A method for extracting EIT-Stark spectral features of Rydberg atoms

Abstract

This invention discloses a method for extracting EIT-Stark spectral features of Rydberg atoms, comprising the following steps: A signal acquisition module acquires the initial EIT-Stark spectral signal, performs wavelet transform, calculates wavelet coefficients, and plots a two-dimensional image of the wavelet coefficients; the wavelet coefficients of the EIT-Stark spectral signal undergo a natural logarithmic transform and are classified, the inter-class variance of the two classes of wavelet coefficients is calculated, an optimization objective function is established, and the peak search range is obtained using the optimization objective function; within the peak search range, the local maximum values ​​of the wavelet coefficients are obtained through a sliding window with a fixed step size, and the corresponding local maximum values ​​at adjacent scales are connected to obtain ridge lines; based on the position of the maximum wavelet coefficient value at any scale on the ridge line, the centroid position of the spectral peak of the EIT-Stark spectral signal is obtained. This method achieves accurate, automatic, and real-time extraction of transmission peak positions and movement features, providing a reliable data foundation for electric field measurement and promoting the engineering application of electric field measurement based on the EIT-Stark effect.

Description

Technical Field

[0001] This invention relates to the field of spectral feature extraction, specifically to a method for extracting EIT-Stark spectral features of Rydberg atoms. Background Technology

[0002] With the maturity of laser technology and the development of laser-based precise manipulation of atomic quantum states, electric field measurements in laboratory settings have been achieved using electromagnetically induced transparency (EIT) based on Rydberg atoms to detect the Stark frequency shift generated by the electric field. In the measurement experiment, the simultaneous interaction of the probe light and the coupling light is required to excite cesium atoms in the gas chamber to the Rydberg state, thereby observing the EIT-Stark spectrum. Therefore, unavoidable laser power fluctuations and environmental influences introduce unavoidable noise and baseline fluctuations into the EIT-Stark spectrum. Furthermore, during the electric field interaction, transmission peaks overlap, and line compression and broadening occur, causing difficulties in resolving and locating peaks and a significant reduction in the signal-to-noise ratio. Accurately, automatically, and in real-time extracting the position and movement characteristics of the transmission peaks is quite challenging.

[0003] To extract peak shift information from EIT spectra, most researchers employ the traditional Gaussian fitting method for peak finding, typically implemented offline using software such as Origin and Peakfit. However, this method requires manual adjustment of the fitting parameters under the researcher's intervention to achieve peak finding. Its accuracy is affected by human factors and is difficult to automate in real time, making it suitable for laboratory research but not for engineering applications. Summary of the Invention

[0004] To address the aforementioned shortcomings of existing technologies, this invention provides a method for extracting EIT-Stark spectral features of Rydberg atoms.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0006] A method for extracting EIT-Stark spectral features of Rydberg atoms is provided, which includes the following steps:

[0007] S1: The signal acquisition module acquires the initial EIT-Stark spectral signal, performs wavelet transform on the initial EIT-Stark spectral signal, calculates the wavelet coefficients, selects the wavelet scale, and draws a two-dimensional image of the wavelet coefficients.

[0008] S2: Perform natural logarithmic transform on the wavelet coefficients of the EIT-Stark spectral signal, classify the wavelet coefficients after natural logarithmic transform, calculate the inter-class variance of the two classes of wavelet coefficients, establish the optimization objective function, and use the optimization objective function to obtain the peak range.

[0009] S3: Within the peak-finding range, based on the two-dimensional image of wavelet coefficients at the same wavelet scale, the local maximum value of the wavelet coefficients is obtained through a sliding window with a fixed step size. Then, the corresponding local maximum values ​​at adjacent scales are connected to obtain the ridge line.

[0010] S4: Based on the position of the maximum wavelet coefficient at any scale on the ridge, obtain the centroid position of the EIT-Stark spectral signal peak.

