An optical phase measurement method based on phase-sensitive non-hermitian four-wave mixing

Abstract

The application provides an optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing, comprising generating a phase-sensitive non-Hermitian four-wave mixing process; detecting signal light and idler light emitted in the four-wave mixing process to obtain measurement results of a type-1 entanglement criterion and a type-2 entanglement criterion, and using the measurement results of the type-1 entanglement criterion and the type-2 entanglement criterion to realize measurement of an optical phase. The application uses a principle mechanism of the phase-sensitive non-Hermitian four-wave mixing process, and through non-Hermitian characteristics and optical phase sensitivity of the phase-sensitive non-Hermitian four-wave mixing process, measurement of a type-1 entanglement criterion is used to realize high-sensitivity optical phase measurement, and the application has the advantages of high robustness and higher sensitivity. The optical phase measurement method based on the phase-sensitive non-Hermitian four-wave mixing process has the advantage of high feasibility in realizing high-sensitivity optical phase measurement in combination with existing homodyne detection technology.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical phase measurement, and particularly to an optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing. BACKGROUND

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

[0003] Existing optical phase measurement methods using quantum technology are basically divided into two types. One is to couple quantum state resources such as squeezed states and particle number states into a Mach-Zehnder interferometer or the like to realize the enhancement of the sensitivity of optical phase measurement. The other is to use a four-wave mixing process to amplify the output signal of the interferometer to realize the enhancement of the sensitivity of optical phase measurement. The above methods also have some defects. For example, using four-wave mixing to realize parametric amplification requires perfect phase matching conditions to achieve the best efficiency. In actual operation, phase mismatch caused by small disturbances will affect the final effect of phase measurement. SUMMARY

[0004] In view of the deficiencies of the prior art, the present application provides an optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing. The present application uses a four-wave mixing process, based on its non-Hermitian property and phase-sensitive property, to realize high-sensitivity optical phase measurement through detection of a type-1 entanglement criterion.

[0005] The technical scheme of the present application is as follows: 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), detecting the signal light and idler light emitted in the four-wave mixing process to obtain measurement results of a type-1 entanglement criterion and a type-2 entanglement criterion, and using the measurement results of the type-1 entanglement criterion and the type-2 entanglement criterion to realize measurement of the optical phase.

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

[0009] Preferably, in step S1), the pump light has a to-be-measured phase And with signal light and idle frequency light together into the nonlinear medium, four-wave mixing occurs, in the process of each annihilation 2 pump photons, while generating 1 signal photon and 1 idle frequency photon.

[0010] As preferred, in step S1), the expression of the four-wave mixing process dynamics coupled equation is:

[0011]

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

[0013] The non-Hermite Hamiltonian matrix H corresponding to the four-wave mixing process dynamics coupled equation APT Satisfies the APT symmetry, H APT Has an adjustable non-Hermite parameter in the middle.

[0014] As preferred, in step S1), the expression of the non-Hermite Hamiltonian matrix H APT Is:

[0015]

[0016] In the formula, the detuning amount Δ = -Δk / 2, κ represents the real number nonlinear coupling coefficient; i represents the imaginary unit; φ is the phase; The measured phase of the pump light is represented; 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 the pump light, signal light and idle frequency light respectively, and θ is the included angle of the pump light and signal light.

[0017] As preferred, in step S1), the pair of eigenvalues λ ± of the non-Hermite Hamiltonian matrix H APT Is:

[0018]

[0019] Wherein, λ represents one of the eigenvalues of H APT ; k represents the real number nonlinear coupling coefficient; i represents the imaginary unit; δ = |Δ / κ| represents the non-Hermite characteristic value;

[0020] When δ < 1, the eigenvalue is a pair of complex conjugate pure imaginary numbers, 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 represents H APT In this state, the eigenvalue appears spontaneous symmetry breaking.

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

[0022] As preferred, in step S2), the zero difference detection technology is used to detect the emitted signal light and idler light, and the measurement results of the 1-type entanglement criterion and the 2-type entanglement criterion are obtained.

[0023] As preferred, in step S2), the expression of the 1-type 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 parentheses; q s represents the signal field generalized position operator; q i represents the idler field generalized position operator; p s represents the signal field generalized momentum operator; and p i represents the idler field generalized momentum operator.

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

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

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

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

[0030] As preferred, in step S2), the calculation expression of the type 1 entanglement criterion E1 and the type 2 entanglement criterion E2 is as follows:

[0031]

[0032] In the formula, E1 and E2 represent the type 1 entanglement criterion and the type 2 entanglement criterion respectively, z represents the evolution distance, the detuning amount Δ = -Δk / 2, Δk represents the phase mismatch, κ represents the real number nonlinear coupling coefficient, and φ represents the phase. H represents one of the eigenvalues of H APT , z represents the evolution distance, the detuning amount Δ = -Δk / 2, Δk represents the phase mismatch, κ represents the real number nonlinear coupling coefficient, and φ represents the phase. represents the measured phase of the pump light.

