High-precision phase measurement method based on induced coherence of passing through ultra-stable interferometer for multiple times

Abstract

The invention relates to the technical field of optical phase measurement, in particular to a high-precision phase measurement method based on induced coherence through an ultra-stable interferometer for multiple times. Measuring light is selected to be input into an input mode a and an input mode b of the ultra-stable interferometer respectively, and signal light corresponding to the input mode a and first idler frequency light corresponding to the input mode b are obtained; the first idler frequency light passes through the first nonlinear beam splitter, passes through the phase shifter for q times, then passes through the second nonlinear beam splitter and reaches the beam splitter; inputting the measuring light into an input mode c of the ultra-stable interferometer to obtain second idler frequency light corresponding to the input mode c; the second idler frequency light sequentially passes through the first nonlinear beam splitter and the second nonlinear beam splitter and then reaches the beam splitter; the first idler frequency light and the second idler frequency light are mixed in the beam splitter to output a mode Db and a mode Dc, and a phase measurement error is determined by adopting an intensity difference method. According to the invention, the influence of noise is suppressed through a measurement method of intensity subtraction, so that the measurement precision is greatly improved.

Description

Technical Field

[0001] The invention relates to the technical field of optical phase measurement, and in particular to a high-precision phase measurement method based on multiple passes through an ultra-stable interferometer to induce coherence. Background Art

[0002] Precise measurement is crucial to the entire scientific field. It is the basis of all quantitative sciences. In particular, optical phase measurement is used to accurately measure length, displacement, velocity, optical properties, etc. Accurate phase measurement is of particular importance for various applications such as imaging, sensing, and information processing. It is widely used in optical imaging, fiber-optic communications, and other fields. With the continuous advancement of technology, phase measurement has developed into a high-precision, high-resolution measurement technology, and its application range covers mechanics, electronics, optics, materials, biology, and other fields.

[0003] The basic principle of optical interferometry phase measurement is to use the interference phenomenon to measure the phase difference of light. Classical interferometry, typified by the Mach-Zehnder interferometer, splits light into two modes before recombining them. One mode interacts with the object being measured (i.e., the sample), so that the interference pattern generated can provide phase information about the sample. This interferometer and its improved versions usually rely on classical light for measurement, which makes the minimum measurable phase shift no less than is called the shot noise limit or standard quantum limit (SNL); where is the smallest measurable phase shift (or accuracy, error), <N coh > is the average number of photons of classical or coherent light. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a high-precision phase measurement method based on multiple passes through an ultra-stable interferometer to induce coherence. The scheme includes: selecting the measurement light to be input into the input mode a and the input mode b of the ultra-stable interferometer respectively, obtaining the signal light corresponding to the input mode a and the first idler light corresponding to the input mode b; the first idler light passes through the first nonlinear beam splitter, passes through the second nonlinear beam splitter after passing through the phase shifter q times, and reaches the beam splitter; the measurement light is input into the input mode c of the ultra-stable interferometer, and the second idler light corresponding to the input mode c is obtained; the second idler light passes through the first nonlinear beam splitter and the second nonlinear beam splitter in sequence, and reaches the beam splitter; the first idler light and the second idler light are mixed in the beam splitter to output the mode D b and module D c , the phase measurement error is determined by using the intensity difference method. The present invention suppresses the influence of noise by using the intensity subtraction measurement method, thereby greatly improving the measurement accuracy.

[0005] The present invention adopts the following technical solution, which is a high-precision phase measurement method based on multiple passes through an ultra-stable interferometer to induce coherence, including:

[0006] Selecting measurement light to be input into input mode a and input mode b of the ultra-stable interferometer respectively, to obtain signal light corresponding to input mode a and first idler light corresponding to input mode b;

[0007] The first idler light first passes through the first nonlinear beam splitter, passes through the phase shifter q times, and then passes through the second nonlinear beam splitter to reach the 50:50 beam splitter; wherein q=2 n , n is a positive integer;

[0008] Inputting the measurement light into the input mode c of the ultra-stable interferometer to obtain the second idler light corresponding to the input mode c;

[0009] The second idler light passes through the first nonlinear beam splitter and the second nonlinear beam splitter in sequence and then reaches the 50:50 beam splitter;

[0010] The first idler light and the second idler light are mixed in the 50:50 beam splitter to output mode D b and module D c , the phase measurement error is determined using the intensity difference method.

