions, take the average of the accumulated data to obtain an average spectral signal, thereby eliminating the error caused by power drift. Among them, the spectral signal is the EIT spectral signal in the electric field to be measured, that is, the EIT spectral signal formed by the interaction of the probe light and the coupling light with Rydberg atoms.

[0039] The spectral signal of each sampling can be expressed as the true signal plus noise, that is

[0040] S j = Strue + ε j

[0041] where Strue is the true signal, and ε j is the noise of the jth sampling, and the noise is independently distributed. When multiple samplings are performed and averaged, the influence of the noise will cancel each other out statistically. After averaging the sampled spectral signals, the average spectral signal S avg is expressed as:

[0042] S avg = S true + Σε j / N

[0043] As the number of averages N increases, the noise term Σε j / N gradually approaches zero. Therefore, the average spectral signal is closer to the true spectral signal. AsFigure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 As shown in Figure 7 , as the average number increases, the noise in the spectral signal is gradually cancelled out.

[0044] S3. Measure the amplitude peak and amplitude valley of the average spectral signal, and invert the amplitude of the electric field to be measured according to the measurement results.

[0045] In the present invention, the optical Bloch equation is used to describe the interaction and dynamic evolution of the optical field and the atomic system, and its expression is:

[0046]

[0047] where ρ is the density matrix under the ladder three-level system, H is the system Hamiltonian, L(ρ) is the Lindblad superoperator, t is the time, and i is the imaginary part of the complex number, and h is the Planck constant.

[0048] The Hamiltonian H is:

[0049]

[0050] where Δ p and Δ c are the detuning amounts of the probe light and the coupling light respectively, that is, the difference between the laser frequency and the atomic transition frequency, and Δ E represents the change amount of the electric field intensity; Ω p and Ω c are the Rabi frequencies of the probe light and the coupling light respectively, and * represents the complex conjugate of the function.

[0051] The matrix form of L(ρ) is:

[0052]

[0053] where Г ab is the spontaneous emission rate from energy level a to energy level b, and the diagonal density matrix element ρ aa represents the population probability of energy level a, and ρ ab represents the population probability from energy level a to energy level b.

[0054] Let dρ / dt = 0 to solve for the steady-state response, where ρ 21 reflecting the characteristics of the probe light is expressed as:

[0055]

[0056] Furthermore, the complex susceptibility χ can be obtained:

[0057]

[0058] where N is the Rydberg atom density, μ 21 is the transition dipole moment of the energy level corresponding to the probe light, ε0 is the permittivity, and I 0p is the initial light intensity of the incident light.

[0059] The imaginary part χ" of χ reflects the absorption characteristics of the atoms for the probe light and can also be used to describe the EIT-Stark spectrum. Therefore, the expression of χ" can be deduced as follows:

[0060]

[0061] where E represents the electric field strength and α represents the polarizability.

[0062] Based on the Beer-Lambert law, the light intensity I p transmitted through the atomic cell can be expressed as:

[0063]

[0064] where L represents the length of the atomic cell, λ p represents the wavelength of the probe light, π is the pi, and e is the natural constant.

[0065] With the fixed parameters of the atomic system, the equivalent expression of I p is:

[0066]

[0067] a, b, and c respectively represent fitting constants, n is a positive integer, E represents the electric field strength, and I p is the light intensity.

[0068] In this embodiment, peak detection is performed on the average spectral signal to obtain the amplitude peak of the average spectral signal; the average spectral signal is negated, and peak detection is performed on the negated average spectral signal to obtain the amplitude valley of the average spectral signal.

[0069] Based on the peak of the average spectral signal and the valley of the average spectral signal, the amplitude of the electric field to be measured is inverted: multiple groups of known electric field measurement data and the corresponding light intensity data are loaded, and the known electric field measurement data and the corresponding light intensity data are substituted into the equivalent expression of I p to calculate the values of the fitting constants a, b, and c; let the value of I p be equal to the amplitude peak of the average spectral signal, and according to the equivalent expression of I p , the amplitude valley of the electric field to be measured is obtained; let the value of I p be equal to the amplitude valley of the average spectral signal, and according to the equivalent expression of I pThe equivalent expression is used to obtain the amplitude peak of the electric field to be measured; the amplitude peak of the electric field to be measured is subtracted from the amplitude valley of the electric field to be measured to obtain the amplitude value of the electric field to be measured.