[0033] The present application has the following beneficial effects:

[0034] 1. The present application uses the principle mechanism of the phase-sensitive non-Hermitian four-wave mixing process, realizes high-sensitivity optical phase measurement by measuring the type 1 entanglement criterion through the non-Hermitian characteristics and optical phase sensitivity exhibited by the process, and has the advantages of strong robustness and higher sensitivity.

[0035] 2. The present application has the advantage of high feasibility because the optical phase measurement method based on the phase-sensitive non-Hermitian four-wave mixing process realizes high-sensitivity optical phase measurement in combination with the existing homodyne detection technology. BRIEF DESCRIPTION OF DRAWINGS

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

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

[0038] Figure 3 is a diagram showing the change of the type 1 entanglement criterion and the type 2 entanglement criterion with the phase of the pump light in various states of the present application; wherein (a1) is a diagram showing the change of the type 1 entanglement criterion with the phase of the pump light in the APT symmetric state; (a2) is a diagram showing the change of the type 2 entanglement criterion with the phase of the pump light in the APT symmetric state; (b1) is a diagram showing the change of the type 1 entanglement criterion with the phase of the pump light in the singular point state; (b2) is a diagram showing the change of the type 2 entanglement criterion with the phase of the pump light in the singular point state; (c1) is a diagram showing the change of the type 1 entanglement criterion with the phase of the pump light in the APT broken state; and (c2) is a diagram showing the change of the type 2 entanglement criterion with the phase of the pump light in the APT broken state. DETAILED DESCRIPTION

[0039] The specific embodiments of the present application will be further described below with reference to the accompanying drawings.

[0040] As Figure 1 shown, the 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] As Figure 2 shown in (a) of the figure, the embodiment uses an input pump light ω with a phase of p An input signal light ω s in a coherent state, and an idler light ω i are incident into a nonlinear medium, and in the process, for every 2 pump photons annihilated, 1 signal photon and 1 idler photon are simultaneously generated;

[0043] The embodiment represents the coupling equation between the signal field operator a s and the idler field operator a i as:

[0044]

[0045] In the formula, i represents an imaginary unit; represents the partial derivative with respect to the evolution distance z; represents the Hermitian conjugate symbol; H APT represents a non-Hermitian Hamiltonian matrix; a s is a signal field operator, and a i is an idler field operator; wherein

[0046] The non-Hermitian Hamiltonian matrix H APT corresponding to the dynamic coupling equation of the four-wave mixing process satisfies the APT symmetry, and H APT has an adjustable non-Hermitian parameter. The expression of the non-Hermitian Hamiltonian matrix H APT is:

[0047]

[0048] In the formula, the detuning Δ = -Δk / 2, κ represents a real nonlinear coupling coefficient; i represents an imaginary unit; and φ is a phase; is a to-be-measured phase of the pump light; Δk represents a phase mismatch; as Figure 2 shown in (b) of the figure, Δk = 2k p -(k s +k i )cosθ; k p , k s , and k iThe wave numbers of the pump light, the signal light and the idler light respectively, and theta is the included angle between the pump light and the signal light;

[0049] H APT The controllable non-Hermitian parameters are phase Real nonlinear coupling coefficient K, and the detuning amount Delta = -DeltaK / 2.

[0050] H APT Satisfies {H APT , PT} = 0, wherein P is a parity operator, and T is a time reversal operator. This indicates that H APT satisfies APT symmetry. Since H APT does not contain any gain or loss, the Langevin noise term does not need to be included in the coupling equation, so the commutation relation is maintained.

[0051] The pair of eigenvalues lambda APT of the non-Hermitian Hamiltonian matrix H ± are:

[0052]

[0053] Wherein, lambda represents one of the eigenvalues of H APT ; k represents a real nonlinear coupling coefficient; i represents an imaginary unit; delta = |Delta / k| represents a non-Hermitian characteristic value;

[0054] When delta < 1, the eigenvalue is a pair of complex conjugate pure imaginary numbers, and the process is in an APT symmetric state; when delta > 1, the eigenvalue is a real number, and the process is in an APT broken state; when delta = 1, the process is in a singular point state, and lambda0=0 represents the eigenvalue of H APT in this state, spontaneous symmetry breaking occurs.

[0055] S2), the signal light and the idler light emitted in the four-wave mixing process are detected, the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion are obtained, and the optical phase is measured by using the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion.

[0056] In this embodiment, the homodyne detection technology is used to detect the signal light and the idler light emitted in the four-wave mixing process, the measurement results of the type 1 entanglement criterion and the type 2 entanglement criterion are obtained, and high-precision measurement of the optical phase is realized by using the measurement results of the entanglement criterion.

[0057] 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 denotes the variance operation; q s denotes the signal field generalized position operator; q i denotes the idler field generalized position operator; p s denotes the signal field generalized momentum operator; p i denotes the idler field generalized momentum operator.

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

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

[0062] where Var denotes the variance operation; q s denotes the signal field generalized position operator; q i denotes the idler field generalized position operator; p s denotes the signal field generalized momentum operator; p i denotes the idler field generalized momentum operator.