[0011] Furthermore, the measurement light input into the input mode b is coherent light.

[0012] Furthermore, the intensity difference method is used to perform phase measurement, including:

[0013] The output operator is expressed by the input operator, and the measurement operation of the output module is expressed as the form of the operator acting on the initial state;

[0014] Measuring the intensity of each output mode and obtaining an intensity operator based on the intensity difference;

[0015] The modulus D is obtained according to the intensity operator, the first compression factor of the first nonlinear beam splitter, and the second compression factor of the second nonlinear beam splitter. b and module D c The minimum phase measurement error between

[0016] Furthermore, the output operator is expressed by the input operator, and the measurement operation of the output module is expressed as the form of the operator acting on the initial state, specifically:

[0017]

[0018]

[0019] in, I nThe subscript n indicates the order of the identity matrix, μ i =coshγ i , represents the compression factor of the i-th nonlinearity, is the phase shift, BS represents the beam splitter, S1 represents the first compression, S2 represents the second compression, Indicates the phase to be measured, A in is the input operator consisting of all operators;

[0020] The operator that obtains the output modulus by applying the transformation is: out =BS·S2·Φ1·S1·A in .

[0021] Furthermore, the intensity of each output mode is measured, and the intensity operator is obtained according to the intensity difference, specifically:

[0022] The intensity of each output mode is measured as:

[0023] The intensity operator is obtained by using the intensity difference method according to the intensity of each output mode. The expression is: Among them, the subscripts i and j are any two modules among A, B, and C.

[0024] Further, obtain the module D b and module D c The minimum phase measurement error between

[0025]

[0026] in, Indicates the measurement phase The minimum value of the mean square error, q represents the measured phase times, β represents the amplitude of the coherent state, γ1 represents the first nonlinear compression factor, and γ2 represents the second nonlinear compression factor.

[0027] The beneficial effects of the present invention are as follows: the present invention utilizes the light compression state to enable the phase measurement accuracy to break the standard quantum limit and even approach the Heisenberg limit. At the same time, the present invention is based on an ultra-stable interferometer that passes through multiple times (set as q times), and a simple measurement structure can be used to further improve the phase measurement accuracy, and its accuracy can be increased by q times compared to a single pass. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0029] Figure 1 It is a flow chart of a high-precision phase measurement method based on multiple passes through an ultra-stable interferometer to induce coherence according to an embodiment of the present invention;

[0030] Figure 2 A schematic diagram of the principle of achieving q-times phase shift by q-times passing according to an embodiment of the present invention;

[0031] Figure 3 Schematic diagram of minimum measurable error varying with compression factor according to an embodiment of the present invention. DETAILED DESCRIPTION

[0032] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0033] The high-precision phase measurement method based on multiple passes through an ultra-stable interferometer to induce coherence in an embodiment of the present invention includes:

[0034] Selecting measurement light to be input into input mode a and input mode b of the ultra-stable interferometer respectively, to obtain signal light corresponding to input mode a and first idler light corresponding to input mode b;

[0035] The first idler light first passes through the first nonlinear beam splitter, passes through the phase shifter q times, and then passes through the second nonlinear beam splitter to reach the 50:50 beam splitter; wherein q=2 n , n is a positive integer;

[0036] Inputting the measurement light into the input mode c of the ultra-stable interferometer to obtain the second idler light corresponding to the input mode c;

[0037] The second idler light passes through the first nonlinear beam splitter and the second nonlinear beam splitter in sequence and then reaches the 50:50 beam splitter;

[0038] The first idler light and the second idler light are mixed in the 50:50 beam splitter to output mode D b and module D c , the phase measurement error is determined using the intensity difference method.

