Weak measurement system comprising a phase carrier modulation and related methods

Abstract

The application discloses a weak measurement system comprising phase carrier modulation and demodulation and a related method, and the weak measurement system comprises a front-state preparation part, a light beam splitting part, a rear-state setting part, a phase carrier modulation generating part and a phase demodulation algorithm implementing part, wherein the front-state preparation part comprises a light source, a front-state polarizer and a to-be-measured signal introduction part; the light source emits light which forms polarized light after passing through the front-state polarizer and is introduced into a to-be-measured phase difference signal by the to-be-measured signal introduction part; the polarized light is modulated by the phase carrier modulation generating part and then enters the light beam splitting part to be divided into a first light beam and a second light beam; the first light beam and the second light beam enter the rear-state setting part located in a first weak measurement channel and the rear-state setting part located in a second weak measurement channel respectively, and then the first light beam and the second light beam enter the phase demodulation algorithm implementing part for demodulation to obtain the to-be-measured phase difference signal.

Description

Technical Field

[0001] This invention relates to the field of optical measurement, specifically to an optical phase weak measurement system and related methods based on quantum weak measurement technology. It provides a weak measurement system based on phase carrier modulation and demodulation technology and a phase carrier modulation and demodulation method for this system. This optical phase measurement device, as a module, can be widely used in fields such as fiber optic sensing and geometric precision optical measurement. Background Technology

[0002] In 1988, Aharonov, Albert, and Vaidman (AAV) first proposed the concept of weak measurements. Weak measurement is a measurement technique characterized by post-selection, and is therefore sometimes called post-selected weak measurement. The weak measurement model can be described as follows: after a system in a certain initial state (pre-selection) undergoes a weak interaction with an auxiliary system (generally called a measuring instrument), a suitable post-selection is applied to the system's states, ultimately extracting the pointer offset from the spatial distribution of the measuring instrument, thereby obtaining information about the system and its observables. AAV discovered that when the pre-selected and post-selected states of the system are nearly orthogonal, the pointer offset will far exceed the eigenspectral range of the system's observables. This phenomenon is called the weak-value amplification effect or the AAV effect. Due to the existence of the weak-value amplification effect, weak measurements can be widely used in the field of precision measurement. Furthermore, compared to traditional measurement methods, weak measurements not only do not increase the requirements for experimental detection devices, but are also applicable to almost all traditional detection systems.

[0003] Furthermore, the important research results reported by Salazar-Serrano et al. (Salazar-Serrano LJ, et al., Optics Letters, 2014, 39:4478-4481) confirm that weak measurements can be achieved in any wave-based interferometric system, providing a basis for the selection and application development of weak measurement systems. In 2013, a research group at the University of Science and Technology of China constructed an optical weak measurement structure using a white LED light source to achieve phase measurement of light. Their experimental results showed that the phase measurement accuracy could reach 10⁻⁶. -4 rad. In 2017, a physics research group at Sichuan University conducted experiments to measure the phase of light using a single-frequency light source and a weak optical measurement structure with the same optical path. The experimental results showed that the minimum phase change of light could reach 10 rad. -5 rad.

[0004] Since the phase noise caused by the light source linewidth is smaller in weak measurement optical paths, weak value amplification technology can effectively suppress phase noise. While amplifying useful micro-phase changes, it does not increase the noise level of the system, enabling weak measurement systems to have lower noise floor and higher measurement accuracy. It has important application prospects in the fields of fiber optic sensing and optical precision measurement.

[0005] In traditional optical interferometry phase measurement devices, the main principle is to convert the physical quantity to be measured into optical phase, and then measure the corresponding optical phase based on changes in interference fringes. To further reduce the influence of low-frequency phase noise caused by active devices such as light sources and detectors, modulation and demodulation methods are introduced. By demodulating the phase information using appropriate demodulation algorithms, the measured optical phase and the system's low-frequency phase noise can be separated, thereby improving the signal-to-noise ratio of the system's phase measurement. Commonly used modulation and demodulation methods include heterodyne methods, phase-shifting methods, phase generation carrier (PGC) methods, and wavelength modulation methods.