[0011] Further, step S1 includes:

[0012] S11: The signal acquisition module acquires the initial EIT-Stark spectral signal, which is represented as follows:

[0013] S(t)=P(t)+B(t)+N(t)+C, t∈[t1,t2];

[0014] Where t is the time series of the signal, S(t) is the initial EIT-Stark spectral signal, P(t) is the effective transmission peak signal, B(t) is the baseline signal with a mean of 0, N(t) is the noise signal, C is the signal constant, and [t1,t2] is the non-stationary time series signal region where peak finding is required;

[0015] S12: Perform wavelet transform on the initial EIT-Stark spectral signal S(t);

[0016]

[0017] Where a is the wavelet scale, b is the wavelet translation, ψ(.) is the mother wavelet function, and ψ a,b (.) represents the wavelet basis functions after scaling and translation, and C(a,b) represents the wavelet coefficients;

[0018] S13: Combining steps S11 and S12, the wavelet coefficients C(a,b) of the EIT-Stark spectral signal are obtained;

[0019]

[0020] The mother wavelet function is chosen to be the Mexican cap wavelet, which is similar to the EIT transmission peak shape. The function expression of the Mexican cap wavelet is as follows:

[0021]

[0022] During the wavelet transform process, the natural exponent is used to optimize and select the wavelet scale 'a'; a two-dimensional image of the wavelet coefficients is plotted at the selected wavelet scale.

[0023] a = 2.1362·e 0.3285ii = 0, 1, 2, ...;

[0024] Where i is a natural number.

[0025] Further, step S2 includes:

[0026] S21: Based on the wavelet coefficients C(a,b) of the EIT-Stark spectral signal, perform a natural logarithmic transformation on all data in the wavelet coefficient matrix of the two-dimensional image to obtain the wavelet coefficients after the natural logarithmic transformation, and plot the histogram of the wavelet coefficients after the natural logarithmic transformation.

[0027] S22: Set a threshold for the wavelet coefficients, and use this threshold to classify all wavelet coefficients after natural logarithmic transformation into two classes. Calculate the inter-class variance s between the two classes of wavelet coefficients. B ;

[0028] s B =w0(m0-m c ) 2 +w1(m1-m c ) 2 ;

[0029] Where m0 and m1 are the mean values ​​of the two types of wavelet coefficients, respectively. c Let w0 and w1 be the mean of all wavelet coefficients, and w0 and w1 be the weights of the two types of wavelet coefficients, respectively.

[0030] S23: Utilizing the inter-class variance s of the two types of wavelet coefficients B Based on the bimodal characteristics in the wavelet coefficient histogram, the optimization range ν is determined, the optimization objective function is constructed, and a threshold with the largest inter-class variance is determined within the optimization range ν.

[0031]

[0032] S24: Obtain the maximum threshold S of the wavelet coefficients using the optimization objective function. Bmax The corresponding wavelet coefficients m0 and m1 are output, and they will be less than the maximum threshold S within the range [m0, m1]. Bmax By setting the wavelet coefficients to zero, the peak-finding range can be obtained.

[0033] The beneficial effects of this invention are as follows: This invention improves the multi-scale continuous wavelet transform analysis technique commonly used in mass spectrometry analysis for EIT-Stark spectroscopy, optimizes the scale selection method to reduce computational redundancy, adds automatic limitation of the feature extraction range to reduce the false detection rate, and balances the operation time with the peak finding performance. Thus, it achieves accurate, automatic, and real-time extraction of transmission peak position and movement features, effectively obtains the frequency shift, provides a reliable data foundation for electric field measurement, and promotes the engineering application of electric field measurement based on the EIT-Stark effect.

[0034] This invention proposes a scale optimization selection method based on natural index calculation, which focuses on overlapping peak information at small scales while also taking into account broadened peak information at large scales. At the same time, it reduces computational redundancy, improves computational speed, and enhances the real-time performance of the electric field measurement system.

[0035] This invention proposes an automatic region limitation method based on natural logarithm calculation and inter-class variance maximization, which reduces the false detection rate of peak finding, largely avoids the situation of finding the wrong peak, and improves the stability of the electric field measurement system.

[0036] This invention estimates the centroid position of a spectral peak by using the position of the maximum wavelet coefficient at a certain scale on a single ridge, ensuring the accuracy of peak finding and avoiding the errors introduced by manual peak marking in traditional methods. Attached Figure Description

[0037] Figure 1 This is a flowchart of the EIT-Stark spectral feature extraction method for Rydberg atoms.

[0038] Figure 2 To output the wavelet signal graph.

[0039] Figure 3 This is a two-dimensional image of the multi-scale continuous wavelet transform coefficients at wavelet scales a = 1-200.

