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Journal of Northwest University

The effect of unequal-order N_j-th power H-squeezing on a new type of multi-mode superimposition state light field with two state superimpositions

Hong Xue

Published Jan 1, 2002• 0 citations
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Abstract

By utilizing the theory of multi-mode squeezed states, the property is studied on the generalized nonlinear unequal-order N j -th power Y-squeezing on a new type of multi-mode superimposition state light field | Ψ (2) msc q with distinguishable two quantum states. It is found that when squeezed orde N j=2p , no matter what p=2m+1(m=0,1,2,...) ,while the initial phases of corresponding mode φ j(j=1,2,3...,q) , the difference of initial phasas of states [θ (R) nq -θ (I) nq -∑[DD(]qj=1R 2 j] and the range of phonton interence term, etc., the first and the second quadrature component of state | Ψ (2) msc q is a typical multi-mode nonclasical light field. And it can display unequal-order N j -thpower Y-squeezing effects that change periodicall under the other conditions. and the range of phonton interence term, etc., the first and the second quadrature component of state | Ψ (2) msc q is a typical multi-mode nonclasical light field. And it can display unequal-order N j -thpower Y-squeezing effects that change periodicall under the other conditions.

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By utilizing the theory of multi-mode squeezed states, the property is studied on the generalized nonlinear unequal-order N j -th power Y-squeezing on a new type of multi-mode superimposition state light field | Ψ (2) msc q with distinguishable two quantum states. It is found that when squeezed orde N j=2p , no matter what p=2m+1(m=0,1,2,...) ,while the initial phases of corresponding mode φ j(j=1,2,3...,q) , the difference of initial phasas of states [θ (R) nq -θ (I) nq -∑[DD(]qj=1R 2 j] and the range of phonton interence term, etc., the first and the second quadrature component of state | Ψ (2) msc q is a typical multi-mode nonclasical light field. And it can display unequal-order N j -thpower Y-squeezing effects that change periodicall under the other conditions. and the range of phonton interence term, etc., the first and the second quadrature component of state | Ψ (2) msc q is a typical multi-mode nonclasical light field. And it can display unequal-order N j -thpower Y-squeezing effects that change periodicall under the other conditions.
The multi-mode squeezed state theory is utilized to study the effects of higher order unequal-order N_jth power H-squeezing on the multi-mode quantum superposition state |ψ〉_q that is made of the linear superpositinos of the two nonsymmetry multi-mode coherent states |{z~((a)~*)_j}〉_q and |-{z~((b)~*)_j}〉_q, it is found that two quardrature phase components in state |ψ〉_q can always display respectively the generalized nonliear higher-order unequal -order N_jth power Y-squeezing effects which changes periodically while some conditions are satisfied respectively by the sum ∑qj=1N_jφ_j of the multiplication N_jφ_j of the initial phase φ_j of each mode and squeezing order number N_j of each mode(here j=1,2,3,…,q), and by the initial phase difference θ~((R))_(pq)-θ~((R))_(nq) between the two components of state |ψ〉_q. The squeezing intensity is bigger when sum ∑qj=1N_j of squeezing order number N_j of each mode is odd number.
The multi-mode squeezed state theory was utilized to study the effects of higher order unequal-order N_jth power Y-squeezing on the multi-mode quantum superposition state |Ψ_q that was made of the linear superpositions of the two nonsymmetry multi-mode coherent states |{z~((a)*)_j}_q and |{-z~((b)*)_j}_q.It was found that two quardrature phase components in state |Ψ_q could always display respectively the generalized nonliear higher-order unequal order N_jth power Y-squeezing effects which change periodically while some conditions are satisfied respectively by the product N_jφ_j of the initial phase φ_j of each mode, moreover the squeezing order number N_j of each mode(here j=1,2,3,...,q), and by the initial phase difference θ~((R))_(pq)-θ~((R))_(nq) between the two components of state |Ψ_q.The squeezing intensity was bigger when all of squeezing order number N_j of each mode were odd number.
The State |Ψ (ab) q=C (aI) pq |{iZ (a) * j} q+C (bI) nq |{-iZ (b) * j} q is a new type of unsymmetrical multi-mode superposition state light field. By using the unequalled-order squeezing general theory of multi-mode ridiative light field, the property of generalized nonlinear unequalled-order N j-thpower H-squeezing of the state |Ψ (ab) q mentioned above is studied firstly in detail. It is found that the two perpendicular component of the state |Ψ (ab) q can presents respectively any unequalled-order N j-th power H-squeezing effect that changes periodically and unequalled-order N j-H minimum uncertainty state under the different some conditions. The results show that the state |Ψ (ab) q is a kind of typical nonclassical multi-mode light field.
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.
In this paper, the multi-mode squeezed state theory is utilized to study the effects of even number-order unequal-power Njth power Y-squeezing on the two kind of multi-mode quantum superposition statesψ(2)± ■ that is made of the linear superposition of the multimode coherent stateR(a)j exp(-iφ■)■ and the multi-mode imaginary coherent states±iR(b)j exp(-iφ■)■.when the squeezing order number Nj of each mode is even number, viz. Nj=2pj(j=1,2,3,......q, pj=1,2,3,......), it is found that two kind ofψ(2)± ■can always display respectively the generalized nonlinear even-number-order unequal-power Njth power Y-squeezing effects which changes periodically while the some conditions are satisfied respectively by the initial phase φj of each mode,and by initial mixing-phase (θ[R]pq -θ(I)nq )■■R(a)j R(b)j which is composed of the initial phase difference θ(R)pq -θ(I)nq between the two components of the stateψ(2)± ■mentioned above and the sum ■R(a)j R(b)j of the products R(a)j R(b)j of amplitudes R(a)j and R(b)j .The squeezing-intensity is bigger when the pj is odd number.
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.