[0006] Weak measurement essentially sacrifices photon detection probability to improve measurement accuracy. Compared to interferometric methods with equivalent equipment, weak measurement systems detect fewer photons, making them susceptible to various detection noises, such as light source stability, phase shift caused by rotating polarization devices, polarizer extinction ratio, and detector electronic noise. These factors all affect the final signal-to-noise ratio (SNR) of the measurement system, especially the SNR of low-frequency optical phase signals. Current weak measurement systems directly measure the optical phase under test. The inherent phase noise of the system, such as that of the light source and detector, cannot be effectively separated in the detection principle. Device disturbances and detection noise are directly superimposed and reflected in the output of the measured phase, affecting the detection capability of weak signals.

[0007] Drawing on the system noise suppression approach of traditional fiber optic interferometry phase carrier modulation and demodulation (PGC), a weak measurement system incorporating phase modulation and demodulation is designed. By using optical phase carrier modulation and demodulation, the influence of measurement noise and interference can be reduced, thereby improving the detection signal-to-noise ratio of the weak measurement system.

[0008] When phase carrier modulation is introduced into a traditional interferometric system, assuming the phase carrier amplitude is C and the frequency is ω0, the expression for the output light intensity I after passing through the interferometric system is as follows (1).

[0009]

[0010] Where A and B are the coefficients of the light intensity signal model, which are constants, and t is time. Given the optical phase signal to be measured, the trigonometric function expansion of formula (1) yields the output light intensity I, which is expressed as formula (2).

[0011]

[0012] In the formula, J k (C) represents the first-order k-th order Bessel function. It is clear from equation (2) that the optical phase signal to be measured... They are respectively loaded onto each harmonic component of the high-frequency carrier.

[0013] After modulation, traditional interferometric signals contain components of the target signal in both the fundamental frequency and the higher harmonics sidebands of the carrier signal. Therefore, traditional interferometric demodulation can extract the fundamental frequency and second harmonic sideband signals of the modulated signal, and then obtain a pair of orthogonal signals through filtering and subsequent algorithms. The signal can then be demodulated by outputting the light intensity through a single channel.

[0014] As is well known in this technical field, demodulation methods can effectively separate and suppress detection noise introduced by active devices such as light sources and detectors. Depending on the specific demodulation method, different phase modulation depths C are preferred. For example, in the Differential Cross-Multiplication (PGC-DCM) demodulation method, the phase modulation depth is typically chosen to be 2.37 rad, while in the Arctangent (PGC-Arctan) demodulation method, the phase modulation depth is typically chosen to be 2.63 rad. The Differential Cross-Multiplication (DCM) method is characterized by its simplicity and low hardware requirements. The initial demodulation scheme for PGC was DCM, which used analog circuits. However, with the development of modern electronic technology and the advantages of digital circuits in signal processing, PGC's DCM schemes generally adopt digital demodulation schemes. DCM has become quite mature and is used in various fiber optic sensing systems.

[0015] The schematic diagram of the traditional differential cross-multiplication demodulation algorithm is as follows: Figure 1 As shown, the phase signal to be measured is first modulated by a carrier wave in the interferometric measurement system to obtain the interference light intensity signal. Then, it is mixed with the fundamental frequency and the second harmonic of the modulating carrier wave, respectively. After that, low-pass filtering, differential cross-multiplication, integration, and high-pass filtering are performed to finally complete the signal demodulation.

[0016] In weak measurement optical paths, because the measured phase and phase modulation depth are both much less than 1 rad, the signal only has a significant component in the fundamental frequency sideband of the carrier. In the second harmonic and higher regions of the carrier, the relevant signal components are very small and difficult to detect. Therefore, the effective measured modulation component obtained in a weak measurement system can only be extracted from the fundamental frequency carrier sideband to obtain a sufficient detection signal-to-noise ratio. Thus, a weak measurement system with only a single-channel output cannot extract a pair of orthogonal signals from the carrier fundamental frequency and second harmonic sideband signals as in traditional interferometric demodulation, and then use a demodulation algorithm to extract the measured phase and improve the detection signal-to-noise ratio. Summary of the Invention

[0017] To address the aforementioned technical problems, this invention provides a weak measurement system incorporating phase carrier modulation and demodulation, and a phase carrier modulation and demodulation method for this system. This method is adaptable to the characteristics of small measured phase and small phase carrier modulation in weak measurement systems, effectively reducing the impact of low-frequency noise from light sources, detectors, etc., on the system's phase noise, thereby improving the detection signal-to-noise ratio of the weak measurement system, especially the detection signal-to-noise ratio in the low-frequency band.

