Phase measurement system and method for achieving heisenberg limit precision using classical light

Abstract

The application discloses a phase measurement system and method for realizing Heisenberg limit precision by using classical light, and relates to the technical field of precision measurement. The phase measurement system comprises N sets of single-beam light phase measurement devices; wherein the single-beam light phase measurement device comprises a laser, a light beam displacer, a light blocking plate, a half-wave plate, a polarization beam splitter, a sample, a plane mirror, a depolarization beam splitter and a light detector. The phase measurement system and method for realizing Heisenberg limit precision by using classical light provided by the application utilize the correlation of classical statistical light fields, break through the classical measurement limit to the Heisenberg limit in phase measurement precision, improve the sampling efficiency and the anti-interference ability to environmental noise, and reduce the device cost. Compared with the quantum precision measurement scheme, the phase measurement system and method of the application is easy to expand, has good stability, and has a wider application prospect.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and in particular to a phase measurement system and method that utilizes classical light to achieve Heisenberg-limit precision. Background Technology

[0002] Precision measurement has always been a key research area in natural sciences. Whether for discovering new laws of nature or for meeting the demand for higher precision in production and daily life, more precise measurement methods have always been among the most reliable and effective tools. Since many actual physical signals to be measured can be converted into phase information of light or electric fields using certain methods, phase estimation is a crucial problem in precision measurement. For example, high-precision phase estimation plays a key role in many fields such as biomedical imaging, satellite sensing, and gravitational wave detection.

[0003] Factors affecting measurement accuracy can be mainly divided into two categories: one is the random error caused by factors such as imperfect experimental equipment and environmental disturbances; the other is the inherent error constrained by mathematical statistical methods and the Heisenberg uncertainty principle. In classical measurement problems, constrained by the central limit theorem, the optimal measurement accuracy limit can only reach n. -1 / 2 The order of magnitude of the quantum number of samples is n. This classical measurement limit is often referred to as the Standard Quantum Limit (SQL). In recent years, much research in the field of quantum metrology has shown that by utilizing quantum entanglement or correlation as a resource, the measurement precision can be improved to n... -1 The magnitude of this phenomenon is known as the Heisenberg Limit (HL). However, the large-scale preparation of multi-particle entangled states presents significant challenges. Quantum entangled states are highly susceptible to decoherence due to environmental disturbances, and quantum experimental devices are expensive with relatively low sampling efficiency. These difficulties have prevented the widespread application of quantum precision measurement technology. Summary of the Invention

[0004] The purpose of this invention is to provide a phase measurement system and method that achieves Heisenberg-limit precision using classical light. This system can improve measurement accuracy to the Heisenberg limit in a classical light field, while also increasing sampling efficiency, improving resistance to environmental noise, and reducing device costs.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A phase measurement system achieving Heisenberg-limit precision using classical light includes N sets of single-beam phase measurement devices; N is an integer greater than 1; each single-beam phase measurement device includes: a laser, a beam shifter, a light-blocking plate, a half-wave plate, a polarizing beam splitter, a sample, a first plane mirror, a second plane mirror, a third plane mirror, a fourth plane mirror, a fifth plane mirror, a sixth plane mirror, a seventh plane mirror, a first depolarizing beam splitter, a second depolarizing beam splitter, a third depolarizing beam splitter, a fourth depolarizing beam splitter, a first photodetector, a second photodetector, a third photodetector, and a fourth photodetector;

[0007] In the single-beam phase measurement device, the beam shifter is located on the output optical path of the laser; the laser beam emitted from the laser is converted into two linearly polarized beams, one horizontally polarized and the other vertically polarized, by the beam shifter; the light-blocking plate is located on the output optical path of one of the linearly polarized beams; the half-wave plate is located on the output optical path of the other linearly polarized beam to change its polarization state, resulting in 45° linearly polarized light; the first plane mirror is located on the output optical path of the 45° linearly polarized light; and the polarization beam splitter is located on the reflection of the first plane mirror. The second plane mirror is located on the transmission path of the polarization beam splitter; the first depolarization beam splitter is located on the reflection path of the second plane mirror; the third plane mirror is located on the transmission path of the first depolarization beam splitter; the second depolarization beam splitter is located on the reflection path of the third plane mirror; the fourth plane mirror is located on the reflection path of the first depolarization beam splitter; the second depolarization beam splitter is located on the reflection path of the fourth plane mirror; the two mixed beams output by the second depolarization beam splitter are received by the first photodetector and the second photodetector, respectively.

