Optical phase measurement method based on phase-sensitive non-Hermite four-wave mixing

Abstract

The invention provides an optical phase measurement method based on phase-sensitive non-Hermite four-wave mixing. The optical phase measurement method comprises the following steps: generating a phase-sensitive non-Hermite four-wave mixing process; signal light and idler frequency light emitted in the four-wave mixing process are detected, measurement results of a type 1 entanglement criterion and a type 2 entanglement criterion are obtained, and the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion are used for achieving measurement of the optical phase. According to the invention, a principle mechanism of a phase-sensitive non-Hermite four-wave mixing process is used, high-sensitivity optical phase measurement is realized by measuring a type 1 entanglement criterion through a non-Hermite characteristic and optical phase sensitivity shown by the phase-sensitive non-Hermite four-wave mixing process, and the phase-sensitive non-Hermite four-wave mixing process has the advantages of strong robustness and higher sensitivity; according to the optical phase measurement method based on the phase-sensitive non-Hermite four-wave mixing process, high-sensitivity optical phase measurement is achieved in combination with an existing homodyne detection technology, and the method has the advantage of being high in feasibility.

Description

Technical Field

[0001] The invention relates to the technical field of optical phase measurement, in particular to an optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing. Background Art

[0002] The most classic method to achieve optical phase measurement is to use the interference effect of light. The superposition state of two interfering light fields contains the optical path difference and phase difference information of the two light fields. Due to vacuum noise and photon fluctuations of the light field, the sensitivity of optical phase measurement cannot break through the shot noise limit. Studies have shown that it is impossible to eliminate this limitation by using classical optical methods, but quantum technology can break through this limitation.

[0003] There are basically two types of existing optical phase measurement methods using quantum technology. One is to enhance the sensitivity of optical phase measurement by coupling quantum state resources such as squeezed states and particle number states into classical interferometers such as Mach-Zehnder. The other is to enhance the sensitivity of optical phase measurement by amplifying the output signal of the interferometer using parametric amplification processes such as four-wave mixing. The above methods also have some defects. For example, the use of four-wave mixing to achieve parametric amplification requires perfect phase matching conditions to achieve optimal efficiency. In actual operation, phase mismatch caused by small disturbances will affect the final effect of phase measurement. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides an optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing. The present invention uses the four-wave mixing process, based on its non-Hermitian properties and phase-sensitive properties, to achieve high-sensitivity optical phase measurement by detecting type-1 entanglement criterion.

[0005] The technical solution of the present invention is: an optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing, comprising the following steps:

[0006] S1), generating a phase-sensitive non-Hermitian four-wave mixing process;

[0007] S2), the signal light and the idler light emitted in the four-wave mixing process are detected to obtain the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion, and the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion are used to realize the measurement of the optical phase.

[0008] Preferably, in step S1), the four-wave mixing process is produced by the interaction of signal light, idler light, pump light and nonlinear medium.

[0009] Preferably, in step S1), the pump light has a phase to be measured. It is incident into the nonlinear medium together with the signal light and the idler light, and four-wave mixing occurs. During the process, for every annihilation of two pump photons, one signal photon and one idler photon are generated at the same time.

[0010] Preferably, in step S1), the expression of the dynamic coupling equation of the four-wave mixing process is:

[0011]

[0012] In the formula, i represents the imaginary unit; Indicates the partial derivative of the evolution distance z; H represents the Hermitian conjugation symbol; APT represents the non-Hermitian Hamiltonian matrix; a s is the signal field operator, a i is the idle frequency field operator;

[0013] The non-Hermitian Hamiltonian matrix H corresponding to the dynamic coupling equation of the four-wave mixing process is APT Satisfying APT symmetry, H APT It has controllable non-Hermitian parameters.

