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Journal of Guangzhou University

Higher power squeezing properties of a class of the superposition of the q-deformed generalized coherent states

Shutian Liu

Published Jan 1, 2009• 0 citations
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Abstract

We proposed a class of the superposition state α|β+beiφ|βeiδ based on the q-deformed generalized coherent states.The higher power squeezing properties of these superposition states are studied.The results show that the power of the squeezing can be expressed as k≠2πn/δ,with n an integer and δ the phase difference between the two generalized coherent states.When δ=π,the power of squeezing can only be odd,when δ takes other values,the squeezing power can be even.These results show that the parameter phase difference δ plays an important role in determining the possible squeezing power,the role of a(b) and β can not be neglected.

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We proposed a class of the superposition state α|β+beiφ|βeiδ based on the q-deformed generalized coherent states.The higher power squeezing properties of these superposition states are studied.The results show that the power of the squeezing can be expressed as k≠2πn/δ,with n an integer and δ the phase difference between the two generalized coherent states.When δ=π,the power of squeezing can only be odd,when δ takes other values,the squeezing power can be even.These results show that the parameter phase difference δ plays an important role in determining the possible squeezing power,the role of a(b) and β can not be neglected.
The amplitude-kth power characters of the superposition state |ψ=a|β+be~(iφ)|mβe~(iδ) of the generalized coherent states are studied, the results show that the possible kth-power squeezing can be expressed as k≠2nπ/δ when m=i, with n an integer and δthe phase difference between the two generalized coherent states; When m≠1, the kth-power can be even and odd; when δ=π the power of the squeezing can only be odd; when δ=π/2, the power of squeezing can be even and odd. These results show that the parameter phase difference δ plays the key role in determining the possible power of squeezing.
In this paper, the quantum statistical properties of a class of superposed q-deformed generalized coherent states |ψ>=a|β>+beiφ|βeiδ> are studied. The results show that the superposition of q-deformed coherent generalized states generally exhibits squeezing and anti-bunching effects. The change of the phase difference between two generalized coherent states, the phase difference between two superposition coefficients, and both the amplitude and phase of the inner product of two generalized coherent states play important roles in squeezing effect and anti-bunching effect.
The characteristics of the k th-power squeezing of a class of superposition states which involving two orthonormalized eigenstates of photon annihilation operator aN are studied.The result show that the characteristics of the k th-power squeezing of a class of superposition states which involving two orthonormalized eigenstates of photon annihilation operator aN are different from the characteristics of the k th-power squeezing of the orthonormalized eigenstates of photon annihilation operator aN clearly.No matter what N is an odd number or even number,the superposition states own amplitude k(k=Nt or Nt/2) th-power squeezing,but for the orthonormalized eigenstates of aN,only when N is even number there exist amplitude k(k=(2P+1)N/2) th-power squeezing.Owing to that,when phase difference δ=2mπ/t(m is integer),the superposition states don′t own amplitude k th-power squeezing;when δ=π,only N and t are odd number simultaneously,the superposition states may own amplitude k th-power squeezing;when δ=π/2,t≠4m,the superposition states own amplitude k th-power squeezing;thus the phase difference of parameter has key effect on amplitude k th-power squeezing.
The superposition states, which are composed of the generalized q-coherent states of the non-harmonic oscillator, are presented. The quantum statistical properties of these states are studied. Then the influence of the superposition phase δ and the deformation parameter q on these nonclassical properties are discussed. It is shown that the superposition states exhibit higher-order (order of odd number) squeezing effect and antibunching effect respectively. When the superposition phase δ is taken values approach to 0 or π/2, these results approach the properties of the even or odd generalized q-coherent states of the non-harmonic oscillator. Especially, the effects are influenced by the parameter q. When the values of q is taken departure from 1 greatly, the nonclassical properties are more evidently.