[0008] The fifth plane mirror is located on the reflected light path of the polarization beam splitter; the third depolarization beam splitter is located on the reflected light path of the fifth plane mirror; the sample and the sixth plane mirror are sequentially located on the transmitted light path of the third depolarization beam splitter; the fourth depolarization beam splitter is located on the reflected light path of the sixth plane mirror; the seventh plane mirror is located on the reflected light path of the third depolarization beam splitter; the fourth depolarization beam splitter is located on the reflected light path of the seventh plane mirror; the two mixed beams output by the fourth depolarization beam splitter are received by the third photodetector and the fourth photodetector, respectively.

[0009] A phase measurement method achieving Heisenberg-limit precision using classical optics, the phase measurement method being based on the phase measurement system of claim 1; the phase measurement method comprising:

[0010] For the nth single-beam phase measurement device in N single-beam phase measurement devices, a polarization beam splitter is used to split the 45° linearly polarized light. The path corresponding to the horizontal polarization component after beam splitting is denoted as f. H The path corresponding to the vertical polarization component is denoted as f. V ;

[0011] Receive f using the first and second photodetectors H Two optical intensity signals output from the path and Receive f using the third and fourth photodetectors V Two optical intensity signals output from the path and

[0012] Based on light intensity signal and Calculate f H Path relative light intensity difference The value is equal to f H The real part of the autocorrelation function of the path electric field Based on light intensity signal and Calculate f V Path relative light intensity difference The value is equal to f V The real part of the autocorrelation function of the path electric field The superscript * indicates the complex conjugate operation; f represents the nth single-beam phase measurement device H Electric field strength before the path interacts with the sample; f represents the nth single-beam phase measurement device H The electric field strength after the path interacts with the sample; f represents the nth single-beam phase measurement device V Electric field strength before the path interacts with the sample; f represents the nth single-beam phase measurement device V The electric field strength after the path interacts with the sample;

[0013] Using the first depolarization beam splitter to target f H The path beam is split into multiple beams, and the resulting f-beams are split into multiple beams. H A first phase plate with a delay phase of π / 2 is inserted into the path reference optical path, and the first and second photodetectors are used to receive the value at this time f. H Two optical intensity signals output from the path and

[0014] Using the third depolarization beam splitter to target f V The path beam is split into multiple beams, and the resulting f-beams are split into multiple beams. V A second phase plate with a delay phase of π / 2 is inserted into the path reference optical path, and the third and fourth photodetectors are used to receive the value at this time f. V Two optical intensity signals output from the path and

[0015] Based on the light intensity signal when the first phase plate was inserted and Calculate f H Path relative light intensity difference The value is equal to f H Imaginary part of the autocorrelation function of the path electric field Based on the light intensity signal when the second phase plate is inserted and Calculate f V Path relative light intensity difference The value is equal to f V Imaginary part of the autocorrelation function of the path electric field

[0016] f H Path relative light intensity difference and Add them together and calculate f. H Complex values ​​of the autocorrelation function of the path electric field f V Path relative light intensity difference and Add them together and calculate f. V Complex values ​​of the autocorrelation function of the path electric field Where i represents the imaginary unit;

[0017] According to f H Complex values ​​of the autocorrelation function of the path electric field and f V Complex values ​​of the autocorrelation function of the path electric field Calculate the correlation function;

[0018] The phase value introduced by the sample is calculated based on the correlation function.

[0019] Optionally, the f H Path and the f V The path satisfies the relation ∫f H f V dr=0 and Where r represents spatial coordinates.

