Weak measurement based noise spectrum detection method and system

Abstract

The application provides a noise spectrum detection method and system based on weak measurement, comprising the following steps: step 1, building a quantum weak measurement optical platform for noise spectrum detection, introducing noise in the weak coupling process to generate a time-varying phase parameter, step 2, determining the frequency position f to be detected, and adjusting two post-selection states according to the frequency position f, step 3, receiving the spectrum center after weak measurement through a spectrometer, and calculating the noise spectrum at the frequency f, step 4, repeatedly executing steps 2 and 3 to realize real-time detection of the noise power spectrum, and step 5, after the measurement is completed, performing data processing on the estimated results according to actual needs. The application makes up for the defects of small bandwidth and easy aliasing distortion of the existing noise detection technology, utilizes the weak value amplification technology, can achieve very high sensitivity and precision, and expands the application scenarios of a plurality of measurement systems based on weak measurement as a theory, and can be extended to the scene of noisy signal recovery.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of weak measurement, in particular, to a noise spectrum detection method and system based on weak measurement. BACKGROUND

[0002] The noise obtained in the measurement process is the common product of all objects involved in the measurement system, including the measuring instrument, the measured object, the environment and the measurement method. Therefore, by analyzing the noise data obtained by measurement, the structure and characteristics of the entire measurement system can be studied. A common analysis method for noise is to calculate various statistics thereof, such as characteristic function, k-order moment, etc. Among these statistics, the most important one is the power spectrum, which is related to the autocorrelation function of the noise through Fourier transform and essentially reflects the time correlation of the noise in various time scales. In recent years, due to the proposal of fast Fourier transform (FFT), people can process digital signals at super high speed, so the power spectrum of noise has important applications in more and more physical scenarios. The existing noise spectrum detection scheme obtains noise data by uniform sampling at a certain frequency, which may cause serious aliasing distortion, which greatly reduces the accuracy of noise analysis, and there are defects such as small detection bandwidth, complex experimental structure, and difficult experiment, which may limit the noise spectrum detection technology.

[0003] In the patent document with publication number CN112925008A, a high-precision mode-preserving fiber polarization light earthquake gyroscope based on quantum weak measurement is disclosed, which comprises a light-emitting diode, a Gaussian filter, a half-mirror, a first polarization controller, a polarization beam splitter, a SOLEIL-BABINET compensator, a second collimating lens, a first collimating lens, a polarization maintaining fiber ring, a second polarization controller, a first spectrometer, a second spectrometer, an AD acquisition module, an FPGA data processing module, a DA conversion module, and an LED display and USB storage module. After being collected by the AD acquisition module, the data are transmitted to the FPGA data processing module, and then the obtained spectrum is compared with the initial spectrum to calculate the movement of the center wavelength, and then the relationship between the movement of the center wavelength and the rotation angular velocity of the earthquake gyroscope is obtained, so as to achieve the purpose of detecting high-precision mode-preserving fiber polarization light through weak measurement.

[0004] Therefore, it is necessary to propose a new technical solution to improve the above technical problems. SUMMARY

[0005] In view of the defects in the prior art, the purpose of the present application is to provide a noise spectrum detection method and system based on weak measurement.

[0006] According to the noise spectrum detection method based on weak measurement provided by the present application, the method comprises the following steps:

[0007] Step S1: build a quantum weak measurement optical platform for noise spectrum detection, and introduce noise in the weak coupling process to generate time-varying phase parameters;

[0008] Step S2: determine the frequency position f to be detected, and adjust the two-way post-selection states according to this;

[0009] Step S3: receive the spectrum center after weak measurement by the spectrometer, and calculate the noise spectrum at the frequency f;

[0010] Step S4: repeat steps S2 and S3 to perform real-time detection on the noise power spectrum;

[0011] Step S5: after the measurement is completed, perform data processing on the estimation results according to actual needs.

