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Journal of Xi'an University of Post and Telecommunications

Classical intensity and amplitude effect on generalized nonlinear equal-power N th power Y-squeezing

Lei Xiao-li

Published Jan 1, 2009• 0 citations
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Abstract

Constructs the three-state superposition multimode superposition state light field that is composed of multimode coherent state,multimode complex conjugated coherent state and its opoosite state,which are superposed linearly.This paper takes Gaussian laser beam,Hermitian-Gaussian laser beam,Laguerre-Gaussian laser beam,ground mode elliptical-Gaussian laser beam and Hermitian-ellptical Gaussian laser beam as examples seperately,through large data computation and computer graphing,and with the multimode squeezed state theory,studys in detail how the spatial round Gaussian distribution and ellipse distribution of classical intensity,classical amplitude and classical phase affect the generalized nonlinear equal-power N-th power Y-squeezing of the three-state superposition multimode superposition light field.

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The Properties of Unequal-power N_j-th Power Y-squeezing in the Third Kind of Multimode Superposition State Light Field with the Superposition of Three Quantum States

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The third of the three state superpositions multimode superposition state light field |ψ(3)3q was constructed by linear superposition of multimode complex conjugation coherent state,|{Zj}q multimode complex conjugation imaginary coherent state |{iZj}q and multimode vaecum state |{0j}q.By utilizing the theory of multimode squeezed states,the properties of generalized nonlinear unequalpower Njth power Ysqueezing (or amplitude squeezing) in the state |ψ(3)3q was discussed.It is found that when the squeezing power of each mode Nj is even number only,and some certain conditions are satisfied,the first or second perpendicular phase component in the state |ψ(3)3q can always display any even number power generialized nonlinear unequalpower Njth power Ysqueezing effeets respectively,which is comlementary,also changes periodically.

Journal of Optoelectronics·laser•Jan 1, 2003•1 citation
Constructs the three-state superposition multimode superposition state light field that is composed of multimode coherent state,multimode complex conjugated coherent state and its opoosite state,which are superposed linearly.This paper takes Gaussian laser beam,Hermitian-Gaussian laser beam,Laguerre-Gaussian laser beam,ground mode elliptical-Gaussian laser beam and Hermitian-ellptical Gaussian laser beam as examples seperately,through large data computation and computer graphing,and with the multimode squeezed state theory,studys in detail how the spatial round Gaussian distribution and ellipse distribution of classical intensity,classical amplitude and classical phase affect the generalized nonlinear equal-power N-th power Y-squeezing of the three-state superposition multimode superposition light field.
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.
On the bases of the linear superposition principle of quantum state in quantum mechanics, |ψ (3) 3q -the third kind of the three state superposition multimode superposition state light field is constructed that is composed of linear superposition of multimode complex conjugation coherent state |{Z * j} q ?multimode complex conjugation imaginary coherent state |{iZ * j} q and multimode vaccum state |{0 j} q . By utilizing the theory of multimode squeezed states, the properties of generalized nonlinear unequal-power N j-th power H-squeezing in the state |ψ (3) 3q is studied in detail. It is found that when the sum of the squeezing power of each mode is even number only and certain conditions are satisfied, the first perpendicular phase component and the second one of the state |ψ (3) 3q can always display any power generalized nonlinear unequal-power N j-th power H-squeezing effects that change periodically, respectively.
It is constructed in this paper that the three-states superposition multimode functional superposition state light field ｜ψ~((3))_f〉_q is made up of the multimode vacuum state ｜{0_j}〉_q, and the two different multimode complex functional coherent states ｜{f~~((a)*)_f(x,y,z)}〉_q and ｜{f~~((b)*)_f(x,y,z)}〉_q which have rather different spatial intensity distribution characteristic according to the superposition principle of quantum state in quantum mechanics. The properties of equal-power higher-power amplitude-squeezing (Y-squeezing) of generalized magnetic field component of the state ｜ψ~((3))_f〉_q is studied firstly by utilizing the multimode squeezed state theory. It is shown that under a series of fixed conditions, the generalized magnetic-field component of the state ｜ψ~((3))_f〉_q can display the effect of generalized nonlinear equal-power higher-power Y-squeezing which changes periodically and alternatively; and the asymmetrical spatial distribution of the classical intensity and the classical amplitude, and the spatial distribution features of the initial classical phase of light-field in the state ｜ψ~((3))_f〉_q would have a direct influence upon the squeezed degree of equal-power higher-power Y-squeezing present by the generalized magnetic-field component in the state ｜ψ~((3))_f〉_q.
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.
By utilizing the theory of multimode squeezed state,the characteristics of generalized nonlinear equal-power amplitude squeezing of the multimode functional even coherent state is studied,and it is found, when the squeezed number is an odd number,the two quadrature components of the state can present symmetry equal-power amplitude squeezing effect,the squeezed degree,the squeezed depth and the squeezed amplitude are related intensively to the squeezed number,the superposition probability, the classical intensity and initial phase of each mode of the state and other parameters.The further research shown that the conclusions are not completely the same as the theoretical results if the classical intensity of the two three light-fields of the multimode functional even coherent state according to ground mode circular Gaussian distribution.
The third of the three state superpositions multimode superposition state light field |ψ(3)3q was constructed by linear superposition of multimode complex conjugation coherent state,|{Zj}q multimode complex conjugation imaginary coherent state |{iZj}q and multimode vaecum state |{0j}q.By utilizing the theory of multimode squeezed states,the properties of generalized nonlinear unequalpower Njth power Ysqueezing (or amplitude squeezing) in the state |ψ(3)3q was discussed.It is found that when the squeezing power of each mode Nj is even number only,and some certain conditions are satisfied,the first or second perpendicular phase component in the state |ψ(3)3q can always display any even number power generialized nonlinear unequalpower Njth power Ysqueezing effeets respectively,which is comlementary,also changes periodically.