[0014] Preferably, in step S1), the non-Hermitian Hamiltonian matrix H APT The expression is:

[0015]

[0016] Where, detuning Δ = -Δk / 2, κ represents the real nonlinear coupling coefficient; i represents the imaginary unit; φ is the phase; is the phase of the pump light to be measured; Δk represents the phase mismatch; Δk=2k p -(k s +k i )cosθ; k p , k s and k i are the wave numbers of pump light, signal light and idler light respectively, and θ is the angle between pump light and signal light.

[0017] Preferably, in step S1), the non-Hermitian Hamiltonian matrix H APT A pair of eigenvalues ​​λ ± for:

[0018]

[0019] Where λ represents H APT One of the eigenvalues ​​of ; k represents the real nonlinear coupling coefficient; i represents the imaginary unit; δ = |Δ / κ| represents the non-Hermitian characteristic quantity;

[0020] When δ<1, the eigenvalue is a pair of pure imaginary numbers that are complex conjugates to each other, and the process is in the APT symmetric state; when δ>1, the eigenvalue is a real number, and the process is in the APT broken state; when δ=1, the process is in the singular point state, and λ0=0 means H APT The eigenvalues ​​in this state show spontaneous symmetry breaking.

[0021] Preferably, in step S1), the signal light and the idler light are both in a coherent state.

[0022] Preferably, in step S2), the emitted signal light and idler light are detected using homodyne detection technology to obtain measurement results of type 1 entanglement criterion and type 2 entanglement criterion.

[0023] Preferably, in step S2), the expression of the type 1 entanglement criterion E1 is as follows:

[0024] E1=Var(q s -q i )+Var(p s +p i );

[0025] In the formula, Var represents the variance of the physical quantity in the brackets; q s represents the generalized position operator of the signal field; q i represents the generalized position operator of the idler field; p s represents the generalized momentum operator of the signal field; p i represents the idler field generalized momentum operator.

[0026] Preferably, in step S2), the expression of the type 2 entanglement criterion E2 is as follows:

[0027] E2=Var(q s +q i )+Var(p s -p i );

[0028] Where, Var represents variance processing; q s represents the generalized position operator of the signal field; q i represents the generalized position operator of the idler field; p s represents the generalized momentum operator of the signal field; p i represents the idler field generalized momentum operator.

[0029] Preferably, in step S2), when the type 1 entanglement criterion E1<1 or the type 2 entanglement criterion E2<1, it corresponds to a weak entanglement criterion; when the type 1 entanglement criterion E1<0.5 or the type 2 entanglement criterion E2<0.5, it corresponds to a strong entanglement criterion; the closer the values ​​of E1 and E2 are to 0, the higher the degree of entanglement.

[0030] Preferably, in step S2), the calculation expressions of the type 1 entanglement criterion E1 and the type 2 entanglement criterion E2 are:

[0031]

[0032] In the formula, Indicates H APT One of the eigenvalues ​​of , z represents the evolution distance, the detuning amount Δ=-Δk / 2, Δk represents the phase mismatch; κ represents the real nonlinear coupling coefficient; φ is the phase; is the phase of the pump light to be measured.

[0033] The beneficial effects of the present invention are:

[0034] 1. The present invention uses the principle mechanism of the phase-sensitive non-Hermitian four-wave mixing process, and through its non-Hermitian characteristics and optical phase sensitivity, measures the type 1 entanglement criterion to achieve high-sensitivity optical phase measurement, which has the advantages of strong robustness and higher sensitivity;

[0035] 2. The optical phase measurement method of the present invention is based on a phase-sensitive non-Hermitian four-wave mixing process and is combined with the existing homodyne detection technology to achieve high-sensitivity optical phase measurement, which has the advantage of high feasibility. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a flow chart of the method of the present invention;

[0037] Figure 2 Schematic diagram of the phase-sensitive non-Hermitian four-wave mixing process of the present invention; wherein (a) is a schematic diagram of the principle of the phase-sensitive non-Hermitian four-wave mixing process, and (b) is a schematic diagram of the source of phase mismatch in the four-wave mixing process;