[0039] Specifically, Figure 1 As shown, the embodiment of the present invention performs phase measurement based on an improved ultra-stable interferometer, and the two input modes are and It is composed of, which respectively represent the signal and the first idler, and then is input to the first nonlinear beam splitter NL1, the compression factor of the first nonlinear beam splitter is γ1; then to the second nonlinear beam splitter NL2, and the compression factor of the second nonlinear beam splitter is γ2, the second nonlinear input is the shared signal and the second idler, which is composed of Indicates that between NL1 and NL2, the signal interacts with the phase shifter (i.e., the sample). Since it passes through q times, the phase shift is After NL2, the A mode light is discarded, and then the idler B and C are mixed on a 50:50 beam splitter and then on D b and D c From the above measurement, we know that any of the three input lights can be coherent light, but only when the coherent light is incident on the first idler can the measurement accuracy be significantly improved. Figure 2 It can be seen that the phase shift produced by the light mode interacting with the sample is It does not need to be at the same frequency as the measurement optical mode, and can use a certain frequency to obtain the sample phase shift, and use two idle frequencies of another frequency for phase measurement.

[0040] It should be noted that the embodiment of the present invention uses coherent light to be incident on the idle frequency B. This light will not interact with the phase recording sample and can significantly improve the sensitivity.

[0041] The embodiment of the present invention further represents the output operator by the input operator, as follows:

[0042]

[0043]

[0044] in, I n The subscript n indicates the order of the identity matrix, μ i =coshγ i , represents the compression factor of the i-th nonlinearity, is the phase shift, BS represents the beam splitter, S1 represents the first compression, S2 represents the second compression, Indicates the phase to be measured, A in is the input operator consisting of all operators;

[0045] The operator that obtains the output modulus by applying the transformation is: out=BS·S2·Φ1·S1·A in

[0046] Then, any detection operation at the output can be written as the input operation operator acting on the initial state. In the embodiment of the present invention, the initial state is considered to be a coherent state, that is, the eigenstate of the annihilation operator. Then, in the phase measurement, the minimum error of the phase shift is usually:

[0047]

[0048] in, is a general measurement operator whose squared variance is:

[0049]

[0050] Consider further that the intensity measure for each output mode is:

[0051] The embodiment of the present invention adopts a strength difference measurement method to obtain the strength operator between any two output modes:

[0052]

[0053] Among them, the subscript gives the corresponding module, i, j are any two non-repeating output modules in A, B, C.

[0054] It should be noted that in the embodiment of the present invention, the output detection is set to be module D b In order to achieve the greatest measurement accuracy, each mode should be measured as much as possible. In order to consider "low cost", it is best to use coherent light as the incident mode to mode B, because it does not pass through the sample and has the same impact on the measurement accuracy as mode C; and for the measurement of mode A, because it must pass through the sample, its intensity will become lower as a result; it is worth noting that, firstly, compared with the compression in the second crystal, the compression in the first crystal has a great influence on the minimum measurable phase; secondly, the second nonlinearity only needs to cause consistency between the optical modes, and further compressing the vacuum cannot improve the measurement accuracy because the mode will no longer interact with the measurement mode.

[0055] In the embodiment of the present invention, the intensity difference measurement method is adopted to eliminate the common intensity noise of the two light beams and obtain better fringe visibility. Therefore, the coherent light is input into mode B, and the minimum measurement error of the intensity difference between modes B and C can be calculated as:

[0056]

[0057] in, Indicates the measurement phase The minimum value of the mean square error, q represents the measured phase times, β represents the amplitude of the coherent state, γ1 represents the first nonlinear compression factor, and γ2 represents the second nonlinear compression factor.

[0058] The measurement method proposed in the present invention can reduce the measurement error by q compared with a single pass. 2 times.