[0018] According to a first aspect of the present invention, a weak measurement system including phase carrier modulation and demodulation is provided. The weak measurement system includes: a pre-selection state preparation section, a beam splitting section, and a post-selection state setting section. The weak measurement system further includes a phase carrier modulation generation section and a phase demodulation algorithm implementation section. The pre-selection state preparation section includes: a light source, a pre-selection polarizer, and a signal to be measured introduction section. Light emitted from the light source is polarized by the pre-selection polarizer and then introduced into the signal to be measured phase difference signal by the signal to be measured introduction section. The polarized light is modulated by the phase carrier modulation generation section and then enters the beam splitting section to split into a first beam and a second beam. The first beam and the second beam enter the post-selection state setting section located in a first weak measurement channel and the post-selection state setting section located in a second weak measurement channel, respectively. Then, the first beam and the second beam enter the phase demodulation algorithm implementation section for demodulation to obtain the signal to be measured phase difference signal.

[0019] In a preferred embodiment, the phase carrier modulation generation section includes a carrier modulation signal generator and a phase modulator. The carrier modulation signal generator applies a driving voltage to the phase modulator, thereby generating a phase modulation change function between two orthogonal polarization directions. The carrier modulation frequency of this function is controlled by the carrier modulation signal generator, and the carrier modulation frequency is higher than the highest frequency of the operating frequency band of the phase under test.

[0020] Preferably, the phase modulator is an electro-optic modulator, such as a lithium niobate electro-optic crystal modulator; or a liquid crystal optical modulator; or a piezoelectrically driven fiber stretching modulator; or an electrically controlled phase modulator.

[0021] In a preferred embodiment, the signal to be measured introduction part includes: an optical fiber, an optical fiber coupler, and an optical fiber collimator. The optical fiber is affected by changes in external physical quantities, which will cause a phase difference signal to be measured in two orthogonal polarization directions. The light emitted by the light source is polarized by a pre-selective linear polarizer, and the optical fiber coupler and optical fiber collimator connect the optical fiber to the weak measurement system, thereby introducing the phase difference signal to be measured.

[0022] In another preferred embodiment, the beam splitting section includes a beam splitter; or, the beam splitting section includes an optical fiber beam splitter and an optical fiber combiner.

[0023] In another preferred embodiment, the first weak measurement channel and the second weak measurement channel each include: a phase compensator, a post-selected linear polarizer, a photodetector, and a detection and acquisition module, wherein the post-selected parameters of the first weak measurement channel and the second weak measurement channel are κ1 and κ2, respectively, and κ1≠κ2.

[0024] Preferably, the phase compensator is composed of a half-wave plate and a quarter-wave plate, which are adjusted by relative rotation; optionally, the phase compensator is an electro-optic crystal modulator; wherein, the post-selected linear polarizer is a Glan-Taylor prism polarizer or a metal wire grid polarizer; the photodetector is an avalanche photodiode (APD), a photodiode (PD), a single-photon avalanche diode (SPAD), a photomultiplier tube (PMT), or a single-photon counter.

[0025] In another preferred embodiment, the phase demodulation algorithm implementation part uses a dual-channel differential cross arcsine demodulation method to obtain the phase difference signal to be measured.

[0026] According to a second aspect of the present invention, a method for phase carrier modulation and demodulation of a weak measurement system according to various embodiments of the first aspect is provided, the method comprising: setting different post-selection parameters for a first weak measurement channel and a second weak measurement channel respectively; mixing and low-pass filtering the light intensity signals of the first weak measurement channel and the second weak measurement channel with a carrier modulation signal respectively; performing differential cross-multiplication on the two low-pass filtered signals to obtain a third signal and a fourth signal respectively; performing addition and subtraction operations on the third signal and the fourth signal to obtain a fifth signal and a sixth signal; and performing division and arcsine on the fifth signal and the sixth signal to obtain a phase difference signal to be measured.

[0027] According to a third aspect of the present invention, a phase modulation and demodulation module for a weak measurement system according to various embodiments of the first aspect is provided, wherein the phase modulation and demodulation module includes the phase carrier modulation generation part and the phase demodulation algorithm implementation part.

