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Acta Sinica Quantum Optica

Effects of Generalized Nonlinear Higher-power Amplitude Squeezing ofGeneralized Electric Field Components in the Multimode State LightFields with Quasi-symmetrical Superposition

孙中禹 SUN Zhong-yu, 杨志勇 YANG Zhi-yong, 杨春燕 YANG Chun-yan

Published Jan 1, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.3788/asqo20131903.0207

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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.
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.
It is Constructied in this paper that the three_states superposition multimode functional superposition state light field ｜ψ~((3))_f〉_q is made up of the two different multimode complex functional coherent states ｜｛f~((a))_j(x,y,z)｝〉_q and ｜｛f~((b))_j(x,y,z)｝〉_q which have rather different spatial intensity distribution characteristic, and the multimode vacuum state ｜｛0_j｝〉_q according to the superposition principle of quantum state in quantum mechanics. the properties of equal_power higher_power H_squeezing of generalized electric field component (or the second perpendicular phase 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 electric_field component of the state( ｜ψ~((3))_f〉_q) can display the effect of generalized nonlinear equal_power higher_power H_squeezing which changes periodically and alternatively; and the any asymmetrical spatial distribution of the classical intensity and the classical amplitude, and the any spatial distribution features of the initial classical phase of light_field in the state ｜ψ~((3))_f〉_q will have a direct influence upon the squeezed degree and squeezed depth of equal_power higher_power H_squeezing present by the generalized electric_field component in the state ｜ψ~((3))_f〉_q.
In this paper, the multimode squeezed state theory is utilized to study the characteristics of generalized nonlinear-unequal-power higher-power sum-squeezing of generalized magnetic-field component in the state |ψ(f)(2)q made up of the linear superposition of multimode functional coherent state |{fj(x,y,z)}q and its contrary state |{-fj(x,y,z)}q according to the superposition principle of quantum state in quantum mechanics. It is found that: 1) under the condition of the sum of squeezing-power-number being an any even-number, thestate |ψ(f)(2)q can always stay in the generalized nonlinear unequal-power Nj-H minimum uncertainty state;and 2) under the condition of the sum of squeezing-power-number being an anyodd-number, while some other fixed conditions are satisfied by the state |ψ(f)(2)q the state mentioned can display the effects of generalized nonlinear unequal-power Nj-th power H-squeezing that changes periodically and alternatively.
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.
In this paper,the multimode squeezed state theory is utilized to study the characteristics of generalized nonlinear-unequal-power N j -th power H-squeezing of generalized electric-field component in the state |Ψ (2) (f) g, made up of the linear superposition of multimode functional coherent state |{f j (x,y,z) } g and its contrary state |{-f j( x,y,z )} g according to the superposition principle of quantum state in quantum mechanics.It shows the results:under the condition of the sum of squeezing-power-number being an any odd-number,while some other fixed conditions are satisfied by the suate |Ψ (2) (f) g the state |Ψ (2) (f) g can display the effects of any generalized nonlinear unequal-power N j -th power H-squeezing that changes periodically and alternatively.
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.