[0040] Figure 4 This is a two-dimensional image of multi-scale wavelet transform coefficients selected based on natural index-optimized wavelet scale.

[0041] Figure 5 This is the histogram of wavelet coefficients after natural logarithmic transformation.

[0042] Figure 6 This is a graph showing the calculated ridge line. Detailed Implementation

[0043] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0044] like Figure 1 As shown, a method for extracting EIT-Stark spectral features of Rydberg atoms includes the following steps:

[0045] S1: The signal acquisition module acquires the initial EIT-Stark spectral signal, performs wavelet transform on the initial EIT-Stark spectral signal, calculates the wavelet coefficients, selects the wavelet scale, and plots a two-dimensional image of the wavelet coefficients. Step S1 specifically includes:

[0046] S11: The signal acquisition module acquires the initial EIT-Stark spectral signal, which is represented as follows:

[0047] S(t)=P(t)+B(t)+N(t)+C, t∈[t1,t2];

[0048] Where t is the time series of the signal, S(t) is the initial EIT-Stark spectral signal, P(t) is the effective transmission peak signal, B(t) is the baseline signal with a mean of 0, N(t) is the noise signal, C is the signal constant, and [t1,t2] is the non-stationary time series signal region where peak finding is required;

[0049] S12: Perform wavelet transform on the initial EIT-Stark spectral signal S(t);

[0050]

[0051] Where a is the wavelet scale, b is the wavelet translation, ψ(.) is the mother wavelet function, and ψ a,b (.) represents the wavelet basis function after scaling and translation, and C(a,b) represents the wavelet coefficients; the larger the wavelet coefficients, the better the matching performance between the EIT-Stark spectral signal and the mother wavelet;

[0052] S13: Combining steps S11 and S12, the wavelet coefficients C(a,b) of the EIT-Stark spectral signal are obtained;

[0053]

[0054] When the mother wavelet function ψ(.) is a symmetric wavelet function, and the baseline fluctuation is slowly varying and locally monotonic within a certain region, the second term in the wavelet coefficient calculation formula can be approximately zero, thus mathematically offsetting the influence of baseline variation on the extraction of transmission peak features.

[0055] In this embodiment, the mother wavelet function ψ(.) is selected as the Mexican cap wavelet, which is similar to the EIT transmission peak shape. After scaling transformation, the Mexican cap wavelet can better match the waveform trend of the transmission peak. The function expression of the Mexican cap wavelet is as follows:

[0056]

[0057] During the wavelet transform process, the natural exponent is used to optimize and select the wavelet scale 'a'; a two-dimensional image of the wavelet coefficients is plotted at the selected wavelet scale.

[0058] a = 2.1362·e 0.3285i i = 0, 1, 2, ...;

[0059] Where i is a natural number.

[0060] In this embodiment, wavelet transform is performed based on the selected wavelet scale, and the output wavelet signal is shown in the figure. Figure 2 As shown, Figure 2 The EIT-Stark spectral signal to be processed is given when an electric field of E = 24.39 V / cm is applied.

[0061] like Figure 3 and Figure 4 As shown, Figure 3 This is a two-dimensional image of the multi-scale continuous wavelet transform coefficients at wavelet scales a = 1-200. Figure 4 This is a two-dimensional image of multi-scale wavelet transform coefficients selected based on the natural index-optimized wavelet scale. It is evident that the computational load and redundancy are significantly reduced, greatly improving the speed of a single run, making it suitable for real-time EIT-Stark spectral processing during electric field measurements. Furthermore, this wavelet scale selection method focuses on the identification of overlapping peaks, reducing noise impact while paying attention to transitional scale regions, and also considering weak peak identification.

[0062] S2: Perform a natural logarithmic transform on the wavelet coefficients of the EIT-Stark spectral signal, classify the transformed wavelet coefficients, calculate the inter-class variance of the two classes of wavelet coefficients, establish an optimization objective function, and use the optimization objective function to obtain the peak range. Step S2 specifically includes:

[0063] S21: Based on the wavelet coefficients C(a,b) of the EIT-Stark spectral signal, perform a natural logarithmic transform on all data in the wavelet coefficient matrix of the two-dimensional image to obtain the wavelet coefficients after the natural logarithmic transform, and plot the histogram of the wavelet coefficients after the natural logarithmic transform, as shown below. Figure 5 As shown, in order to highlight the differences between wavelet coefficients, compress the dynamic range of the data, and filter out negative wavelet coefficients to reduce the influence of noise in the data, this paper performs a natural logarithmic transformation on all data in the two-dimensional wavelet coefficient matrix.