[0012] Preferably, the step S1 comprises the following steps:

[0013] Step S1.1: modulate the photons emitted by the light source into two linearly superimposed states of orthogonal polarization for noise spectrum detection;

[0014] Step S1.2: modulate the light into a pre-selection state

[0015] Step S1.3: in the weak coupling process, introduce noise to generate time-varying phase parameters n(t), and the interaction is represented as wherein, is the observable of the system, and the state of the output light after interaction is represented as

[0016] Step S1.4: modulate the post-selection state into |f(t)>, project the light after weak coupling onto the post-selection state, and the state of the output light after projection is represented as |φ f (t)> = <f | Φ i >.

[0017] Preferably, in the step S2, the two-way post-selection states are modulated as and

[0018] Preferably, in the step S3, the center frequency of the photons is used as the detection index The output of the spectrometer is Collect data to estimate the noise power spectrum with high precision;

[0019] The two-way spectrometer outputs corresponding to the post-selection states |f1(t)> and |f2(t)> aref T , respectively, calculate the real part and the imaginary part of the spectrum of the noise corresponding to the frequency f and According to the real part and the imaginary part of the spectrum of the noise corresponding to the frequency f at this time, the spectrum of the noise corresponding to the frequency f is calculated

[0020] Preferably, in the step S4, the power spectrum of the stationary noise is given by the Wiener-Sinai theorem: Each time the detection is set for a long detection time T, and the detection is performed multiple times, and the power spectrum S of the noise at the frequency f is obtained by taking the average of the results of each detection of the step S3 N (f).

[0021] The present application also provides a weak measurement-based noise spectrum detection system, the system comprising the following modules:

[0022] Module M1: build a quantum weak measurement optical platform for noise spectrum detection, and introduce noise in the weak coupling process to generate a time-varying phase parameter;

[0023] Module M2: determine the frequency position f to be detected, and adjust the two-path post-selection state according to this;

[0024] Module M3: receive the spectrum center after weak measurement through the spectrometer, and calculate the noise spectrum at the frequency f;

[0025] Module M4: repeatedly call modules M2 and M3 to perform real-time detection on the noise power spectrum;

[0026] Module M5: after the measurement is completed, perform data processing on the estimation results according to actual needs.

[0027] Preferably, the module M1 comprises the following modules:

[0028] Module M1.1: modulate the photons emitted by the light source into two linearly superimposed states of orthogonal polarization for noise spectrum detection;

[0029] Module M1.2: modulate the light into a pre-selection state

[0030] Module M1.3: introduce noise in the weak coupling process to generate a time-varying phase parameter n(t), and the interaction is represented as wherein, is the observable of the system, and the state of the output light after the interaction is represented as

[0031] ​Module M1.4: modulate the post-selection state to |f(t)>, project the light after weak coupling to the post-selection state, and the state of the output light after projection is represented as |φ f (t)> = <f|φ i .

[0032] Preferably, in the module M2, the frequency f to be detected as needed is modulated to two post-selection states and

[0033] Preferably, in the module M3, the central frequency of the photon is used as a detection index The output of the spectrometer is Collect data for high-precision noise power spectrum estimation;

[0034] The two spectrometer outputs <p f > T , are calculated respectively and According to the real part and the imaginary part of the spectrum of the noise corresponding to the frequency f, the spectrum of the noise corresponding to the frequency f is calculated

[0035] Preferably, in the module M4, the power spectrum of the stationary noise is given by the Wiener-Sinai theorem: Each time the detection is set to a long detection time T, and the detection is performed multiple times, and the average of the module M3 of each detection result is obtained, that is, the power spectrum S N () of the noise at the frequency f.

[0036] Compared with the prior art, the present application has the following beneficial effects:

[0037] 1. The present application makes up for the defects of small detection bandwidth and easy aliasing distortion in the prior art;

[0038] 2. The present application uses weak value amplification technology to achieve very high sensitivity and precision;

[0039] 3. The present application expands the application scenarios of numerous measurement systems based on weak measurement theory, and extends to the scenario of noisy signal recovery. BRIEF DESCRIPTION OF DRAWINGS

[0040] Other features, objects and advantages of the present application will become more apparent from the following detailed description of non-limiting embodiments, made with reference to the accompanying drawings:

[0041] Figure 1 Fig. 1 is a schematic diagram of the principle of the present application.