[0028] This invention provides a weak measurement system with phase carrier modulation and demodulation, achieving high-precision optical phase measurement. Based on the weak value amplification effect, the weak measurement system can measure extremely small optical phase signals with high sensitivity. However, existing weak measurement methods that directly measure phase, such as those using active devices like light sources and detectors, struggle to effectively distinguish low-frequency phase noise from the measured phase. Introducing phase carrier modulation effectively solves this problem. Considering the inherent characteristics of weak measurement systems, this invention proposes a dual-channel differential cross-multiplication demodulation method. By setting two weak measurement post-selection state measurement channels with different post-selection angles, high-precision demodulated signal recovery of the measured phase is achieved. Furthermore, this demodulation method is unaffected by parameter errors in actual weak measurement systems, such as phase modulation depth drift and carrier phase delay, effectively improving the detection signal-to-noise ratio of the weak measurement system, especially for low-frequency measured signals. Attached Figure Description

[0029] The technical solution of the present invention can be better understood through the accompanying drawings and the following related description, wherein:

[0030] Figure 1 A schematic diagram of the differential cross-multiplication demodulation method after phase carrier modulation based on the traditional interference principle is shown.

[0031] Figure 2 A schematic diagram of a weak measurement system including phase carrier modulation and demodulation according to the present invention is shown;

[0032] Figure 3 A schematic diagram of the dual-channel differential cross-multiplication demodulation method for phase carrier modulation of weak measurement systems, proposed according to the present invention, is shown.

[0033] Figure 4 A schematic diagram of a single-arm fiber optic sensing weak measurement system incorporating phase carrier modulation and demodulation according to a first embodiment of the present invention is shown; and

[0034] Figure 5 A schematic diagram of a dual-arm fiber optic sensing weak measurement system incorporating phase carrier modulation and demodulation, according to a second embodiment of the present invention, is shown. Detailed Implementation

[0035] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0036] Figure 2A schematic diagram of a weak measurement system incorporating phase carrier modulation and demodulation according to the present invention is shown. The weak measurement system includes: a pre-selection state preparation section A, a phase carrier modulation generation section B, a post-selection state measurement dual channel (i.e., channel C1 and channel C2), and a demodulation algorithm implementation module 8, etc. The pre-selection state preparation section A includes: a narrowband light source 1, a pre-selection polarizer 2 for generating linearly polarized light P0, which can then be converted into a measured optical phase signal at the measured signal introduction section 2' and introduced into the weak measurement system. A high-frequency carrier modulation signal is generated by the carrier modulation signal generator 4 in the phase carrier modulation generation section B and acts on the optical phase modulator 3 in the measurement system, causing a change in the optical phase introduced by the high-frequency carrier modulation. The phase modulator causes a change in the phase difference of the beam in two orthogonal polarization directions to produce a specified carrier modulation function, generated by the phase modulation signal generator 4 driving the phase modulator, and the set phase carrier modulation frequency is higher than the highest frequency of the measured phase operating frequency band. Then, the optical beam splitter 5 divides the optical path into two identical post-selection measurement channels C1 and C2. These two post-selection measurement channels respectively include polarization adjustment phase compensators 61 and 71, post-selection polarizers 62 and 72, photodetectors 63 and 73, and photodetector acquisition modules 64 and 74. Phase compensators 61 and 71 are mainly used to compensate for phase errors in the measurement system of the optical path. Post-selection polarizers 62 and 72 are used to achieve a suitable post-selection angle for the weak measurement channel. Detectors 63 and 73, and photodetector acquisition modules 64 and 74 jointly complete the photodetection of the output signal and output it to the modulation / demodulation algorithm implementation module 8. After being processed by the modulation / demodulation algorithm implementation module 8, the phase to be measured is recovered, completing the reconstruction of the phase signal to be measured. The output signal S1 (i.e., ...) is... ).

[0037] To achieve weak amplification in a measurement system, pre-selection and post-selection states need to be constructed for the probe optical path. For a beam of single-frequency coherent light, pre-selection is performed using a linear polarizer P1 to obtain the initial quantum state |ψ| of the system. i >For (see formula (3)):

[0038]

[0039] In formula (3), |H> represents the horizontal polarization state of light, and |V> represents the vertical polarization state of light.

[0040] In a measurement system, when the physical quantity to be measured causes a very slight phase difference between two polarized light components... At that time, the overall quantum state of the system can be expressed as formula (4):

[0041]

[0042] where A=|H><H|-|V><V|, and i is the imaginary unit.

[0043] Assume that post-selection as shown in the following formula (5) is introduced

[0044]

[0045] where in the formula, ± represents the phase advance or delay of the post-selection in the horizontal polarization direction and the vertical polarization direction, and κ represents the phase value generated by the post-selection to the system when there is no input signal.