[0020] Optionally, the step of basing the light intensity signal and Calculate f H Path relative light intensity difference Specifically, it includes:

[0021] Using formula Calculate f H Path relative light intensity difference

[0022] Optionally, the step of basing the light intensity signal and Calculate f V Path relative light intensity difference Specifically, it includes:

[0023] Using formula Calculate f V Path relative light intensity difference

[0024] Optionally, the step of determining the light intensity signal based on the insertion of the first phase plate... and Calculate f H Path relative light intensity difference Specifically, it includes:

[0025] Using formula Calculate f H Path relative light intensity difference

[0026] Optionally, the step of adjusting the light intensity signal when inserting the second phase plate... and Calculate f V Path relative light intensity difference Specifically, it includes:

[0027] Using formula Calculate f V Path electric field relative light intensity difference

[0028] Optionally, the statement based on f H Complex values ​​of the autocorrelation function of the path electric field and f V Complex values ​​of the autocorrelation function of the path electric field Calculating the correlation function specifically includes:

[0029] Using formula Calculate the correlation function P ± .

[0030] Optionally, the step of calculating the phase value introduced by the sample based on the correlation function specifically includes:

[0031] According to the correlation function P ± Using formula The phase value θ introduced by the sample is calculated.

[0032] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0033] This invention provides a phase measurement system and method that achieves Heisenberg-limit precision using classical light. Inspired by quantum precision measurement schemes, it utilizes the correlation relationships of classical statistical optical fields to break through the classical measurement limit to the Heisenberg limit in phase measurement accuracy. It also effectively improves sampling efficiency and immunity to environmental noise, while reducing device costs. Compared to quantum precision measurement schemes, this invention's phase measurement system, achieving Heisenberg-limit precision using classical light, is easily scalable and highly stable, offering broader application prospects. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 A schematic diagram of the phase measurement system that utilizes classical light to achieve Heisenberg-limit precision, provided by the present invention;

[0036] Figure 2 This is an experimental data graph of the phase measurement method provided in an embodiment of the present invention; wherein... Figure 2 (b) is the correlation function P when N=2. ± Schematic diagram showing the results of the change in phase θ of the sample under test; Figure 2 (c) is the correlation function P when N=4 ± Schematic diagram showing the results of the change in phase θ of the sample under test; Figure 2 (d) is the correlation function P when N=6. ± Schematic diagram showing the results of the change in phase θ of the sample under test; Figure 2 (e) is a schematic diagram showing the change of the measurement standard error σ with the phase θ of the sample when N=2; Figure 2 (f) is a schematic diagram showing the change of the measurement standard error σ with the phase θ of the sample when N=4; Figure 2 (g) is a schematic diagram showing the change of the measurement standard error σ with the phase θ of the sample under test when N=6.

[0037] Symbol explanation:

[0038] Laser—1, Beam shifter—2, Light blocker—3, Half-wave plate—4, First plane mirror—5, Polarizing beam splitter—6, Second plane mirror—7, First depolarizing beam splitter—8, Fourth plane mirror—9, Third plane mirror—10, Second depolarizing beam splitter—11, First photodetector—12, Second photodetector—13, Fifth plane mirror—14, Third depolarizing beam splitter—15, Seventh plane mirror—16, Sample—17, Fourth depolarizing beam splitter—18, Sixth plane mirror—19, Third photodetector—20, Fourth photodetector—21. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] The purpose of this invention is to provide a phase measurement system and method that achieves Heisenberg-limit precision using classical light. This system can improve measurement accuracy to the Heisenberg limit in a classical light field, while also increasing sampling efficiency, improving resistance to environmental noise, and reducing device costs.

[0041] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] Figure 1 This is a schematic diagram of the phase measurement system that utilizes classical light to achieve Heisenberg-limit precision, as provided by the present invention. Figure 1 As shown, the present invention provides a phase measurement system that achieves Heisenberg-limit precision using classical light, comprising N sets of single-beam phase measurement devices, where N is an integer greater than 1. Specifically, the single-beam phase measurement device includes: a laser 1, a beam shifter 2, a light-blocking plate 3, a half-wave plate 4, a first plane mirror 5, a polarizing beam splitter 6, a second plane mirror 7, a first depolarizing beam splitter 8, a fourth plane mirror 9, a third plane mirror 10, a second depolarizing beam splitter 11, a first photodetector 12, a second photodetector 13, a fifth plane mirror 14, a third depolarizing beam splitter 15, a seventh plane mirror 16, a sample 17, a fourth depolarizing beam splitter 18, a sixth plane mirror 19, a third photodetector 20, and a fourth photodetector 21.