[0064] like Figure 5As shown, the wavelet coefficient histogram exhibits a significant bimodal characteristic. This is because the vast majority of the calculated wavelet coefficients are concentrated in small values ​​close to 0, meaning that these locations do not contain effective feature signals that need to be extracted; while a small portion of the coefficients are concentrated in larger values, indicating that they contain effective transmission peak signals that match the characteristics of the mother wavelet and require special attention. However, the boundary between these two parts of data is fuzzy, necessitating the setting of a threshold to limit the effective feature extraction range.

[0065] S22: Set a threshold for the wavelet coefficients, and use this threshold to classify all wavelet coefficients after natural logarithmic transformation into two classes. Calculate the inter-class variance s between the two classes of wavelet coefficients. B ;

[0066] s B =w0(m0-m c ) 2 +w1(m1-m c ) 2 ;

[0067] Where m0 and m1 are the mean values ​​of the two types of wavelet coefficients, respectively. c Let w0 and w1 be the mean of all wavelet coefficients, and w0 and w1 be the weights of the two types of wavelet coefficients, respectively.

[0068] The classification process is as follows: when the wavelet coefficients after the natural logarithm transformation are less than or equal to the wavelet coefficient threshold, they are classified into one category; when they are greater than the wavelet coefficient threshold, they are classified into another category.

[0069] S23: Utilizing the inter-class variance s of the two types of wavelet coefficients B Based on the bimodal characteristics in the wavelet coefficient histogram, the optimization range ν is determined, the optimization objective function is constructed, and a threshold with the largest inter-class variance is determined within the optimization range ν.

[0070]

[0071] S24: Obtain the maximum threshold S of the wavelet coefficients using the optimization objective function. Bmax The corresponding wavelet coefficients m0 and m1 are output, and they will be less than the maximum threshold S within the range [m0, m1]. Bmax By setting the wavelet coefficients to zero, the peak-finding range can be obtained.

[0072] For the wavelet data with an applied electric field E = 24.39 V / cm in this embodiment, the optimal wavelet coefficient threshold is calculated to be 0.09074. Based on the calculated optimal wavelet coefficient threshold, wavelet coefficients smaller than this threshold are set to zero, thereby limiting the peak-finding range.

[0073] The morphology of transmission peaks in the EIT-Stark spectrum changes depending on the magnitude of the applied electric field, potentially resulting in weak peaks with reduced signal-to-noise ratio or overlapping peaks. Therefore, different thresholds need to be set in real time for different EIT-Stark spectra under different electric fields.

[0074] S3: Within the peak-finding range, based on the two-dimensional image of wavelet coefficients at the same wavelet scale 'a', the local maxima of the wavelet coefficients are obtained through a sliding window with a fixed step size. Then, the corresponding local maxima at adjacent scales are connected to obtain the ridge lines, such as... Figure 6 As shown in the figure, this is a diagram of the ridge line calculation results in this embodiment.

[0075] The specific process for obtaining the ridge line is as follows:

[0076] S31: Initialize the ridge line based on the local maximum point A identified at the maximum wavelet scale, which is the last row of the wavelet coefficient matrix reflected in the two-dimensional image. At this time, the number of rows in the wavelet coefficient matrix is ​​n.

[0077] S32: For each ridge, search for the nearest maximum point B in the next adjacent wavelet scale, at which point the wavelet coefficient matrix has n-1 rows;

[0078] S33: If the distance between the maximum point B and the local maximum point A is less than the size of the sliding window, then connect the maximum point B and the local maximum point A to form a ridge.

[0079] S34: If there is no maximum point B and local maximum point A whose distance is less than the size of the sliding window, then increment the ridge gap count and return to step S32;

[0080] S35: Until the maximum value point B is found, reset the gap count to zero and return to step S32.

[0081] The length of the ridge is the number of local maximum points A connected during the ridge identification process.

[0082] S4: Based on the position of the maximum wavelet coefficient at any scale on the ridge, obtain the centroid position of the EIT-Stark spectral signal peak.