[0042] wherein:

[0043] post-selection process 4

[0044] pre-selection process 2 spectrometer 5

[0045] weak coupling process 3 computer 6 DETAILED DESCRIPTION

[0046] The present application will be described in detail below with specific embodiments. The following examples will help those skilled in the art to further understand the present application, but do not limit the present application in any form. It should be noted that for those skilled in the art, without departing from the concept of the present application, a number of changes and improvements can be made. These are within the scope of the present application.

[0047] Example 1

[0048] According to the noise spectrum detection method based on weak measurement provided by the present application, the method comprises the following steps:

[0049] Step S1: build a quantum weak measurement optical platform for noise spectrum detection, and introduce noise in the weak coupling process to generate a time-varying phase parameter;

[0050] Step S1.1: modulate the photons emitted by the light source into two linearly superimposed states of orthogonal polarization for noise spectrum detection;

[0051] Step S1.2: modulate the light into a pre-selected state

[0052] Step S1.3: in the weak coupling process, introduce noise to generate a time-varying phase parameter n(t), and the interaction is represented as wherein, is the observable of the system, and the state of the output light after interaction is represented as

[0053] Step S1.4: modulate the post-selected state into |f(t)>, project the light after weak coupling onto the post-selected state, and the state of the output light after projection is represented as |φ f (t)> = <f | Φ i >.

[0054] Step S2: determine the frequency position f to be detected, and adjust the two post-selected states according to this; according to the frequency f to be detected, the two post-selected states are modulated as and

[0055] Step S3: receiving the spectrum center of the light after weak measurement by the spectrometer, calculating the noise spectrum at frequency f; taking the center frequency of the photon as the detection index Detecting by the spectrometer, the detection time of the spectrometer is T, and the output of the spectrometer is Collecting data for high-precision noise power spectrum estimation; calculating the real part and the imaginary part of the spectrum corresponding to the post-selection state |f1(t)> and |f2(t)> respectively f T , respectively And According to the real part and the imaginary part of the spectrum of the noise corresponding to frequency f, the spectrum of the noise corresponding to frequency f is calculated

[0056] Step S4: repeatedly performing steps S2 and S3 to detect the noise power spectrum in real time; the power spectrum of the stationary noise is given by Wiener-Sin theorem: Set a long detection time T for each detection, and detect multiple times, and take the modulus of the detection results of step S3 to obtain the power spectrum S N (f) of the noise at frequency f.

[0057] Step S5: after the measurement is completed, the estimation result is processed according to the actual needs.

[0058] The application also provides a weak measurement-based noise spectrum detection system, which is realized by performing the flow steps of the weak measurement-based noise spectrum detection method, that is, the weak measurement-based noise spectrum detection method is understood by those skilled in the art as the preferred embodiment of the weak measurement-based noise spectrum detection system.

[0059] Example 2

[0060] The application also provides a weak measurement-based noise spectrum detection system, which comprises the following modules:

[0061] Module M1: building a quantum weak measurement optical platform for noise spectrum detection, and introducing noise in the weak coupling process to generate a time-varying phase parameter;

[0062] Module M1.1: modulating the photons emitted by the light source into two linearly superimposed states of orthogonal polarization for noise spectrum detection;

[0063] Module M1.2: modulating the light into a pre-selection state

[0064] ​Module M1.3: Introduce noise in the weak coupling process, generate time-varying phase parameter n(t), and the interaction is represented as where, is the observable of the system, and the state of the output light after interaction is represented as

[0065] Module M1.4: Modulate the post-selection state as |f(t)>, project the light after weak coupling to the post-selection state, and the state of the output light after projection is represented as |f f (t)> = <f|f i >.