[0063] In the embodiment, the 1-type entanglement criterion E1 and the 2-type entanglement criterion E2 also represent the two-mode squeezing characteristics of the process; when the 1-type entanglement criterion E1 < 1 or the 2-type entanglement criterion E2 < 1, it corresponds to a weak entanglement criterion; when the 1-type entanglement criterion E1 < 0.5 or the 2-type 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.

[0064] The calculation expression of the 1-type entanglement criterion E1 and the 2-type entanglement criterion E2 is as follows:

[0065]

[0066] where, denotes one of the eigenvalues of H APT , z denotes the evolution distance, the detuning amount Δ = -Δk / 2, Δk denotes the phase mismatch; κ denotes the real number nonlinear coupling coefficient; φ is the phase; is the measured phase of the pump light.

[0067] Considering that the input light field is in a coherent state, the entanglement criterion is irrelevant to the intensity of the input light field, is related to the non-Hermite parameter κ and Δ, and also contains the information of the phase φ.

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

[0069] From the above results of the entanglement criterion of type 1 / type 2, under the condition that the non-Hermite parameters κ and Δ and the evolution distance κz are fixed, the entanglement criterion E1 of type 1 and the entanglement criterion E2 of type 2 are measured by using a homodyne detection technique, the phase φ can be determined from the measurement result, and the optical phase to be measured

[0070] The above embodiments and descriptions only illustrate the principles and the best embodiments of the present application, and the present application can have various changes and improvements without departing from the spirit and scope of the present application, and these changes and improvements all fall within the scope of the present application.​

Claims

1. An optical phase measurement method based on phase-sensitive non-Hermitian four-wave mixing, characterized by, The method comprises the following steps: S1), generating a phase-sensitive non-Hermite four-wave mixing process; The four-wave mixing process is generated by the interaction of signal light, idler light, pump light and a nonlinear medium; The pump light has a phase to be measured And the signal light and the idler light are incident into a nonlinear medium to generate a four-wave mixing process, in which two pump photons are annihilated, and one signal photon and one idler photon are generated simultaneously. The expression of the four-wave mixing process dynamic coupling equation is: where i represents the imaginary unit; denotes the partial derivative with respect to the evolution distance z; denotes the Hermitian conjugate symbol; H APT denotes the non-Hermitian Hamiltonian matrix; a s is the signal field operator, a i is the idler field operator; The four-wave mixing process dynamics coupling equation corresponds to the non-Hermitian Hamiltonian matrix H APT Satisfies the APT symmetry, H APT Has a controllable non-Hermitian parameter in the middle The non-Hermitian Hamiltonian matrix H APT The expression for H is where the detuning Δ = -Δk / 2, represents a real nonlinear coupling coefficient; i represents an imaginary unit; is a phase; is a measured phase of the pump light; Δk represents a phase mismatch; Δk = 2k p - (k s + k i ) cos θ; k p , k s , and k i are wave numbers of the pump light, the signal light, and the idler light, respectively, and θ is an included angle between the pump light and the signal light. H APT The controllable non-Hermitian parameters in the middle are: phase Real nonlinear coupling coefficient , the detuning amount Δ = -Δk / 2; S2), detecting the signal light and idler light emitted in the four-wave mixing process to obtain the measurement results of the type-1 entanglement criterion and the type-2 entanglement criterion, and realizing the measurement of the optical phase by using the measurement results of the type-1 entanglement criterion and the type-2 entanglement criterion; The signal light and idler light emitted are detected by using a homodyne detection technology to obtain the measurement results of the type-1 entanglement criterion and the type-2 entanglement criterion; 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 denotes the variance operation; q s denotes the signal-field generalized position operator; q i denotes the idler-field generalized position operator; p s denotes the signal-field generalized momentum operator; p i denotes the idler-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 denotes the variance operation; q s denotes the signal-field generalized position operator; q i denotes the idler-field generalized position operator; p s denotes the signal-field generalized momentum operator; p i denotes the idler-field generalized momentum operator; 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 to 0, the higher the degree of entanglement; The calculation expressions of the type-1 entanglement criterion E1 and the type-2 entanglement criterion E2 are as follows: wherein represents H APT one of the eigenvalues of the matrix z represents the evolution distance, the detuning Δ = -Δk / 2, Δk represents the phase mismatch; represents the real nonlinear coupling coefficient; is the phase; is the measured phase of the pump light.

2. The method of claim 1, wherein the phase-sensitive non-Hermitian four-wave mixing is used for optical phase measurement. In step S1), the pair of eigenvalues λ APT of the non-Hermitian Hamiltonian matrix H ± is: wherein represents a real nonlinear coupling coefficient; λ represents H APT one of the eigenvalues of A; i represents the imaginary unit; δ = |Δ / κ| represents a non-Hermitian eigenvalue; When δ < 1, the eigenvalue is a pair of complex conjugate pure imaginary numbers, 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 indicates that H APT The eigenvalue in this state is spontaneous symmetry breaking.

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