[0043] like Figure 1As shown, in each single-beam phase measurement device, a beam displacementr (BD) 2 is located in the output optical path of the laser 1; the laser beam emitted from the laser 1 is converted into two linearly polarized beams, one horizontally polarized and the other vertically polarized, by the beam displacementr 2. A light barrier 3 is located in the output optical path of one of the two linearly polarized beams; a half-wave length plate (HWP) 4 is located in the output optical path of the other linearly polarized beam, used to change the polarization state of the other linearly polarized beam to obtain 45° linearly polarized light.

[0044] The first plane mirror 5 is located on the output light path of the 45° linearly polarized light; the polarized beam splitter (PBS) 6 is located on the reflected light path of the first plane mirror 5; the second plane mirror 7 is located on the transmitted light path of the polarized beam splitter 6; the first non-polarized beam splitter (NPBS) 8 is located on the reflected light path of the second plane mirror 7; the third plane mirror 10 is located on the transmitted light path of the first non-polarized beam splitter 8; the second non-polarized beam splitter 11 is located on the reflected light path of the third plane mirror 10; the fourth plane mirror 9 is located on the reflected light path of the first non-polarized beam splitter 8; the second non-polarized beam splitter 11 is located on the reflected light path of the fourth plane mirror 9; the two mixed beams output by the second non-polarized beam splitter 11 are received by the first photodetector 12 and the second photodetector 13, respectively.

[0045] The fifth plane mirror 14 is located on the reflected light path of the polarization beam splitter 6; the third depolarization beam splitter 15 is located on the reflected light path of the fifth plane mirror 14; the sample 17 and the sixth plane mirror 19 are located sequentially on the transmitted light path of the third depolarization beam splitter 15; the fourth depolarization beam splitter 18 is located on the reflected light path of the sixth plane mirror 19; the seventh plane mirror 16 is located on the reflected light path of the third depolarization beam splitter 15; the fourth depolarization beam splitter 18 is located on the reflected light path of the seventh plane mirror 16; the two mixed beams output by the fourth depolarization beam splitter 18 are received by the third photodetector 20 and the fourth photodetector 21, respectively.

[0046] The single-beam phase measurement device described above is in an inactive state. When the single-beam phase measurement device starts working, the measurement process of the phase measurement system of the present invention mainly includes four steps: initial state preparation, phase encoding, measurement, and statistical estimation, which are described below.

[0047] In the initial state preparation stage, this invention prepares a multi-beam probe with classical correlation as the input light source for the phase measurement system. A laser with a center wavelength of 632.8 nm input from laser 1 is passed through a beam shifter 2 to generate two linearly polarized beams: one horizontally polarized (H) and the other vertically polarized (V). One beam is blocked by a light-blocking plate 3, and the other beam is passed through a half-wave plate 4 to change its polarization state, resulting in 45° linearly polarized light. Subsequently, a polarization beam splitter 6 is used to split the 45° linearly polarized light, with the horizontally polarized component passing directly through. The corresponding path is denoted as f. H (r), where r represents the spatial coordinates; the vertical polarization component is obtained after one reflection, and the corresponding path is denoted as f. V (r). And f H and f V Satisfying relation ∫f H f V dr=0, The above process completes the initial state preparation of a single beam of light. Repeating this process yields N probe beams required for phase measurement, whose optical field can be obtained using formula (1):

[0048] E n,ini (r)=f H (r)h+f V (r)v (1)

[0049] Where n = 1, 2, ..., N; E represents the electric field intensity of the probe beam; the subscript n indicates the nth probe beam; ini refers to the initial state; h and v refer to the horizontal (H) and vertical (V) components of the electric field, respectively. This state actually corresponds to the GHZ state commonly used in quantum entanglement enhancement measurements, which is why Heisenberg-limiting precision measurements can be achieved. Figure 1 The diagram only shows the case where N=2, but the phase measurement system provided by this invention not only includes the case where N=2, but also for a larger number of incident beams N (N>>1), the above-mentioned single-beam phase measurement device structure can be repeatedly constructed.