[0066] Module M2: Determine the frequency position f to be detected, and adjust the two post-selection states according to this; according to the frequency f to be detected, the two post-selection states are modulated as and

[0067] Module M3: Receive the spectral center of the light after weak measurement by the spectrometer, and calculate the noise spectrum at frequency f; use the center frequency of the photon as the detection index Detect with the spectrometer, and the output of the spectrometer is Collect data to estimate the high-precision noise power spectrum;

[0068] Corresponding to the two post-selection states |f1(t)> and |f2(t)>, the outputs of the two spectrometers are <p f > T , respectively, and and Corresponding to the real part and the imaginary part of the spectrum of the noise at frequency f, calculate the spectrum of the noise at frequency f

[0069] Module M4: Repeat the calling of Module M2 and Module M3 to detect the noise power spectrum in real time; the power spectrum of stationary noise is given by Wiener-Khintchine theorem as: Set a long detection time T for each detection, and perform multiple detections, and take the modulus average of the detection results of Module M3 to obtain the power spectrum S N () of the noise at frequency f.

[0070] Module M5: After the measurement is completed, perform data processing on the estimation results according to actual needs.

[0071] Example 3

[0072] In view of the defects in the prior art, the purpose of the present application is to provide a noise power spectrum detection scheme based on weak measurement technology.

[0073] The noise obtained in the measurement process is the common product of all objects involved in the measurement system, including the measuring instrument, the measured object, the environment and the measurement method, so the structure and characteristics of the entire measurement system are studied by analyzing the noise data obtained by measurement. A common analysis method for noise is to calculate its various statistics, such as characteristic function, k-th moment, etc. Among these statistics, the most important one is the power spectrum, which is related to the autocorrelation function of the noise through Fourier transform and essentially reflects the time correlation of the noise in various time scales. In recent years, due to the introduction of fast Fourier transform (FFT), people can process digital signals at super high speed, so the power spectrum of noise has important applications in more and more physical scenarios. The existing noise spectrum detection scheme obtains noise data by uniform sampling at a certain frequency, which may cause serious aliasing distortion, which greatly reduces the accuracy of noise analysis, and there are defects such as small detection bandwidth, complex experimental structure, and difficult experiment. The above defects may limit the noise spectrum detection technology. The purpose of the present application is to provide a high-precision noise spectrum detection scheme based on quantum weak measurement theory.

[0074] As shown in Figure 1 The present application provides a high-precision real-time estimation method for time-varying phase based on quantum weak measurement theory, which comprises: 1-a light source; 2-a pre-selection process 3-a weak coupling process; 4-a post-selection process; 5-a spectrometer; 6-a computer.

[0075] The light emitted by the light source 1 passes through the pre-selection process 2, then generates a phase caused by noise in the weak coupling process 3, and is received by the spectrometer 5 for center frequency detection after the post-selection process 4. The spectrometer 5 is connected to the computer 6 for data processing of the detection results, including the following steps:

[0076] Step 1: build a quantum weak measurement optical platform for noise spectrum detection, and introduce noise in the weak coupling process to generate a time-varying phase parameter.

[0077] Step 2: determine the frequency position f to be detected, and adjust the two post-selection states accordingly.

[0078] Step 3: calculate the noise spectrum at the frequency f by receiving the spectrum center of the weak measurement light by the spectrometer.

[0079] Step 4: repeat steps 2 and 3 to realize real-time detection of the noise power spectrum.

[0080] Step 5: after the measurement is completed, the estimation results are processed according to the actual needs.

[0081] The step 1 comprises the following steps:

[0082] Step 1.1: The photons emitted from the light source are modulated into two linear superposition states of orthogonal polarization for noise spectrum detection.

[0083] Step 1.2: Modulate the light into a pre-selected state

[0084] Step 1.3: Introduce noise in the weak coupling process to generate a time-varying phase parameter n(t), and the interaction is represented as Wherein, is the observable of the system, and the state of the output light after interaction is represented as

[0085] Step 1.4: Modulate the post-selected state into |f(t)>, project the light after weak coupling onto the post-selected state, and the state of the output light after projection is represented as |φ f (t)>=<f∣Φ i >.