[0059] Furthermore, in another specific embodiment of the present invention, only the mode B is input with relatively strong coherent light, and its phase is set to zero as a reference, such as Figure 3 The figure shows the minimum measurable error diagram with two compression factors, where q = 4. Figure 3 In (a), the top 1 is β1=1000, the 2nd is β2=1008, the 3rd is β3=1016 and the bottom 4 is β4=1024. Figure 3 In (b), the first item at the top is β1=1000, the second item is β2=1400, the third item is β3=1800 and the fourth item at the bottom is β4=2200; for simplicity, all other parameters are set to zero in the embodiment of the present invention; Figure 3 From the curve in (a), we can see that as γ1 increases, the mean square error of phase measurement decreases and the measurement accuracy increases. Figure 3 In (b), as γ2 increases, the mean square error shows a U-shaped valley change, with a certain optimal compression value, the mean square error has a minimum value, and the measurement accuracy can reach the highest.

[0060] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A high-precision phase measurement method based on multiple passes through an ultrastable interferometer to induce coherence, characterized in that: include: Selecting measurement light to be input into input mode a and input mode b of the ultra-stable interferometer respectively, to obtain signal light corresponding to input mode a and first idler light corresponding to input mode b; The first idler light first passes through the first nonlinear beam splitter, passes through the phase shifter q times, and then passes through the second nonlinear beam splitter to reach the 50:50 beam splitter; wherein q=2 n , n is a positive integer; Inputting the measurement light into the input mode c of the ultra-stable interferometer to obtain the second idler light corresponding to the input mode c; The second idler light passes through the first nonlinear beam splitter and the second nonlinear beam splitter in sequence and then reaches the 50:50 beam splitter; The first idler light and the second idler light are mixed in the 50:50 beam splitter to output mode D b and module D c , the intensity difference method is used to determine the phase measurement error.

2. The high-precision phase measurement method based on multiple passes through an ultra-stable interferometer to induce coherence according to claim 1, characterized in that: The measurement light input into the input mode b is coherent light.

3. The high-precision phase measurement method based on multiple passes through an ultrastable interferometer to induce coherence according to claim 1, characterized in that: Phase measurement using the intensity difference method, including: The output operator is expressed by the input operator, and the measurement operation of the output module is expressed as the form of the operator acting on the initial state; Measuring the intensity of each output mode and obtaining an intensity operator based on the intensity difference; The modulus D is obtained according to the intensity operator, the first compression factor of the first nonlinear beam splitter, and the second compression factor of the second nonlinear beam splitter. b and module D c The minimum phase measurement error between 4. The high-precision phase measurement method based on multiple passes through an ultrastable interferometer to induce coherence according to claim 3, characterized in that: The output operator is expressed by the input operator, and the measurement operation of the output module is expressed as the form of the operator acting on the initial state, specifically: in, I n represents the n-order identity matrix, μ i =coshγ i , γ i represents the compression factor of the i-th nonlinearity, is the phase shift, BS represents the beam splitter, S1 represents the first compression, S2 represents the second compression, Indicates the phase to be measured, A in is the input operator consisting of all operators; The operator that obtains the output modulus by applying the transformation is: out =BS·S2·Φ1·S1·A in .

5. The high-precision phase measurement method based on multiple passes through an ultra-stable interferometer to induce coherence according to claim 3, characterized in that: Measure the intensity of each output mode and obtain the intensity operator based on the intensity difference, specifically: The intensity of each output mode is measured as: The intensity operator is obtained by using the intensity difference method according to the intensity of each output mode. The expression is: Among them, the subscripts i and j are any two modules among A, B, and C.

6. The high-precision phase measurement method based on multiple passes through an ultra-stable interferometer to induce coherence according to claim 3, characterized in that: Get module D b and module D c The minimum phase measurement error between in, Indicates the measurement phase The minimum value of the mean square error, q represents the measured phase times, β represents the amplitude of the coherent state, γ1 represents the first nonlinear compression factor, and γ2 represents the second nonlinear compression factor.

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