[0038] Figure 3 The present invention shows the variation of type 1 entanglement criterion and type 2 entanglement criterion with the phase of pump light in various states; wherein, (a1) shows the variation of type 1 entanglement criterion with the phase of pump light in the APT symmetric state; (a2) shows the variation of type 2 entanglement criterion with the phase of pump light in the APT symmetric state; (b1) shows the variation of type 1 entanglement criterion with the phase of pump light in the singular point state; (b2) shows the variation of type 2 entanglement criterion with the phase of pump light in the singular point state; (c1) shows the variation of type 1 entanglement criterion with the phase of pump light in the APT breaking state; (c2) shows the variation of type 2 entanglement criterion with the phase of pump light in the APT breaking state. DETAILED DESCRIPTION

[0039] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings:

[0040] like Figure 1 As shown, this embodiment provides an optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing, comprising the following steps:

[0041] S1), generating a phase-sensitive non-Hermitian four-wave mixing process;

[0042] like Figure 2 As shown in (a) in FIG. 1 , this embodiment adopts a phase of The input pump light ω p With the coherent input signal light ω s 、Idle light i When incident into a nonlinear medium, for every annihilation of two pump photons, one signal photon and one idler photon are generated simultaneously.

[0043] In this embodiment, the signal field operator a s and the idler field operator a i The coupling equation between them is expressed as:

[0044]

[0045] In the formula, i represents the imaginary unit; Indicates the partial derivative of the evolution distance z; Represents the Hermitian conjugation symbol; H APT represents the non-Hermitian Hamiltonian matrix; a s is the signal field operator, a i is the idler field operator;

[0046] The non-Hermitian Hamiltonian matrix H corresponding to the dynamic coupling equation of the four-wave mixing process is APT Satisfying APT symmetry, H APT The non-Hermitian Hamiltonian matrix H APT The expression is:

[0047]

[0048] Where, detuning Δ = -Δk / 2, κ represents the real nonlinear coupling coefficient; i represents the imaginary unit; φ is the phase; is the phase of the pump light to be measured; Δk represents the phase mismatch; Figure 2 As shown in (b), Δk = 2k p -(k s +k i )cosθ; k p , k s and k iare the wave numbers of pump light, signal light and idler light respectively, and θ is the angle between pump light and signal light;

[0049] Among them, H APT The non-Hermitian parameters that can be controlled in are: Phase Real nonlinear coupling coefficient κ, detuning amount Δ = -Δk / 2.

[0050] H APT Satisfy {H APT ,PT}=0, where P is the parity operator and T is the time reversal operator. This shows that H APT Satisfies APT symmetry. Since H APT Without any gain or loss involved, there is no need to include Langevin noise terms in the coupling equations, so the commutation relationship is preserved.

[0051] The non-Hermitian Hamiltonian matrix H APT A pair of eigenvalues ​​λ ± for:

[0052]

[0053] Where λ represents H APT One of the eigenvalues ​​of ; k represents the real nonlinear coupling coefficient; i represents the imaginary unit; δ = |Δ / k| represents the non-Hermitian characteristic quantity;

[0054] When δ<1, the eigenvalue is a pair of pure imaginary numbers that are complex conjugates to each other, and the process is in the APT symmetric state; when δ>1, the eigenvalue is a real number, and the process is in the APT broken state; when δ=1, the process is in the singular point state, and λ0=0 means H APT The eigenvalues ​​in this state show spontaneous symmetry breaking.

[0055] S2), the signal light and the idler light emitted in the four-wave mixing process are detected to obtain the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion, and the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion are used to realize the measurement of the optical phase.

[0056] This embodiment uses homodyne detection technology to detect the signal light and idler light emitted during the four-wave mixing process, obtains the measurement results of type 1 entanglement criterion and type 2 entanglement criterion, and uses the measurement results of the entanglement criterion to achieve high-precision measurement of the optical phase.

