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Journal of Atomic and Molecular Physics

Generalized nonlinear equal-power difference-squeezing in the arbitrary two-states superposition multimode functional superposition state light-field

Bai Shao

Published Jan 1, 2008• 0 citations
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Abstract

The arbitrary two-states superposition multimode functional superposition state light-field |ψ(2)f〉q is constructed.The general theory of generalized nonlinear equal-power higher-power difference-squeezing of Multimode Radiation Light-Field is utilized to study the properties of equal-power N-power difference-squeezing of generalized magnetic-field component of the state |ψ(2)f〉q.The general theory result is obtained,the properties of equal-power N-power difference-squeezing in two special two-states superposition multimode functional superposition state light-field is discussed.It is shown that:1)When qN is a even-numbers,not appears as the properties of generalized nonlinear equal-power difference-squeezing of generalized magnetic-field component and not appears as N-j minimum uncertainty state in first kind two-states superposition multimode functional superposition state light-field and imaginary number coherent two-states superposition multimode functional superposition state light-field;2) When qN is a odd-numbers,generalized magnetic-field component of the arbitrary two-states superposition multimode functional superposition state light-field can display the effect of generalized nonlinear N-power difference-squeezing which changes periodically and alternatively under a series of fixed conditions.

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Journal of Yanan University•Jan 1, 2004•0 citations
The arbitrary two-states superposition multimode functional superposition state light-field |ψ(2)f〉q is constructed.The general theory of generalized nonlinear equal-power higher-power difference-squeezing of Multimode Radiation Light-Field is utilized to study the properties of equal-power N-power difference-squeezing of generalized magnetic-field component of the state |ψ(2)f〉q.The general theory result is obtained,the properties of equal-power N-power difference-squeezing in two special two-states superposition multimode functional superposition state light-field is discussed.It is shown that:1)When qN is a even-numbers,not appears as the properties of generalized nonlinear equal-power difference-squeezing of generalized magnetic-field component and not appears as N-j minimum uncertainty state in first kind two-states superposition multimode functional superposition state light-field and imaginary number coherent two-states superposition multimode functional superposition state light-field;2) When qN is a odd-numbers,generalized magnetic-field component of the arbitrary two-states superposition multimode functional superposition state light-field can display the effect of generalized nonlinear N-power difference-squeezing which changes periodically and alternatively under a series of fixed conditions.
The general theory of generalized nonlinear equal-power higher-power difference-squeezing of multimode radiation light-field is utilized to study the properties of equal-power N-power difference-squeezing of generalized electric-field component of the arbitrary two-states superposition multimode functional superposition state light-field.The general theory result is obtained,the properties of equal-power N-power difference-squeezing in two special two-states superposition multimode functional superposition state light-field is discussed.It is shown that:1)When qN is a even-numbers,not appears as the properties of generalized nonlinear equal-power difference-squeezing of generalized electric-field component and not appears as N-j minimum uncertainty state in first kind two-states superposition multimode functional superposition state light-field and imaginary number coherent two-states superposition multimode functional superposition state light-field;2) When qN is a odd-numbers,generalized electric-field component of the arbitrary two-states superposition multimode functional superposition state light-field can display the effect of generalized nonlinear N-power difference-squeezing which changes periodically and alternatively under a series of fixed conditions.
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.
By utilizing the theory of multimode squeezed states established recently, the generalized nonlinear even number power equal-power N-th power Y-squeezing effects of generalized magnetic-field component in the new kind of multimode quantum light-field state (｜Ψ~((3))〉_q) is studied firstly in detail, which is composed of the linear superposition of macroscopically distinct three quantum states named multimode complex conjugation imaginary coherent state, the contrary state of multimode complex conjugation imaginary coherent state and multimode complex conjugation coherent state. It is found that under certain and fixed conditions, the generalized magnetic-field component in the state ｜Ψ~((3))〉_q can always display the effects of even number power generalized nonlinear equal-power N-th power Y-squeezing.
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.
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.