[0050] In the phase encoding stage, it is assumed that the sample to be tested 17 introduces only one phase difference e. iθ This does not change the polarization state, frequency, or intensity of the input light. The sample to be tested 17 is placed at ft of each beam of light. V Path. The evolved form of the light field can be written as formula (2):

[0051] E n,evo (r)=f H (r)h+e iθ f V (r)v (2)

[0052] Where n = 1, 2, ..., N; the subscript evo indicates the evolved state after interacting with sample 17, and θ is the phase to be measured.

[0053] In the measurement phase, to maximize the extraction of phase information from the phase measurement system, a higher-order correlation function for the measured optical field is selected. This correlation function can be written as:

[0054]

[0055] The measurement of this correlation function can be achieved as follows: Taking a single beam as an example, the two beams obtained after initial state preparation are passed through a polarization-depolarizing beam splitter (NPBS), resulting in two beams for each beam. One beam serves as the signal beam, participating in the phase encoding process; the other beam serves as the reference beam. These two beams are then mixed and output using another polarization-depolarizing beam splitter, and the intensity of each output beam is measured using a photodetector. The intensity of the nth detection beam E is then measured. n f H Taking the path as an example, the light intensities of the two output ports are denoted as follows: and For f H Path relative light intensity difference Here, Re[*] represents the real part operation, and Im[*] represents the imaginary part operation. For f V Path relative light intensity difference In general, the integral given above is a complex number, and its imaginary part needs to be measured. A phase plate with a delay phase of π / 2 (not shown in the figure) can be inserted into the reference optical path of the probe beam. The measurement result of the relative intensity difference then becomes... This allows for a complete measurement of the integral. Then, the relative intensity differences (real and imaginary parts) obtained from the single-beam probe are summed, and these sums are multiplied for each beam to obtain the correlation function (3) of the target, thus completing the measurement process. In fact, the choice of the correlation function form here also corresponds to the form of the measurement operator of the mechanical quantity to be measured in quantum entanglement-enhanced measurement.

[0056] Based on the aforementioned phase measurement system, this invention also provides a phase measurement method that achieves Heisenberg-limit precision using classical light, comprising:

[0057] S1: For the nth single-beam phase measurement device in N sets of single-beam phase measurement devices, the 45° linearly polarized light is split using polarization beam splitter 6. The path corresponding to the horizontal polarization component after splitting is denoted as f. H The path corresponding to the vertical polarization component is denoted as f. V .

[0058] Specifically, the f H Path and the f V The path satisfies the relation ∫f H f V dr=0 and Where r represents spatial coordinates.

[0059] S2: Receive f using the first photodetector 12 and the second photodetector 13 H Two optical intensity signals output from the path and Receive f using the third photodetector 20 and the fourth photodetector 21 V Two optical intensity signals output from the path and

[0060] S3: Based on the light intensity signal and Calculate f H Path relative light intensity difference The value is equal to f H The real part of the autocorrelation function of the path electric field Based on light intensity signal and Calculate f V Path relative light intensity difference The value is equal to f V The real part of the autocorrelation function of the path electric field The superscript * indicates the complex conjugate operation; f represents the nth single-beam phase measurement device H Electric field strength before the path interacts with the sample; f represents the nth single-beam phase measurement device H The electric field strength after the path interacts with the sample; f represents the nth single-beam phase measurement device V Electric field strength before the path interacts with the sample; f represents the nth single-beam phase measurement device V The electric field strength after the path interacts with the sample.

[0061] With the nth detection beam E n f HTaking the path as an example, the two light intensity signals received by the first photodetector 12 and the second photodetector 13 are respectively denoted as... and f H Path relative light intensity difference We can obtain the following using formula (4):

[0062]

[0063] For f V Path relative light intensity difference Its calculation formula (5) is similar to formula (4), as follows:

[0064]

[0065] In general, the autocorrelation function of the electric field in formula (4), i.e., the integral... Since it is a complex number, its imaginary part also needs to be measured. A phase plate with a delay of π / 2 can be inserted into the reference optical path of the probe beam. Figure 1 (Not shown in the text) to perform the measurement.

