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Effect of unequal-power sum-squeezing of multimode superposition state light-field composed of four different multimode functional coherent states through equal intensity

Liu Bao-ying

Published Jan 1, 2004• 0 citations
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Abstract

It is constructed in this paper that the four-states superposition multimode functional superposition state light-field |Ψ (4) *(f j) q composed of four multimode functional coherent state through equal intensity.Utilized the unequal-power sum squeezing theory,the properties of unequal-power sum squeezing of the state |Ψ (4) *(f j) q is studied,and it is found,when the add of squeezing number,the spatial distribution function of classical initial phase of each vertical order,the spatial distribution function of classical intensity of each mode and other parameters satisfied to different conditions,the state |Ψ (4) *(f j) q can present certain power unequal-power sum squeezing,the squeezing degree and depth of each mode are intensively connected with the spatial distribution function of classical initial phase of each vertical order and the spatial distribution function of classical intensity of each mode of the state |Ψ (4) *(f j) q.

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Acta Sinica Quantum Optica•Jan 1, 2013•0 citations
It is constructed in this paper that the four-states superposition multimode functional superposition state light-field |Ψ (4) *(f j) q composed of four multimode functional coherent state through equal intensity.Utilized the unequal-power sum squeezing theory,the properties of unequal-power sum squeezing of the state |Ψ (4) *(f j) q is studied,and it is found,when the add of squeezing number,the spatial distribution function of classical initial phase of each vertical order,the spatial distribution function of classical intensity of each mode and other parameters satisfied to different conditions,the state |Ψ (4) *(f j) q can present certain power unequal-power sum squeezing,the squeezing degree and depth of each mode are intensively connected with the spatial distribution function of classical initial phase of each vertical order and the spatial distribution function of classical intensity of each mode of the state |Ψ (4) *(f j) q.
A special type of multimode functional superposition state light field is structured which is composed of multimode functional coherent state, multimode complex conjugation functional coherent state and their contrary states by equal intensity. The properties of unequal-power amplitude squeezing of the state ｜ψ~((4))_(f_j)〉_q is studied, and it is found that the squeezing degree and depth of each mode of the state are decided by the spatial distribution function of classical intensity of each mode of the state ｜ψ~((4))_(f_j)〉_q. Especially, the unequal-power amplitude squeezing properties are asymmetrical, nonlinear and anisotropic with the change of the spatial distribution function of classical initial phase and classical intensity of each mode of the state (｜ψ~((4))_(f_j)〉_q).
It is constructed that the four-state superposition multimode functional superposition state light-field│Ψ(fj)〉q composed of the multimode functional coherent state the multimode complex conjugate functional coherent state and their contrary states by equal probability according to the superposition principle of quantum state in quantum mechanics.By utilizing the theory of multimode squeezed state the characteristics of generalized nonlinear equal-power sum-squeezing of the state is studied and it is found when the product of cavity-mode-number and squeezed number is an odd number the two quadrature components of the state can present symmetry equal-power sum-squeezing effect and the squeezed degree the squeezed depth are related intensively to the classical intensity and initial phase of each mode of the state and other parameters.The further research shown that only the second quadrature component of the state can present sum-squeezing effect if the classical intensity of the four three light-fields of the state │Ψ(fj)〉q according to Hermitian Gaussian distribution.
Utilized the general theory of multimode squeezed state, the squeezing properties of a new kind of multimode superposition state which composed by multimode functional coherent state and multimode functional imaginary coherent state is studied, and it is found that, when the products of sum-number of cavity-modes and squeezing number is an even number, the state can present equal-power sum squeezing effect in some special equal-phase-surface; The spatial distribution of classical intensity of the light-field has a direct influence upon the squeezed degree and the squeezed depth of generalized nonlinear equal-power sum-squeezing of the state ,and with the change of the spatial distribution of classical intensity of each mode, the squeezed degree and the squeezed depth of each mode of the state are anisotropic in spatial distribution.
It was constructed that the four-states superposition multimode functional superposition state light-field according to the superposition principle of quantum state in quantum mechanics.The properties of generalized nonlinear unequal-power odd-number-power Y-squeezing of the state was firstly studied in detail by utilizing the multimode squeezed state theory.It is shown that under some certain and fixed conditions,the state can present the effect of any odd-number-power generalized nonlinear unequal-power (2p_j+1)-th-power Y-squeezing (here,p_j=0,1,2,3,…),and the squeezed degree,the squeezed depth,and the squeezed amplitude are intensively nonlinear related to the cavity mode number,the squeezed number,the probability among four states,the spatial distribution function of the classical intnesity and classical amplitude,and the spatial distribution function of the classical initial phase of each mode of the state.Especially,the spatial distribution function of the classical intensity and classical amplitude of the light-field have a direct influence upon the squeezed degree,the squeezed depth,and the squeezed amplitude of generalized nonlinear unequal-power (2p_j+1)-th-power Y-squeezing of the state.
It was constructed firstly that the three-states superposition multimode functional superposition state light-field|ψ~((3))_f_q was made up of the two different multimode complex conjugate functional coherent state |{f~(((a))~*)_j(x,y,z)}_q and |{f~(((b))~*)_j(x,y,z)}_q which had rather different spatial intensity distribution characteristics and the multimode vacuum state |{0_j}_q according to the linear superposition principle of quantum state in quantum mechanics. And then the multimode squeezed state theory was utilized to study the effects of generalized nonlinear unequal-power higher-power Y-squeezing of generalized magnetic-field component in the state|ψ~((3))_f_q. It was shown that under a series of fixed conditions,the generalized magnetic-field component of the state|ψ~((3))_f_q can always display the effects of generalized nonlinear unequal-power higher-power Y-squeezing which changes periodically and alternatively; the any asymmetrical spatial distribution profile of the classical intensity and the classical amplitude,and the any spatial distribution features of the initial classical phase of the quantum light-field state|ψ~((3))_f_q would have a direct influence upon the squeezed degree and squeezed depth of generalized nonlinear unequal-power higher-power Y-squeezing present by the generalized magnetic-field component in the state |ψ~((3))_f_q.
The light field state |ψ(5)(fj)〉q,a five states superposition multimode quantum functional superposition,that is formed by linearly superposing the multi-mode vacuum state |{0j}〉q and four generalized multimode functional coherent states |{f(m)j(x,y,z)}〉q(m=1,2,3,4) and the properties of the GN unequal-power higher-power Nj-power Y-S effects is further studied generally.The results indicate that ① the state |ψ(5)(fj)〉q is a general multimode nonclassical light field of five functional coherent states superposition,when the state |ψ(5)(fj)〉q is a unequal intensity quasi-symmetrical superposition,while some certain conditions are satisfied,the generalized electric field components of the state |ψ(5)(fj)〉q can display any unequal-power GN Nj-power amplitude squeezing effect.② the any quasi-symmetrical spatial distribution of the classical intensity and the classical amplitude,and the spatial arbitrary distribution characterization of the classical amplitude and the classical initial phase of light field in |ψ(5)(fj)〉q would have a direct influence upon the squeezing results and squeezing degree of the unequal-power amplitude squeezing effects presented by the state |ψ(5)(fj)〉q.