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Journal of Optoelectronics·laser

Generalized Nonlinear Equal-power N-thpower X squeezing in Four State Superimposition Multimode Superimposition State Light Field

Xu Chu Ding

Published Jan 1, 2003• 0 citations
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Abstract

The properties of equalpower Nth power X squeezing of the first enen number mode fourstate superimposition multimode superimposition state,which is composed of the linear super positions of the multimode even and odd coherent state that they have as same as even number mode,was studied based on the theory of multimode squeezed states.The results show when the qN(q,cavity mode number) is even number,and the photon numbers nj of any mode is less than N,two quadrature phase components of the state appear as equalorder Nth X squeezing in same time;when qN is odd number,njN, and also other necessary conditions the two quadrature phase components of the state present the equal power Nth power Xsqueezing effect.

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Optoelectronic Technology & Information•Jan 1, 2003•0 citations
The properties of equalpower Nth power X squeezing of the first enen number mode fourstate superimposition multimode superimposition state,which is composed of the linear super positions of the multimode even and odd coherent state that they have as same as even number mode,was studied based on the theory of multimode squeezed states.The results show when the qN(q,cavity mode number) is even number,and the photon numbers nj of any mode is less than N,two quadrature phase components of the state appear as equalorder Nth X squeezing in same time;when qN is odd number,njN, and also other necessary conditions the two quadrature phase components of the state present the equal power Nth power Xsqueezing effect.
According to the linear superposition principle in quantum mechanics,the superposition light field composed by multimode odd coherent state and multimode complex conjugation imaginary odd coherent state Utilized the multimode squeezed state theory.the properties of equal-power N-th power Y-squeezing of the state is studide,and it is found that:1)when squeezing number N=4P (P=1,2,3,...),if the initial phase of each vertical order (?),the phase difference θ1-θ2 and other parameters take different fixed value,the first quadrature component of the state always presents different degree and periodic changing equal-order N-th power Y-squeezing;2)when squeezing number N=4P'-2 (P'=1,2,3,...) if the initial phase of each vertical order (?)j,the phase defference θ1-θ2 and other parameters take different fixed value,the second quadrature component of the state always presents different degree and perindic changing equal-power N-th power Y-squeezing.
By utilizing the multi-mode squeezing state theory,the properties of the equal-order N-th power Y squeezing of stateare studied.According to the linear superposition principle of quantum mechanics,the fourth kind of four-state superposition multi-mode superposition states light field |Ψ~((4))_0,Ⅳ〉_qis constructed with multi-mode complex conjugate-odd coherent state(|Ψ~((2))_0,Ⅳ〉_q) and imaginary-odd coherent state(|Ψ~((2))_i,O〉_q).The new properties of the equal-order N-th power Y squeezing of state |Ψ~((4))_0,Ⅳ〉_qare found.When squeezing order Nis an even number,initial phase φ_j and initial phase difference θ_1-θ_2 indifferent conditions,1) When N=4m(m=1,2,3,…) the first orthogonal phase components of state |Ψ~((4))_0,Ⅳ〉_qrepresents the equal-order N-th power Y squeezing;2).When N=4m′-2(m′=1,2,3,…),the second orthogonal phase components of state |Ψ~((4))_0,Ⅳ〉_qrepresents N-th power Y squeezing effects.
Applying the theory of multi-mode squeezing state, the properties of the generalized nonlinear equal-power difference squeezing of the multi-mode complex conjugation odd- and even-coherent state light field are further studied in detail. The findings demonstrate that if, at least one mode n_j (j = 1, 2, 3,..., 2q) of the photon number is less than squeezing power N and q·N, the products of cavity modes number q and squeezing-power number N, no matter an even-number or odd-number, the generalized both magnetic field and electrical field perpendicular phase component of multi-mode complex conjugation odd- and even-coherent state light field present equal-power difference squeezing conditions at the same time. This phenomenon is called generalized nonlinear equal-power N-th Power X-Strange-Squeezing effect. The result is completely different from what has been reported recently and is not identical with the law of the uncertainty relation. Therefore, the above mentioned illustrates that the multi-mode complex conjugation odd- and even-coherent state light fields are really two types of multi-mode non-classical light field.
By using the theory of multimode squeezed state,the property of generalized nonlinear equal-order N-th power Y-squeezing in the multimode superposition state light field ｜Ψ~((2))〉_q with the superposition of arbitrary two quantum states is studied.It is evinced that the state ｜Ψ~((2))〉_q separately stayed equal-order N-Y minimum uncertainty state、present the effect of half coherent state、the first quadrature component or the second quadrature component present the properties of N-th power Y-squeezing in different conditions.
According to the Linear superpositon principle in quantum mechanics ,the ninth kind of two ligtht Field is constructed that is composed of multimode vaccum state light field And then the multimode squeezed state theory suggested by Yang Zhiyong and Hou Xun and Published in Acta Photonica Sinica is utlized to study the properties of generalized nonlinear equal- power N-th power Y-squeeting of the state mentioned above. It is found that ①、whether the squeezing-power-number N is an odd-number or an even-number, while some certain quantization conditions are satisfied by the initial phase of each mode and by the initial phase difference( ) between two components of the state respectively ,the state can always present any odd-number power any even-number N-th power Y-squeezing effects which changes periodically. ② Compared with the reference [11] ,the state constructed in this paper is rathier different from the state constructed in reference [11] ,under some fixed conditions the states and can display the phenomena of N-th power Y-similitude- squeezing and N-th power Y-degenerate-squeezing.
Based on the superposition theory in the quantum mechanics, the multi-mode superposition light field state is constituted by two nonsymrnetry multi-mode coherent states and which intensities are unequal. By using higer-order squeezing theory in multi-mode states, the equal-power Nth power H-squeezing properties of the is studied. It is found that when the certain phase conditions are satisfied,the two quardrature phase components in the present alternately equal-power Nth power H-squeezing effect which changes periodically, whether qN which is the product of cavity-mode total number q and squeezing -order N is odd number or even number.