Claims

1. A method for extracting EIT-Stark spectral features of Rydberg atoms, characterized in that, Includes the following steps: S1: The signal acquisition module acquires the initial EIT-Stark spectral signal, performs wavelet transform on the initial EIT-Stark spectral signal, calculates the wavelet coefficients, selects the wavelet scale, and draws a two-dimensional image of the wavelet coefficients. S2: Perform natural logarithmic transform on the wavelet coefficients of the EIT-Stark spectral signal, classify the wavelet coefficients after natural logarithmic transform, calculate the inter-class variance of the two classes of wavelet coefficients, establish the optimization objective function, and use the optimization objective function to obtain the peak range. S3: Within the peak-finding range, based on the two-dimensional image of wavelet coefficients at the same wavelet scale, the local maximum value of the wavelet coefficients is obtained through a sliding window with a fixed step size. Then, the corresponding local maximum values ​​at adjacent scales are connected to obtain the ridge line. S4: Based on the position of the maximum wavelet coefficient at any scale on the ridge, obtain the centroid position of the EIT-Stark spectral signal peak.

2. The method for extracting EIT-Stark spectral features of Rydberg atoms according to claim 1, characterized in that, Step S1 includes: S11: The signal acquisition module acquires the initial EIT-Stark spectral signal, which is represented as follows: S(t)=P(t)+B(t)+N(t)+C, t∈[t1,t2]; Where t is the time series of the signal, S(t) is the initial EIT-Stark spectral signal, P(t) is the effective transmission peak signal, B(t) is the baseline signal with a mean of 0, N(t) is the noise signal, C is the signal constant, and [t1,t2] is the non-stationary time series signal region where peak finding is required; S12: Perform wavelet transform on the initial EIT-Stark spectral signal S(t); where a is the wavelet scale, b is the wavelet shift, ψ(.) is the mother wavelet function, ψ a,b (.) is the scaled and shifted wavelet basis function, and C(a,b) is the wavelet coefficient. S13: Combining steps S11 and S12, the wavelet coefficients C(a,b) of the EIT-Stark spectral signal are obtained; The mother wavelet function is chosen to be the Mexican cap wavelet, which is similar to the EIT transmission peak shape. The function expression of the Mexican cap wavelet is as follows: During the wavelet transform process, the natural exponent is used to optimize and select the wavelet scale 'a'; a two-dimensional image of the wavelet coefficients is plotted at the selected wavelet scale. a = 2.1362 e 0.3285i i = 0, 1, 2,...; Where i is a natural number.

3. The method for extracting EIT-Stark spectral features of Rydberg atoms according to claim 1, characterized in that, Step S2 includes: S21: Based on the wavelet coefficients C(a,b) of the EIT-Stark spectral signal, perform a natural logarithmic transformation on all data in the wavelet coefficient matrix of the two-dimensional image to obtain the wavelet coefficients after the natural logarithmic transformation, and plot the histogram of the wavelet coefficients after the natural logarithmic transformation. S22: set a wavelet coefficient threshold, divide all the wavelet coefficients after the natural logarithmic transformation into two categories by using the wavelet coefficient threshold, and calculate the inter-class variance s of the two categories of wavelet coefficients B ; s B = w0(m0- m c ) 2 + w1(m1- m c ) 2 ; where m0, m1 are the mean values of the two types of wavelet coefficients, respectively, m is the mean value of all wavelet coefficients, and w0, w1 are the weights of the two types of wavelet coefficients, respectively. c where m0, m1 are the mean values of the two types of wavelet coefficients, respectively, m is the mean value of all wavelet coefficients, and w0, w1 are the weights of the two types of wavelet coefficients, respectively S23: Utilizing the inter-class variance s of the two types of wavelet coefficients B Based on the bimodal characteristics in the wavelet coefficient histogram, the optimization range ν is determined, the optimization objective function is constructed, and a threshold with the largest inter-class variance is determined within the optimization range ν. S24: Obtain the maximum threshold S of the wavelet coefficients using the optimization objective function. Bmax The corresponding wavelet coefficients m0 and m1 are output, and they will be less than the maximum threshold S within the range [m0, m1]. Bmax By setting the wavelet coefficients to zero, the peak-finding range can be obtained.

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