[0046] After post-selection polarization detection, the quantum state of the system will become as shown in the following formula (6), where φ is the initial state of the entire system, representing the light beam that has undergone pre-selection, and conceptually represents the direct product of the pre-selected polarization state and the measuring instrument in physics:

[0047]

[0048] When the phase to be measured is particularly small, the quantum state of the system can be simplified to formula (7) by linear approximation:

[0049]

[0050] where set is denoted as the weak value. The magnitude of the weak value is related to the post-selection angle. Under the linear approximation condition, the smaller the post-selection angle, the larger the corresponding weak value amplification factor.

[0051] The output light intensity I after post-selection can be obtained by the detector ± is (see formula (8)):

[0052]

[0053] When the phase to be measured and the post-selected state parameter κ are both extremely small values, the output light intensity and the phase value are approximately in a linear relationship.

[0054] Herein, both the pre-selected state polarizer and the post-selected state polarizer can adopt linear polarizers, and the included angle between the polarization direction of the pre-selected state linear polarizer and the orthogonal direction of the polarization direction of the post-selected state linear polarizer is the post-selection angle D. Different post-selection angles D will cause corresponding changes in the post-selected state parameter κ. Adjustments of the phase compensator and the post-selected state polarizer can be used for setting, so that the two channels respectively generate post-selected state parameters κ1 and κ2 with slight differences, and both satisfy the weak value amplification condition in weak measurement.

[0055] Figure 3A flowchart of the dual-channel differential cross arcsine modulated phase carrier for a weak measurement system according to the present invention is shown. Based on the aforementioned basic working principle of weak measurement, as... Figure 2 In the dual-channel weak measurement system shown, the output optical signal of the first weak measurement channel C1 obtained by detector 63 and photoelectric detection and acquisition module 64 is (see formula (9)):

[0056]

[0057] The output optical signal of the second weak measurement channel C2 obtained by detector 73 and photoelectric detection and acquisition module 74 is (see formula (10)):

[0058]

[0059] Where A1 and A2 represent the amplitudes of the DC components of the two light intensity signal outputs, respectively, and B1 and B2 represent the amplitudes of the light intensity signal variation components, respectively. κ1 and κ2 represent the post-selection parameters set for the first and second weak measurement channels, respectively. The phase signal to be measured, The signal is a phase carrier modulated signal, where C is the modulation depth and ω is the phase carrier modulation depth. c t is the phase carrier modulation frequency, and t is time.

[0060] The obtained dual-channel optical intensity signals I1 and I2 are respectively compared with the signal of one harmonic of the carrier modulation signal. The intermediate result obtained after mixing and then filtering by a low-pass filter can be expressed as the following formulas (11) and (12):

[0061]

[0062]

[0063] Where J1(C) is the Bessel function, and the modulation depth C is a constant term after it is determined. The amplitude of the mixing fundamental frequency signal is G. The error caused by the phase carrier delay can be approximated as an invariant here.

[0064] By performing differential cross-multiplication on the two low-pass filtered signals, the intermediate results of the X and Y signals can be obtained, which can be expressed as the following formulas (13) and (14):

[0065]

[0066]

[0067] in Let be the differential function of the phase signal to be measured.

[0068] By adding and subtracting the X and Y signals respectively, we can obtain the following formulas (15) and (16):

[0069]

[0070]

[0071] The result of dividing the P and Q signals can then be expressed as the following formula (17):

[0072]

[0073] The final phase can be obtained by performing an arcsine operation on the signal g (see formula (18) below).

[0074]

[0075] From the above formula (18), it can be seen that the demodulation result is only related to the post-selection parameters κ1 and κ2 of the two outputs, that is, the parameters preset by the weak measurement system. The actual values ​​of the post-selection parameters κ1 and κ2 can be obtained by accurately measuring the maximum and minimum output light intensity in the weak measurement system, and κ1≠κ2.

[0076] The demodulation model of this invention eliminates the phase measurement system error caused by the instability of parameters in weak measurement systems such as carrier phase delay, phase modulation depth, and light intensity, thereby making the final output result more stable.

[0077] Figure 4 A schematic diagram of a weak fiber optic sensing measurement system including phase carrier modulation and demodulation according to a first embodiment of the present invention is shown. It includes a phase carrier modulation and demodulation section 30.

