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Journal of Liaoning University

The Fourth-Order Squeezing Effects of Squeezed Even and odd Coherent States

Tan Tian-ya

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

We can abtain the one-mode squeezed even and odd coherent states applying the one-mode squeezing operator on the one-mode even and odd coherent states.In this paper,the fourth-order squeezing effects of theses states are studied.These states possess strong fourth-order squeezing effects.And the bigger squeezing parameter r,the stronger fourth-order squeezing effects.

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The properties of the two-order and high-order squeezing of phase in generalized Kerr even and odd coherent states have been studied via the measured phase operators introduced by S. M. Barnett and D. T. Pegg. The influences of nonlinear order m of generalized Kerr-medium on squeezing of measured phase operarors have been discussed emphatically. It is shown that the measured phase operator has periodic even-order squeezing in the CS type and di-even-order squeezing in CN type ,in all even and odd coherent states, and the degree of squeezing is relevant to m, |α|2 and δ.

Acta Sinica Quantum Optica•Jan 1, 2002•0 citations
We can abtain the one-mode squeezed even and odd coherent states applying the one-mode squeezing operator on the one-mode even and odd coherent states.In this paper,the fourth-order squeezing effects of theses states are studied.These states possess strong fourth-order squeezing effects.And the bigger squeezing parameter r,the stronger fourth-order squeezing effects.
WT5”BZ]:The properties of the two order and higher order squeezing of phase in Kerr even and odd coherent states have been discussed via the measured phase operator introduced by S.M.Barnett and D.T.Pegg.The results exhibit that the measured phase operator cos M has not only periodic k order squeezing in cs type in even and odd coherent states but the k order squeezing in the type of cN when k is even.They also show that the degree of squeezing is relevant with |α| 2.When |α| 2 is comparatively big,the squeezing in Kerr even coherent states resembles that in Kerr odd coherent states.Nevertheless,when |α| 2 is small,the squeezing in Kerr odd coherent states appears shallow,even no squeezing effect occurs. [WT5”HZ]
By utilizing the multi-mode squeezing state theory,the properties of the equal-order N-th power Y squeezing of stateare studied.According to the linear superposition principle of quantum mechanics,the fourth kind of four-state superposition multi-mode superposition states light field |Ψ~((4))_0,Ⅳ〉_qis constructed with multi-mode complex conjugate-odd coherent state(|Ψ~((2))_0,Ⅳ〉_q) and imaginary-odd coherent state(|Ψ~((2))_i,O〉_q).The new properties of the equal-order N-th power Y squeezing of state |Ψ~((4))_0,Ⅳ〉_qare found.When squeezing order Nis an even number,initial phase φ_j and initial phase difference θ_1-θ_2 indifferent conditions,1) When N=4m(m=1,2,3,…) the first orthogonal phase components of state |Ψ~((4))_0,Ⅳ〉_qrepresents the equal-order N-th power Y squeezing;2).When N=4m′-2(m′=1,2,3,…),the second orthogonal phase components of state |Ψ~((4))_0,Ⅳ〉_qrepresents N-th power Y squeezing effects.
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 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 properties of the two-order and high-order squeezing of phase in generalized Kerr even and odd coherent states have been studied via the measured phase operators introduced by S. M. Barnett and D. T. Pegg. The influences of nonlinear order m of generalized Kerr-medium on squeezing of measured phase operarors have been discussed emphatically. It is shown that the measured phase operator has periodic even-order squeezing in the CS type and di-even-order squeezing in CN type ,in all even and odd coherent states, and the degree of squeezing is relevant to m, |α|2 and δ.