[0057] Furthermore, in this embodiment, the expression of the type 1 entanglement criterion E1 is as follows:

[0058] E1=Var(q s -q i )+Var(p s +p i );

[0059] Where, Var represents variance processing; q s represents the generalized position operator of the signal field; q i represents the generalized position operator of the idler field; p s represents the generalized momentum operator of the signal field; p i represents the idler field generalized momentum operator.

[0060] The expression of the type 2 entanglement criterion E2 is as follows:

[0061] E2=Var(q s +q i )+Var(p s -p i );

[0062] Where, Var represents variance processing; q s represents the generalized position operator of the signal field; q i represents the generalized position operator of the idler field; p s represents the generalized momentum operator of the signal field; p i represents the idler field generalized momentum operator.

[0063] In this embodiment, the type 1 entanglement criterion E1 and the type 2 entanglement criterion E2 also represent the dual-mode compression characteristics of the process; when the type 1 entanglement criterion E1<1 or the type 2 entanglement criterion E2<1, it corresponds to the weak entanglement criterion; when the type 1 entanglement criterion E1<0.5 or the type 2 entanglement criterion E2<0.5, it corresponds to the strong entanglement criterion; the closer the values ​​of E1 and E2 are to 0, the higher the degree of entanglement.

[0064] The calculation expressions of the type 1 entanglement criterion E1 and the type 2 entanglement criterion E2 are:

[0065]

[0066] In the formula, Indicates H APT One of the eigenvalues ​​of , z represents the evolution distance, the detuning amount Δ=-Δk / 2, Δk represents the phase mismatch; κ represents the real nonlinear coupling coefficient; φ is the phase; is the phase of the pump light to be measured.

[0067] Considering that the input light field is in a coherent state, the entanglement criterion is independent of the intensity of the input light field, but is related to the non-Hermitian parameters κ and Δ and the evolution distance κz, and also contains information about the phase φ.

[0068] Figure 3 The figure shows the change of type 1 / type 2 entanglement criterion with the phase of pump light under different states. Figure 3(a1)(b1)(c1) and Figure 3 It can be seen from (a2)(b2)(c2) that the type 1 entanglement criterion E1 and the type 2 entanglement criterion E2 only differ by a pump light phase π, so the type 1 entanglement criterion E1 is selected for key analysis. Figure 3 (a1) in the figure shows that when the system is in the APT symmetric state (δ = 0.8), the evolution distance of the fixed system, the type 1 entanglement criterion E1 will only have a large value in a very narrow phase range, so the measurement result of E1 can be used to achieve high-precision measurement of the optical phase. Figure 3 As shown in (b1) in , when the system is in a singular point state (δ = 1), compared with the APT symmetric state, the type 1 entanglement criterion E1 has a larger value in a wider phase range, and the sensitivity of phase measurement is slightly lower. Figure 3 (c1) in the figure shows that in the APT-breaking state (δ=1.2), the evolution of the system entanglement criterion presents an oscillation mode with a period of T=κπ / λ, so this state is not suitable for phase measurement.

[0069] Based on the results of the above type 1 / type 2 entanglement criterion, when the non-Hermitian parameters κ and Δ and the evolution distance κz are fixed, the type 1 entanglement criterion E1 and the type 2 entanglement criterion E2 are measured by using the homodyne detection technology, and the phase φ can be determined from the measurement results, thereby obtaining the optical phase to be measured.

[0070] The above embodiments and descriptions are only for illustrating the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected.

Claims

1. An optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing, characterized in that: The following steps are involved: S1), generating a phase-sensitive non-Hermitian four-wave mixing process; S2), the signal light and the idler light emitted in the four-wave mixing process are detected to obtain the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion, and the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion are used to realize the measurement of the optical phase.

2. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 1, characterized in that: In step S1), the four-wave mixing process is generated by the interaction of signal light, idler light, pump light and nonlinear medium.

3. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 2, characterized in that: In step S1), the pump light has a phase to be measured It is incident into the nonlinear medium together with the signal light and the idler light to cause four-wave mixing process. During the four-wave mixing process, for every annihilation of two pump photons, one signal photon and one idler photon are generated at the same time.

4. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 3, characterized in that: In step S1), the expression of the dynamic coupling equation of the four-wave mixing process is: In the formula, i represents the imaginary unit; Indicates the partial derivative of the evolution distance z; H represents the Hermitian conjugation symbol; APT represents the non-Hermitian Hamiltonian matrix; a s is the signal field operator, a i is the idler field operator.

5. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 4, characterized in that: In step S1), the non-Hermitian Hamiltonian matrix H corresponding to the dynamic coupling equation of the four-wave mixing process is APT Satisfying APT symmetry, H APT has adjustable non-Hermitian parameters; the non-Hermitian Hamiltonian matrix H APT The expression is: Where, detuning Δ = -Δk / 2, κ represents the real nonlinear coupling coefficient; i represents the imaginary unit; φ is the phase; is the phase of the pump light to be measured; Δk represents the phase mismatch; Δk=2k p -(k s +k i )cosθ; k p , k s and k i are the wave numbers of pump light, signal light and idler light respectively, and θ is the angle between pump light and signal light; H APT The controllable non-Hermitian parameters in are: Phase Real nonlinear coupling coefficient κ, detuning amount Δ = -Δk / 2.

6. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 5, characterized in that: In step S1), the non-Hermitian Hamiltonian matrix H APT A pair of eigenvalues ​​λ ± for: Among them, κ represents the real nonlinear coupling coefficient; λ represents H APT One of the eigenvalues ​​of ; i represents the imaginary unit; δ = |Δ / κ| represents the non-Hermitian characteristic quantity; When δ<1, the eigenvalue is a pair of pure imaginary numbers that are complex conjugates to each other, and the process is in the APT symmetric state; when δ>1, the eigenvalue is a real number, and the process is in the APT broken state; when δ=1, the process is in the singular point state, and λ0=0 means H APT The eigenvalues ​​in this state show spontaneous symmetry breaking.

7. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 1, characterized in that: In step S2), the emitted signal light and idler light are detected using homodyne detection technology to obtain measurement results of type 1 entanglement criterion and type 2 entanglement criterion.

8. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 7, characterized in that: In step S2), the expression of the type 1 entanglement criterion E1 is as follows: E1=Var(q s -q i )+Var(p s +p i ); Where Var represents variance processing; q s represents the generalized position operator of the signal field; q i represents the generalized position operator of the idler field; p s represents the generalized momentum operator of the signal field; p i represents the idle field generalized momentum operator; The expression of the type 2 entanglement criterion E2 is as follows: E2=Var(q s +q i )+Var(p s -p i ); Where Var represents variance processing; q s represents the generalized position operator of the signal field; q i represents the generalized position operator of the idler field; p s represents the generalized momentum operator of the signal field; p i represents the idler field generalized momentum operator.

9. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 8, characterized in that: In step S2), when the type 1 entanglement criterion E1<1 or the type 2 entanglement criterion E2<1, it corresponds to a weak entanglement criterion; when the type 1 entanglement criterion E1<0.5 or the type 2 entanglement criterion E2<0.5, it corresponds to a strong entanglement criterion; the closer the values ​​of E1 and E2 are to 0, the higher the degree of entanglement.

10. The optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing according to claim 9, characterized in that: In step S2), the calculation expressions of the type 1 entanglement criterion E1 and the type 2 entanglement criterion E2 are: In the formula, Indicates H APT One of the eigenvalues ​​of , z represents the evolution distance, the detuning amount Δ=-Δk / 2, Δk represents the phase mismatch; k represents the real nonlinear coupling coefficient; φ is the phase; is the phase of the pump light to be measured.

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