[0070] S4. Obtain the time and period when the first wave valley appears in the average spectral signal, and inversely calculate the phase of the electric field to be measured according to the ratio of the time when the first wave valley appears to the period: identify the wave valleys of the average spectral signal to obtain the position where the first wave valley appears; calculate the phase of the first wave valley according to the relationship between the position where the first wave valley appears and the oscillation period of the average spectral signal to obtain the phase of the electric field to be measured.

[0071] If the difference between the time when the first wave valley appears and 0.25 times the period (T) is x milliseconds, its phase can be expressed as:

[0072]

[0073] In this embodiment, the true values of the parameters of the electric field to be measured and the corresponding values obtained by using the method proposed in the present invention are shown in Table 1.

[0074] Table 1

[0075]

[0076] In summary, the present invention can achieve accurate parameter measurement with relatively low complexity, effectively reducing the influence of power instability on measurement accuracy and improving the stability of measurement signals.

Claims

1. A parameter inversion method based on Rydberg atom low-frequency AC electric field measurement, characterized in that: The following steps are involved: S1, collecting spectral signals, identifying the oscillation frequency of the spectral signals, and inverting the frequency of the electric field to be measured according to the identified oscillation frequency; S2, collecting multiple groups of spectral signals, and averaging the collected spectral signals based on the oscillation frequency of the spectral signals to obtain an average spectral signal; S3, measuring the amplitude peak value and the amplitude valley value of the average spectrum signal, and inverting the amplitude of the electric field to be measured according to the measurement results; S4, obtaining the time and period of the first trough appearance in the average spectrum signal, and inverting the phase of the electric field to be measured according to the ratio of the time and period of the first trough appearance; The electric field parameters to be measured include amplitude, frequency and phase.

2. A parameter inversion method based on Rydberg atom low-frequency alternating current electric field measurement according to claim 1, characterized in that: The spectral signal is an EIT spectral signal in the electric field to be measured, that is, an EIT spectral signal formed by the interaction between the detection light and the coupling light and the Rydberg atoms.

3. The parameter inversion method based on Rydberg atom low-frequency alternating current electric field measurement according to claim 1, characterized in that: Step S1 is specifically as follows: The oscillation period of the spectral signal is calculated according to the oscillation frequency of the spectral signal; the oscillation period of the spectral signal is multiplied by 2 to obtain the frequency of the electric field to be measured.

4. The parameter inversion method based on Rydberg atom low-frequency alternating current electric field measurement according to claim 1, characterized in that: Step S3 is specifically as follows: Performing peak detection on the average spectrum signal to obtain the amplitude peak value of the average spectrum signal; negating the average spectrum signal, performing peak detection on the negated average spectrum signal to obtain the amplitude valley value of the average spectrum signal; The amplitude of the electric field to be measured is inverted based on the peak value of the average spectrum signal and the valley value of the average spectrum signal to obtain the amplitude of the electric field to be measured.

5. The parameter inversion method based on Rydberg atom low-frequency alternating current electric field measurement according to claim 4 is characterized in that: The specific method for inverting the amplitude of the electric field to be measured based on the amplitude peak value of the average spectrum signal and the amplitude valley value of the average spectrum signal to obtain the amplitude of the electric field to be measured is: Load multiple sets of known electric field measurement data and corresponding light intensity data, and bring the known electric field measurement data and corresponding light intensity data into I p Equivalent expression of, calculate the values ​​of fitting constants a, b, c; Order I p The value is equal to the peak amplitude of the average spectral signal. p The equivalent expression of is obtained to obtain the valley value of the electric field to be measured; Order I p The value is equal to the amplitude valley value of the average spectral signal. p The equivalent expression of , the peak amplitude of the electric field to be measured is obtained; Subtracting the peak value of the amplitude of the electric field to be measured from the valley value of the amplitude of the electric field to be measured to obtain the amplitude of the electric field to be measured; Among them I p The equivalent expression is: Where a, b, c represent fitting constants, n is a positive integer, E represents the electric field intensity, I p For light intensity.

6. The parameter inversion method based on Rydberg atom low-frequency alternating current electric field measurement according to claim 1, characterized in that: Step S4 is specifically as follows: The trough of the average spectral signal is identified to obtain the position where the first trough appears; based on the relationship between the position where the first trough appears and the oscillation period of the average spectral signal, the phase of the first trough is calculated to obtain the phase of the electric field to be measured.

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