[0078] The pre-selection state preparation part of the weak measurement system includes a single-wavelength light source 1 and a Glan-Taylor prism polarizer 2. The light emitted from the single-wavelength light source 1 passes through the Glan-Taylor prism polarizer 2 to prepare the pre-selection polarization state for weak measurement, and the initial polarization state is obtained as shown in formula (19):

[0079]

[0080] The wound polarization-maintaining fiber 41 is connected to the weak measurement system via the polarization-maintaining fiber coupler 31 and the polarization-maintaining fiber collimator 51. That is, the change of external physical quantity in the wound polarization-maintaining fiber 41 will cause a phase difference signal in two orthogonal polarization directions, which will result in the phase to be measured between |H> and |V>. It is introduced as the phase signal to be measured.

[0081] In the phase carrier modulation generation section, the fine collimated beam output from the polarization-maintaining fiber collimator 51 is incident on the optical phase modulator 3. This optical phase modulator 3 can be a lithium niobate electro-optic crystal modulator, a liquid crystal optical modulator, or other electrically modulated devices. Its main purpose is to generate a phase modulation change function between the two orthogonal polarization directions |H> and |V> when the carrier modulation signal generator 4 applies a driving voltage to the optical phase modulator 3. Its carrier modulation frequency is controlled by carrier modulation signal generator 4.

[0082] The phase-carrier-modulated light beam is split into two weak measurement channels by a beam splitter 5. In the first channel, the post-selection setting section includes a λ / 2 waveplate 61A and a λ / 4 waveplate 61B, which implement the phase compensation function of this channel. The post-selection setting section also includes a Glan-Taylor prism polarizer 62. The post-selection angle is set jointly by the λ / 2 waveplate 61A, the λ / 4 waveplate 61B, and the Glan-Taylor prism polarizer 62. The generated light intensity signal with modulation information is detected by a high-speed photodetector 63 and converted into a digital signal by the photoelectric acquisition module 64 of this channel. Similarly, in the second weak measurement channel, the post-selection setting section includes a λ / 2 waveplate 71A and a λ / 4 waveplate 71B, and also includes a Glan-Taylor prism polarizer 72. The generated light intensity signal with modulation information is detected by a high-speed photodetector 73 and converted into a digital signal by the photoelectric acquisition module 74 of this channel. The two acquisition modules 64 and 74 respectively introduce the acquired light intensity signals into the beam to realize the... Figure 3 In the digital hardware circuit 30 of the demodulation algorithm shown, according to Figure 3 The demodulation step described above is used for demodulation (see formula (18) above). After obtaining the output result of formula (18) and performing high-pass filtering, the signal to be measured can be obtained.

[0083] Figure 5 A schematic diagram of a fiber optic weak measurement device incorporating phase carrier modulation and demodulation according to a second embodiment of the present invention is shown. The difference from the first embodiment is that, in the second embodiment, a fiber optic beam splitter replaces the beam splitter of the previous embodiment in the weak measurement optical path to split the beam and form a dual-channel weak measurement channel. Furthermore, unlike the first embodiment, in the second embodiment, the phase difference between the two orthogonal polarization directions |H> and |V> is generated by the winding fibers 41a and 41b.

[0084] In this embodiment, the phase modulation and demodulation fiber optic weak measurement system includes: a pre-selection state preparation section, a phase carrier modulation generation section, a beam splitting section, a dual-channel post-selection state setting section, and a demodulation algorithm implementation section for the detection output. The narrowband light source 1, the pre-selection state preparation section, the phase carrier modulation generation section, the beam splitting section, and the post-selection state setting section constitute the weak measurement optical path. The pre-selection state preparation section includes: a narrowband light source 1, a pre-selection linear polarizer Glan-Taylor prism 2, and a first fiber polarization-maintaining collimator 31. The wound polarization-maintaining fibers 41a and 41b are connected to the weak measurement system via a polarization-maintaining fiber coupler 31 and a polarization-maintaining fiber collimator 51. That is, external changes to the wound polarization-maintaining fibers 41a and 41b will respectively induce phase difference signals in two orthogonal polarization directions, thus resulting in a phase difference between |H> and |V>, representing the phase to be measured. The phase signal to be measured is introduced. In the phase carrier modulation generation section, the fine collimated beam output from the polarization-maintaining fiber collimator 51 is incident on the optical phase modulator 3. The optical phase modulator 3 uses a lithium niobate electro-optic crystal modulator, the main purpose of which is to generate a phase modulation change function between the two orthogonal polarization directions |H> and |V> when the carrier modulation signal generator 4 applies a driving voltage to the optical phase modulator 3. Its carrier modulation frequency is controlled by carrier modulation signal generator 4.

