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Acta Sinica Quantum Optica

Higher-Order Squeezing Properties of One class of Eigenstates

Shutian Liu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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Acta Physica Sinica•Jan 1, 1992•1 citation
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 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.
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.
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.