[0066] S4: Using the first depolarization beam splitter 8 pairs of f H The path beam is split into multiple beams, and the resulting f-beams are split into multiple beams. H A first phase plate with a delay phase of π / 2 is inserted into the path reference optical path, and the first photodetector 12 and the second photodetector 13 are used to receive the current f. H Two optical intensity signals output from the path and

[0067] S5: Using the third depolarization beam splitter 15 to pair f V The path beam is split into multiple beams, and the resulting f-beams are split into multiple beams. V A second phase plate with a delay phase of π / 2 is inserted into the path reference optical path, and the third photodetector 20 and the fourth photodetector 21 are used to receive the current f. V Two optical intensity signals output from the path and

[0068] S6: Based on the light intensity signal when the first phase plate is inserted. and Calculate f H Path relative light intensity difference The value is equal to f H Imaginary part of the autocorrelation function of the path electric field Based on the light intensity signal when the second phase plate is inserted and Calculate f V Path relative light intensity difference The value is equal to f V Imaginary part of the autocorrelation function of the path electric field

[0069] f H Taking the path as an example, based on the light intensity signal when the first phase plate is inserted... and Calculate f H Path relative light intensity difference The calculation formula is as follows:

[0070]

[0071] For f V Path relative light intensity difference Its calculation formula (7) is similar to formula (6), as follows:

[0072]

[0073] S7: f H Path relative light intensity difference and Add them together and calculate f. H Complex values ​​of the autocorrelation function of the path electric field Right now f V Path relative light intensity difference and Add them together and calculate f. V Complex values ​​of the autocorrelation function of the path electric field Right now Where i represents the imaginary unit.

[0074] S8: According to f H Complex values ​​of the autocorrelation function of the path electric field and f V Complex values ​​of the autocorrelation function of the path electric field Calculate the correlation function.

[0075] Specifically, using the formula Calculate the correlation function P ± .

[0076] By processing and calculating the parameter measurement results of each probe beam as described above, the correlation function P can be measured. ± The experimental measurements are then used to obtain the spatial distribution phase θ. In fact, the choice of the correlation function form here corresponds to the form of the measurement operator for the mechanical quantity being measured in quantum entanglement enhancement measurements.

[0077] S9: Calculate the phase value introduced by the sample based on the correlation function.

[0078] Since phase is not a directly observable physical quantity, this invention utilizes interferometry to obtain the correlation function P of the spatial light field. ± This allows for the indirect measurement of the spatially distributed phase θ.

[0079] Specifically, according to the correlation function P ± Using formula The phase value θ introduced by the sample is calculated.

[0080] Figure 2 The diagram shows experimental data of the phase measurement method provided in the embodiments of the present invention. Figure 2 (b) Figure 2 (c) and Figure 2 As shown in (d), the correlation function P is illustrated for N = 2, 4, and 6. ± The results show the changes in phase θ of the sample under test. The horizontal axis represents the phase value, and the vertical axis represents the correlation function value. The solid and dashed lines represent P, respectively. + and P - The theoretical value, the scatter points corresponding to the solid and dashed lines represent P respectively. + and P - The experimental measurements. For example... Figure 2 (e) Figure 2 (f) and Figure 2 As shown in (g), the measurement standard error σ varies with the phase θ of the sample under the corresponding conditions. The horizontal axis represents the phase value, and the vertical axis is the reciprocal of the square of the standard error, i.e., σ. -2 The solid line simulates the theoretical value of the standard error curve when the visibility of the interference fringes V = 0.9999, while the scatter points represent the experimental measurements. The dashed line and dotted line represent the theoretical values ​​characterized by the classical measurement limit SQL and the Heisenberg limit HL, respectively.

[0081] In the experiment, by adjusting the piezoelectric ceramic and the extended device, phase measurement was achieved for the phase θ∈[0,π] and the number of incident beams N=2,4,6. Correlation function P ± The direct measurement results are recorded in Figure 2 (b) Figure 2 (c) and Figure 2 (d) Furthermore, this invention utilizes concepts related to Fisher Information (FI) in classical statistics to approximately calculate the standard error limits for N = 2, 4, and 6:

[0082]