[0085] The beam splitting section includes: a fiber beam splitter 9, a fiber polarization-maintaining coupling mirror 9a, and a third fiber polarization-maintaining collimating mirror 9b and a fourth fiber polarization-maintaining collimating mirror 9c, forming two weak measurement channels. The beam modulated by the phase carrier is split into two weak measurement channels by the beam splitter. In the first channel, the post-selection setting section includes a λ / 2 waveplate 61A and a λ / 4 waveplate 61B to realize the phase compensation function of this channel. The post-selection setting section also includes a Glan-Taylor prism polarizer 62. The post-selection angle is set by the λ / 2 waveplate 61A, the λ / 4 waveplate 61B, and the Glan-Taylor prism polarizer 62. The generated light intensity signal with modulation information is detected by a high-speed photodetector 63 and converted into a digital signal by the photoelectric acquisition module 64 of this channel. Similarly, in the second weak measurement channel, the post-selection setting section includes a λ / 2 waveplate 71A and a λ / 4 waveplate 71B, and also includes a Glan-Taylor prism polarizer 72. The generated light intensity signal with modulation information is converted into a digital signal by a high-speed photodetector 73 and then by the photoelectric acquisition module 74 of this channel. The two acquisition modules 64 and 74 respectively introduce the acquired light intensity signal into the system to achieve the desired signal. Figure 3 In the digital hardware circuit 30 of the demodulation algorithm shown, according to Figure 3 The demodulation step described above is used for demodulation.

[0086] In this invention, by combining phase carrier modulation with weak measurement techniques, a phase carrier modulation signal is superimposed on the phase signal under test, constructing a micro-phase carrier modulation measurement method suitable for weak measurement systems. A dual-channel differential cross-arcsine phase demodulation method and apparatus are also proposed. By designing dual-channel weak measurement with slightly different post-selection state parameters κ1 and κ2, a phase-modulated signal under test is output. The carrier fundamental frequency sideband signals of the two signals are then extracted separately, and the signal under test is reproduced through a demodulation algorithm.

[0087] In this invention, the phase carrier modulation signal is generated by a signal generator driving a phase modulator, and the dual-channel post-selection parameter κ is set by rotating the angles of the λ / 2 waveplate and the λ / 4 waveplate. This invention is not limited to using λ / 2 and λ / 4 waveplates to achieve the above setting; any other component capable of achieving this setting, such as a magneto-optic modulator or an electro-optic modulator, can be used as an alternative. In this invention, the linear polarizer can be a Glan-Taylor prism polarizer, a metal wire grid polarizer, or other polarizers capable of performing its function. The phase modulator of this invention can be an electro-optic modulator, such as a lithium niobate electro-optic crystal modulator, a liquid crystal modulator, a piezoelectric-driven fiber stretch modulator, or other electrically controlled phase modulators. The photodetector of this invention can be an avalanche photodiode (APD), a photodiode (PD), a single-photon avalanche diode (SPAD), a photomultiplier tube (PMT), or a single-photon counter, etc.

[0088] Compared to existing weak measurement systems that do not include phase modulation and demodulation, this invention can better suppress low-frequency phase noise caused by system light sources, detectors and other components, further reduce low-frequency noise in current weak measurement systems during phase measurement, and more effectively improve the signal-to-noise ratio of weak measurement systems.

[0089] This invention proposes a weak measurement system with phase carrier modulation and demodulation, achieving high-precision optical phase measurement. Based on the weak value amplification effect, the weak measurement system can measure extremely small optical phase signals with high sensitivity. However, existing weak measurement methods that directly measure phase, such as those using active devices like light sources and detectors, struggle to effectively distinguish low-frequency phase noise from the measured phase. Introducing phase carrier modulation effectively solves this problem. Addressing the inherent characteristics of weak measurement systems, this invention proposes a dual-channel differential cross-multiplication demodulation method. By setting two weak measurement post-selection state measurement channels with different post-selection angles, high-precision demodulated signal recovery of the measured phase is achieved. Furthermore, this demodulation method is unaffected by parameter errors in actual weak measurement systems, such as phase modulation depth drift and carrier phase delay, effectively improving the detection signal-to-noise ratio of the weak measurement system, especially for low-frequency measured signals.

