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中国激光(英文版)

Squeezing and Higherorder Squeezing Properties of Eigenstates of the Operator akqsSupported by the Natural Science Foundation of Shandong Province, China.

Ji‐Suo Wang

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

The squeezing and higherorder squeezing properties of k orthonormalized eigenstates of the higher powers akqs(k≥3) of the annihilation operator of twoparameter deformed harmonic oscillator are investigated. It is found that the Nthpower squeezing [N=(m+1/2)k, m=0,1,2,…] can exist in the all of them when k is even.

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The squeezing and higherorder squeezing properties of k orthonormalized eigenstates of the higher powers akqs(k≥3) of the annihilation operator of twoparameter deformed harmonic oscillator are investigated. It is found that the Nthpower squeezing [N=(m+1/2)k, m=0,1,2,…] can exist in the all of them when k is even.
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.
Coherent states and the extension to the even and odd coherent states, and further to the eigenstates of the higher power of the annihilation operator are basic and important macroscopic quantum states in quantum field theory. Recently, these investigations have been extended to the aharmonic oscillator and the quantum algebra with q -deformed or qs-deformed commutation relations. In this paper,the orthogonal eigenstates of the higher order of the annihilation operator of the q -deformed aharmonic oscillator are also derived. It is pointed out that these different macroscopic quantum states have similar squeezing properties of higher order amplitude. The reason is found that the orthogonal eigenstates of the higher order of the annihilation operator of the harmonic oscillator, the q -deformed oscillator, the qs -deformed oscillator, the Enharmonic oscillator and the q -deformed anharmonic oscillator all have even and odd structure, which is similar to the simple even and odd coherent states. For other systems like the system with SU(1 ,1) Lie algebra or q -deformed quantum algebra also have such properties.
The characteristics of the kth-power squeezing of a class of superposition states which involing two orthonormalized eigenstates of photo annihilation operator aN are studied,the result show that the characteristics of the kth-power squeezing of a class of superposition states which involving two orthonormalized of photon annihilation operator aN are different from the characteristics of the kth-power squeezing of the orthonormalized eigenstates of photo annihilation operator aN clearly.No matter what N is odd number or even number,the superposition states exist 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,when phase difference δ=2mπ/t(m is integer),the superposition states don't exist amplitude k th-power squeezing,when δ=π,only N and t are odd number together,the superposition states may exist amplitude kth-power squeezing,…,thus the phase difference of paramter takes key effect for amplitude kth-power squeezing.The research result also show that j,N,δ, and α play a not be ignored part in squeezing and squeezing region.