[0083] In formula (8), P ±The analytical form is obtained by fitting a function using experimental data. The parameterized form of the fitting function is P. ± = [1±Vcos(Nθ)] / 2. Where V∈(0,1) is the visibility of the interference fringes, describing the influence of environmental disturbances. When V approaches 1, it means the environmental disturbance is minimal, and the obtained standard error σ(θ) approaches 1 / N, which is close to the error accuracy described by the Heisenberg limit. The experimentally obtained standard error curve is shown below. Figure 2 (e) Figure 2 (f) and Figure 2 As shown in (g). Based on the experimental results, the visibility V of the interference fringes was obtained by fitting. N＝2 =0.9859, V N＝4 =0.9816, V N＝6 =0.9996, indicating that environmental noise has minimal impact on the experiments of this invention. The minimum standard error obtained in the three experimental cases are as follows: Compared with the classical measurement limit given Compared to the previous method, the measurement errors of this invention are reduced by 1.44 dB, 2.93 dB, and 3.89 dB, respectively, and are very close to the 1 / N relationship given by the Heisenberg limit. This shows that the classical optical measurement scheme presented in this invention can achieve phase measurement with Heisenberg limit accuracy.

[0084] Experimental results from the phase measurement system and method of this invention, which utilizes classical light to achieve Heisenberg-limit precision, demonstrate that the phase measurement system and method of this invention can improve measurement accuracy to the Heisenberg limit in classical light fields. It should be noted that although only experimental results for single phase parameter measurement are shown, the phase measurement system and method provided by this invention can be easily extended to achieve multi-parameter estimation or spatially distributed phase measurement. Furthermore, compared with quantum measurement schemes that also achieve Heisenberg-limit precision, the classical light scheme of this invention has stronger resistance to environmental noise, and its sampling efficiency and photon utilization are far superior. Based on existing industrial production technologies, classical optical system devices are relatively inexpensive and the technology is more mature; therefore, the phase measurement system and method provided by this invention are expected to be directly applied to existing measuring instruments, possessing significant practical value and promising prospects.

[0085] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0086] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A phase measurement system using classical light to achieve Heisenberg limit precision, characterized in that, It includes N sets of single-beam phase measurement devices; N is an integer greater than 1; the single-beam phase measurement device includes: a laser, a beam shifter, a light-blocking plate, a half-wave plate, a polarization beam splitter, a sample, a first plane mirror, a second plane mirror, a third plane mirror, a fourth plane mirror, a fifth plane mirror, a sixth plane mirror, a seventh plane mirror, a first depolarization beam splitter, a second depolarization beam splitter, a third depolarization beam splitter, a fourth depolarization beam splitter, a first photodetector, a second photodetector, a third photodetector, and a fourth photodetector; In the single-beam phase measurement device, the beam shifter is located on the output optical path of the laser; the laser beam emitted from the laser is converted into two linearly polarized beams, one horizontally polarized and the other vertically polarized, by the beam shifter; the light-blocking plate is located on the output optical path of one of the linearly polarized beams; the half-wave plate is located on the output optical path of the other linearly polarized beam to change its polarization state, resulting in 45° linearly polarized light; the first plane mirror is located on the output optical path of the 45° linearly polarized light; and the polarization beam splitter is located on the reflection of the first plane mirror. The second plane mirror is located on the transmission path of the polarization beam splitter; the first depolarization beam splitter is located on the reflection path of the second plane mirror; the third plane mirror is located on the transmission path of the first depolarization beam splitter; the second depolarization beam splitter is located on the reflection path of the third plane mirror; the fourth plane mirror is located on the reflection path of the first depolarization beam splitter; the second depolarization beam splitter is located on the reflection path of the fourth plane mirror; the two mixed beams output by the second depolarization beam splitter are received by the first photodetector and the second photodetector, respectively. The fifth plane mirror is located on the reflected light path of the polarization beam splitter; the third depolarization beam splitter is located on the reflected light path of the fifth plane mirror; the sample and the sixth plane mirror are sequentially located on the transmitted light path of the third depolarization beam splitter; the fourth depolarization beam splitter is located on the reflected light path of the sixth plane mirror; the seventh plane mirror is located on the reflected light path of the third depolarization beam splitter; the fourth depolarization beam splitter is located on the reflected light path of the seventh plane mirror; the two mixed beams output by the fourth depolarization beam splitter are received by the third photodetector and the fourth photodetector, respectively.

