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Acta Physica Sinica

The quantum statistical properties of a class of superposed q-deformed generalized coherent states

Ren Min, Ma Ai-Qun, Muhammad Ashfaq Ahmad, Ran Zeng, Shutian Liu, MA Zhi-min, (1)广州大学工程抗振中心，广州 510405; (2)哈尔滨工业大学应用物理系，哈尔滨 150001; (3)哈尔滨师范大学呼兰学院物理系，哈尔滨 150050; (4)黑龙江大学物理科学与技术学院，哈尔滨 150080；广州大学城建学院，广州 510905；哈尔滨工业大学应用物理系，哈尔滨 150001

Published Jan 1, 2007• 0 citations
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Abstract

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.

DOI
10.7498/aps.56.845

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In this paper, the quantum statistical properties of the superposition state,a｜ β〉+beiφ｜mβeiδ〉,which involves two arbitrary coh erent states, are investigated. The results show that this kind of super-positio n states generally exhibits squeezing effect or anti-bunching effect. The quantu m effects of the superposed state depend on β2 and the amplitude coe fficient m, as well as the changes of the phase difference between two coherent states δ, and the phase difference between two superposition coefficients φ al so plays an important role in squeezing or anti-bunching effects.
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.
Based on the quantum superposition principle,we construct a new type of superposition composed of coherent state and squeezed state |φ=N(|α+eiφ|βg);and study its squeezing effect and photon anti-bunching effect.The results show that this kind of superposition exhibits fluent quantum properties.When superposed as even/odd coherent states,the superposition exhibits some properties of both even/odd coherent states and squeezed even/odd coherent states.The even/odd coherent and coherent state can be obtained as a special case when the squeezed factor r is zero.
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.