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Journal of Air Force Engineering University

The Difference Squeezing of Mixed State for Multimode Entangled State Light Fields in Decoherence

Sun Zhong-yu, Zhao En-bao

Published Jan 1, 2005• 0 citations
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Abstract

The properties of equal-higher-power difference squeezing of multimode entangled state light - field composed of multimode complex conjugate coherent state, multimode complex conjugate imaginary coherent state and multimode vacuum state are studied by utilizing the multimode squeezing theory in decoherence. The results show that when some fixed conditions are satisfied the mixed entangled state light - field mentioned above not only has the equal - higher - power difference squeezing in one of the quadratures but also displays the similar effects in the quadratures simultaneously, that is called two - sided difference squeezing. This is a newly physical phenomenon which contradicts the principle of uncertainty.

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Journal of Shangluo University•Jan 1, 2003•0 citations
The properties of equal-higher-power difference squeezing of multimode entangled state light - field composed of multimode complex conjugate coherent state, multimode complex conjugate imaginary coherent state and multimode vacuum state are studied by utilizing the multimode squeezing theory in decoherence. The results show that when some fixed conditions are satisfied the mixed entangled state light - field mentioned above not only has the equal - higher - power difference squeezing in one of the quadratures but also displays the similar effects in the quadratures simultaneously, that is called two - sided difference squeezing. This is a newly physical phenomenon which contradicts the principle of uncertainty.
By utilizing the general theory of multimode squeezed states, the effects of generalized nonlinear unequal-power higher-power difference in the multimode Schrodinger-cat state entangled light field is studied, that is formed by the linear superposition of three macroscopical distinguishable quantum states named the multimode complex conjugate coherent state, multimode complex conjugate imaginary coherent state and multimode vacuum state. It is found that 1) the difference of the cat state entangled light field is independent of its vacuum state component; 2) in some cases, the two quadrature phase components of this cat state entangled light field present unequal-power higher-power difference properties respectively ; 3) under some other conditions, the difference effects of two quadrature phase components of the state mentioned above can exist at the same time. The two preceding results stated above are in conformity with the uncertainty principle, but the last is not. It is called two-sided difference squeezing phenomenon and could be very useful in the application of squeezed light on light quanta communication.
By using the general theory of multimode squeezed states, the difference of generalized nonlinear unequal - power higher - power in the multimode Schrodinger -cat state entangled light field is studied in detail. This light field is formed by linear superposition from three quantum states, i.e. multimode complex conjugation coherent state, multimode complex conjugation imaginary coherent state and multimode vacuum state. The conclusion shows that 1) the difference of the cat state entangled light field is independent of the vacuum state; 2) when certain conditions are satisfied, the two quadrature phases of this cat state entangled light field present unequal - power higher - power difference properties respectively, and under some other conditions, the difference effects of two quadrature phases can be displayed at the same time. The former is in conformity with the uncertainty principle. But the later is not, and is called two-sides difference squeezing considering the application of squeezed light in the light communication.
According to the principle of linear superposition of quantum mechanics, the multimode entangled states (as stated below) is formed on the finite-dimensional(N+1) Hilbert space by linearly superposing three quantum states: the multimode complex conjugate coherent state (as stated below), multimode complex conjugate imaginary coherent state (as stated below) and multimode vacuum state (as stated below), and their difference squeezing properties of generalized nonlinear equal-power N-th power is studied by utilizing the general theory of multimode squeezed states. The results show that on the finite -dimensional Hilbert space, while some conditions are satisfied, the two quadratures of the multimode entangled states (as stated below) present the equal-power N-th power difference squeezing properties, but under some other conditions, the difference squeezing effects of two quadratures can be displayed at the same time. The squeezed depth or squeezed degree in this space is different from that on the full-dimensional Hilbert space. The later result is not in conformity with the uncertainty principle. It is called "two -sided〞difference squeezing.
According to the principle of linear suporposition of quantum mechanics,the multimode entangled states ｜｛Ψ~((3))_(2q) is formed by linearly superposing three quantum states: the multimode complex conjugate coherent state ｜｛iZ~_j｝_(2q),multimode complex conjugate imaginary coherent state ｜｛iZ~_j｝_(2q) and multimode vacuum state ｜｛0_j｝_(2q) on the finite-dimensional(N+l) Hilbert space.and their difference squeezing properties of generalized nonlinear equal-power N-th power is studied by utilizing the general theory of multimode squeezed states.The results show that on the finite-dimensional Hilbert space,while some conditions are satisfied,the two quadratures of the state ｜Ψ~((3))_(2q) present the equal-power N-th power difference squeezing properties,but under some other conditions,the difference squeezing effects of two quadratures can be displayed at the same time,and the squeezed depth or squeezed degree in this space is different from that on the full-dimensional Hilbert space.It is called two-sided difference squeezing.
The general theory of generalized nonlinear unequal-power higher-power difference-squeezing of Multimode Radiation Light-Field(abbr.MRLF)is utilized to study the property of second-order unequal-power higher-power difference-squeezing(namely,N_j-th power X-squeezing)of two-state-superposition multimode superposition state light-field Ψ(2)_1_ 2q,which is composed of 2q-modes coherent state and its contrary state according to the state superposition principle in quantum mechanics.It is found that under some certain and fixed conditions,the multimode superposition light-field mentioned above can display the effect of N_j-th power X-squeezing.
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.