2. A method for phase measurement with precision of Heisenberg limit using classical light, characterized in that, The phase measurement method is based on the phase measurement system of claim 1; the phase measurement method includes: For the n th single-beam light phase measurement device of the N single-beam light phase measurement devices, a 45° linearly polarized light is split by a polarization beam splitter, and the horizontal polarization component after splitting is recorded as f H , and the vertical polarization component is recorded as f V ; receiving f H two light intensity signals output by the path and receiving f V two light intensity signals output by the path and Based on light intensity signal and Calculate f H Path relative light intensity difference The value is equal to f H The real part of the autocorrelation function of the path electric field Based on light intensity signal and Calculate f V Path relative light intensity difference The value is equal to f V The real part of the autocorrelation function of the path electric field The superscript * indicates the complex conjugate operation; f represents the nth single-beam phase measurement device H Electric field strength before the path interacts with the sample; f represents the nth single-beam phase measurement device H The electric field strength after the path interacts with the sample; f represents the nth single-beam phase measurement device V Electric field strength before the path interacts with the sample; f represents the nth single-beam phase measurement device V The electric field strength after the path interacts with the sample; The first polarization-eliminating beam splitter is used to split the f H path, and the f H path reference light path is inserted with a first phase plate with a delay phase of π / 2, and the first light detector and the second light detector are used to receive the two light intensity signals output by the f H path and The third polarization beam splitter is used to split the f V path light beams, and the f V path reference light path is inserted with a second phase plate with a delay phase of π / 2, and the third light detector and the fourth light detector are used to receive the two light intensity signals output by the f V path and Based on the light intensity signal when the first phase plate was inserted and Calculate f H Path relative light intensity difference The value is equal to f H Imaginary part of the autocorrelation function of the path electric field Based on the light intensity signal when the second phase plate is inserted and Calculate f V Path relative light intensity difference The value is equal to f V Imaginary part of the autocorrelation function of the path electric field f H Path relative light intensity difference and Add them together and calculate f. H Complex values ​​of the autocorrelation function of the path electric field f V Path relative light intensity difference and Add them together and calculate f. V Complex values ​​of the autocorrelation function of the path electric field Where i represents the imaginary unit; According to f H Complex values ​​of the autocorrelation function of the path electric field and f V Complex values ​​of the autocorrelation function of the path electric field Calculate the correlation function; The phase value introduced by the sample is calculated based on the correlation function.

3. The phase measurement method for achieving Heisenberg-limit precision using classical light according to claim 2, characterized in that, The f H Path and the f V The path satisfies the relation ∫f H f V dr=0 and Where r represents spatial coordinates.

4. The phase measurement method for achieving Heisenberg-limit precision using classical light according to claim 2, characterized in that, According to the light intensity signal and Calculate f H Path relative light intensity difference Specifically, it includes: Using formula Calculate f H Path relative light intensity difference 5. The phase measurement method for achieving Heisenberg-limit precision using classical light according to claim 2, characterized in that, According to the light intensity signal and Calculate f V Path relative light intensity difference Specifically, it includes: Using formula Calculate f V Path relative light intensity difference 6. The phase measurement method for achieving Heisenberg-limit precision using classical light according to claim 2, characterized in that, The light intensity signal when the first phase plate is inserted is used. and Calculate f H Path relative light intensity difference Specifically, it includes: Using formula Calculate f H Path relative light intensity difference 7. The phase measurement method for achieving Heisenberg-limit precision using classical light according to claim 2, characterized in that, The light intensity signal when the second phase plate is inserted is used. and Calculate f V Path relative light intensity difference Specifically, it includes: Using formula Calculate f V Path electric field relative light intensity difference 8. The phase measurement method for achieving Heisenberg-limit precision using classical light according to claim 2, characterized in that, According to f H Complex values ​​of the autocorrelation function of the path electric field and f V Complex values ​​of the autocorrelation function of the path electric field Calculating the correlation function specifically includes: Using formula Calculate the correlation function P ± .

9. The phase measurement method for achieving Heisenberg-limit precision using classical light according to claim 2, characterized in that, The calculation of the phase value introduced by the sample based on the correlation function specifically includes: According to the correlation function P ± Using formula The phase value θ introduced by the sample is calculated.

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