[0086] In step 1.4, according to the frequency f to be detected, the two post-selected states are modulated as And

[0087] The step 3 uses the central frequency of the photons as a detection index The output of the spectrometer is Collect as much data as possible to achieve high-precision noise power spectrum estimation. The two spectrometer outputs <p f > T are calculated respectively And The real part and the imaginary part of the spectrum of the noise corresponding to the frequency f are calculated, so the spectrum of the noise corresponding to the frequency f is further calculated

[0088] The step 4 comprises the following steps:

[0089] Because the power spectrum of the stationary noise is given by the Wiener-Sinai theorem: Therefore, set a long detection time T for each detection, and detect as many times as possible, and take the modulus average of the detection results of step 3 to obtain the power spectrum S N (f) of the noise at the frequency f.

[0090] The time-varying parameter real-time estimation system based on weak measurement technology provided by the application comprises the following modules: module M1: a quantum weak measurement optical platform for noise spectrum detection is built, and noise is introduced in the weak coupling process to generate a time-varying phase parameter. Module M2: the frequency position f to be detected is determined, and the two post-selection states are adjusted accordingly. Module M3: the spectrum center after weak measurement is received by a spectrometer, and the noise spectrum at the frequency f is calculated. Module M4: the real-time detection of the noise power spectrum is realized by repeatedly calling the module M2 and the module M3. Module M5: after the measurement is completed, the estimation results are processed according to actual needs.

[0091] Module M1.1: the light output by the light source is passed through a bifurcated optical fiber bundle, one of which is used for monitoring the light intensity change, and the other of which is used for parameter measurement based on the weak measurement method. Module M1.2: the light in the parameter measurement path is modulated into a pre-selection state |i>. Module M1.3: the photons emitted from the light source are modulated into two linearly superimposed states of orthogonal polarization, which are used for noise spectrum detection. Module M1.4: the light is modulated into a pre-selection state Module M1.5: in the weak coupling process, noise is introduced to generate a time-varying phase parameter n(t), and the interaction is represented as wherein, is the observable of the system, and the state of the output light after the interaction is represented as Module M1.6: the post-selection state is modulated into |f(t)>, the light after weak coupling is projected onto the post-selection state, and the state of the output light after projection is represented as |φ f (t)>=<f∣Φ i >.

[0092] The module M2 comprises: according to the frequency f to be detected, the two post-selection states are modulated into and

[0093] The module M3 comprises: the center frequency of the photons is used as a detection index detected by a spectrometer, and the output of the spectrometer is Data is collected for as long as possible to realize high-precision estimation of the noise power spectrum. The two spectrometer outputs <p f > T are calculated respectively and The real part and the imaginary part of the spectrum of the noise corresponding to the frequency f are calculated, so the spectrum of the noise corresponding to the frequency f is further calculated

[0094] The module M4 comprises: because the power spectrum of the stationary noise is given by Wiener-Khintchine theorem as: Therefore, the longer the detection time T is set and the more times the detection is performed, the more accurate the power spectrum S of the noise at the frequency f can be obtained. N (f).

[0095] Those skilled in the art will understand the present embodiment as a more specific description of Embodiment 1 and Embodiment 2.

[0096] Those skilled in the art know that, in addition to implementing the system provided by the present application and each device, module and unit thereof in the form of pure computer readable program code, the system provided by the present application and each device, module and unit thereof can also be implemented in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers and embedded microcontrollers, etc. by logically programming the method steps to achieve the same functions. Therefore, the system provided by the present application and each device, module and unit thereof are considered as a hardware component, and the devices, modules and units included therein for achieving various functions are also considered as structures within the hardware component; the devices, modules and units for achieving various functions are also considered as both software modules for implementing the method and structures within the hardware component.

[0097] The specific embodiments of the present application are described above. It needs to be understood that the present application is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essential content of the present application. In the case of no conflict, any combination of the embodiments of the present application and the features in the embodiments is allowed.