[0090] It should be noted that any reference numerals placed between parentheses in the claims should not be construed as limiting the claims. The word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several different components and by means of a suitably programmed computer. In claims that enumerate several means, several of these means may be embodied by the same hardware. The use of the terms first, second, third, etc., is merely for convenience of expression and does not indicate any order. These terms can be understood as part of the component names.

[0091] Furthermore, it should be noted that in the description of this specification, the terms "one embodiment," "some embodiments," "embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0092] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the claims should be interpreted to include both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0093] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

Claims

1. A weak measurement system comprising phase carrier modulation and demodulation, the weak measurement system comprising: The system comprises a pre-selection state preparation section, a beam splitting section, and a post-selection state setting section. Its characteristic feature is that the weak measurement system further includes a phase carrier modulation generation section and a phase demodulation algorithm implementation section. The pre-selection state preparation section includes a light source, a pre-selection polarizer, and a signal to be measured introduction section. Light emitted from the light source is polarized by the pre-selection polarizer and then introduced into the signal to be measured by the signal to be measured introduction section. The polarized light is modulated by the phase carrier modulation generation section and then enters the beam splitting section, splitting into a first beam and a second beam. The first beam and the second beam respectively enter the post-selection state setting section located in the first weak measurement channel and the post-selection state setting section located in the second weak measurement channel. Then, the first beam and the second beam... The beam enters the phase demodulation algorithm implementation section for demodulation to obtain the phase difference signal to be measured. The phase carrier modulation generation section includes a carrier modulation signal generator and a phase modulator. The carrier modulation signal generator applies a driving voltage to the phase modulator, generating a phase modulation change function between two orthogonal polarization directions. The carrier modulation frequency of this function is controlled by the carrier modulation signal generator, and this carrier modulation frequency is higher than the highest frequency of the operating frequency band of the phase to be measured. The first and second weak measurement channels each include: a phase compensator, a post-selection linear polarizer, a photodetector, and a detection and acquisition module. The post-selection parameters of the first and second weak measurement channels are respectively... and ,and Furthermore, the phase demodulation algorithm implementation part adopts a dual-channel differential cross arcsine demodulation method to demodulate, thereby obtaining the phase difference signal to be measured.

2. The weak measurement system according to claim 1, characterized in that, Phase modulators are electro-optic modulators, such as lithium niobate electro-optic crystal modulators; liquid crystal optical modulators; piezoelectrically driven fiber stretching modulators; or electrically controlled phase modulators.

3. The weak measurement system according to claim 1, characterized in that, The part for introducing the signal to be measured includes: an optical fiber, an optical fiber coupler, and an optical fiber collimator. The optical fiber is affected by changes in external physical quantities, which will cause the phase difference signal to be measured to have two orthogonal polarization directions. The light emitted by the light source is polarized by a pre-selective linear polarizer. The optical fiber coupler and the optical fiber collimator connect the optical fiber to the weak measurement system, thereby introducing the phase difference signal to be measured.

4. The weak measurement system according to claim 1, characterized in that, The beam splitting section includes a beam splitter; or, the beam splitting section includes an optical fiber beam splitter and an optical fiber beam combiner.

5. The weak measurement system according to claim 4, characterized in that, The phase compensator is composed of a half-wave plate and a quarter-wave plate, which are adjusted by relative rotation; optionally, the phase compensator is an electro-optic crystal modulator; wherein, the post-selected linear polarizer is a Glan-Taylor prism polarizer or a metal wire grid polarizer; the photodetector is an avalanche photodiode, a photodiode, a single-photon avalanche diode, a photomultiplier tube, or a single-photon counter.

6. A method for phase carrier modulation and demodulation of a weak measurement system according to any one of claims 1-5, characterized in that, The method includes: Different post-selection parameters are set for the first weak measurement channel and the second weak measurement channel, respectively. The light intensity signals of the first and second weak measurement channels are mixed with the carrier modulation signal and then low-pass filtered. The two low-pass filtered signals are then subjected to differential cross-multiplication to obtain the third and fourth signals, respectively. The third and fourth signals are added and subtracted to obtain the fifth and sixth signals; and The fifth and sixth signals are divided and arcsined to obtain the phase difference signal to be measured.

7. A phase modulation and demodulation module for a weak measurement system according to any one of claims 1-5, characterized in that, The phase modulation and demodulation module includes the phase carrier modulation generation part and the phase demodulation algorithm implementation part.

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