Claims

1. A weak measurement based noise spectroscopy method, characterized in that, The method comprises the following steps: Step S1: build a quantum weak measurement optical platform for noise spectrum detection, and introduce noise in the weak coupling process to generate time-varying phase parameters; Step S2: determine the frequency position f to be detected, and adjust the two-way post-selection state according to it; Step S3: receive the spectrum center after weak measurement by a spectrometer, and calculate the noise spectrum at the frequency f; Step S4: repeatedly execute step S2 and step S3 to perform real-time detection on the noise power spectrum; Step S5: after the measurement is completed, data processing is performed on the estimation result according to actual needs; In the step S3, the central frequency of the photons is used as a detection index The output of the spectrometer is The data is collected for high-precision noise power spectrum estimation; The two spectrometer outputs <p f > T , respectively, are calculated as and The real and imaginary parts of the spectrum of the noise corresponding to frequency f at this time are calculated as 2. The weak measurement based noise spectroscopy method of claim 1, wherein, The step S1 comprises the following steps: Step S1.1: modulate the photons emitted by the light source into two linearly superimposed states of orthogonal polarization for noise spectrum detection; Step S1.2: Modulating the light into a preselected state Step S1.3: In the weak coupling process, the noise is introduced to generate the time-varying phase parameter n(t), and the interaction is represented as wherein, is the observable of the system, and the state of the output light after the interaction is represented as Step S1.4: Modulate the post-selection state to |f(t)>, project the weakly coupled light onto the post-selection state, the state of the output light after the projection is represented as |φ f (t) = <f | φ i >.

3. The weak measurement based noise spectroscopy method of claim 1, wherein, The two-path post-selection state modulation in step S2 according to the frequency f to be detected is and 4. The weak measurement based noise spectroscopy method of claim 1, wherein, In the step S4, the power spectrum of the stationary noise is given by the Wiener-Sinai theorem as: The long detection time T is set each time of detection, and the detection is performed multiple times, and the power spectrum S of the noise at the frequency f is obtained by averaging the results of each detection of the step S3 N (f).

5. A weak measurement based noise spectroscopy system, comprising: The system comprises the following modules: Module M1: build a quantum weak measurement optical platform for noise spectrum detection, and introduce noise in the weak coupling process to generate time-varying phase parameters; Module M2: determine the frequency position f to be detected, and adjust the two-way post-selection state according to it; Module M3: receive the spectrum center after weak measurement by a spectrometer, and calculate the noise spectrum at the frequency f; Module M4: repeatedly call module M2 and module M3 to perform real-time detection on the noise power spectrum; Module M5: after the measurement is completed, data processing is performed on the estimation result according to actual needs; In the module M3, the central frequency of the photons is used as a detection index The output of the spectrometer is The data is collected for high-precision noise power spectrum estimation; The two spectrometer outputs <p f T are calculated respectively and The real and imaginary parts of the spectrum of the noise corresponding to the frequency f are calculated from the spectrum of the noise corresponding to the frequency f at this time ​ 6. The weak measurement based noise spectroscopy system of claim 5, wherein, The module M1 comprises the following modules: Module M1.1: modulate the photons emitted by the light source into two linearly superimposed states of orthogonal polarization for noise spectrum detection; Module M1.2: Modulating light into a preselected state Module M1.3: Introduce noise in the weak coupling process, resulting in a time-varying phase parameter n(t), the interaction is represented as where, is the observable of the system, and the state of the output light after the interaction is represented as Module M1.4: Modulate the post-selection state to |f(t)>, project the weakly coupled light onto the post-selection state, the state of the output light after projection is represented as |φ f (t) = <f | φ i >.

7. The weak measurement based noise spectroscopy system of claim 5, wherein, The frequency f to be detected in the module M2, the two-way post-selection state modulation is and 8. The weak measurement based noise spectroscopy system of claim 5, wherein, In the module M4, the power spectrum of the stationary noise is given by the Wiener-Sinai theorem: Each time the detection is set for a long detection time T, and the detection is performed multiple times, and the average of the results of each detection of the module M3 is taken to obtain the power spectrum S of the noise at the frequency f N (f).

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