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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Higher-order squeezing of orthonormatized eigenstates of the annihilation operator akfor k≥3

Jinzuo Sun, Ji‐Suo Wang, Chuan‐Kui Wang

Published Oct 28, 1992• 0 citations
Publisher

Abstract

According to the higher-order squeezing defined by Zhang et al., the properties of higher- order squeezing of the orthonormalized eigenstates of the higher powers ak (k>= 3) of the annihilation operator a are studied. Our results show that all of them are minimum uncertainty states of the operators Z1(N) and Z2(N) (N equals mk, m equals 1, 2, ...) for even and odd k, and all of them have the Nth-order squeezing [N equals (m + 1/2)k, m equals 0, 1, 2, ...] for even k.

DOI
10.1117/12.130406

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Acta Physica Sinica•Jan 1, 1992•1 citation
According to the higher-order squeezing defined by Zhang et al., the properties of higher- order squeezing of the orthonormalized eigenstates of the higher powers ak (k>= 3) of the annihilation operator a are studied. Our results show that all of them are minimum uncertainty states of the operators Z1(N) and Z2(N) (N equals mk, m equals 1, 2, ...) for even and odd k, and all of them have the Nth-order squeezing [N equals (m + 1/2)k, m equals 0, 1, 2, ...] for even k.
In this paper, we study first the connection of the k orthonormalized eigenstates of ak{\mathit{a}}^{\mathit{k}}ak with coherent states, then, according to the higher-order squeezing defined by Zhang et al. [Phys. Lett. A 150, 27 (1990)], study the properties of the higher-order squeezing of k orthonormalized eigenstates. Our results show that the k orthonormalized eigenstates can be represented as a linear superposition of k coherent states, and that all of them are minimum uncertainty states of the operators Z1{\mathit{Z}}_{1}Z1​(N) and Z2{\mathit{Z}}_{2}Z2​(N) (N=mk, m=1,2,3, . . .) for even and odd k, and all of them have the Nth-order squeezing [N=(m+1/2)k, m=0,1,2, . . .] for even k.
A method for construction of the k orthonormalized quantum eigenstates of the higher powers ak{\mathit{a}}^{\mathit{k}}ak of the quantum-annihilation operator a is proposed, and their physical meaning is explored. Nonclassical properties of these quantum eigenstates are studied and the main results are as follows: (1) All of the eigenstates can be expressed as a linear superposition of k quantum-coherent states; (2) all of them are generalized quantum-coherent states; (3) for k\ensuremath{\ge}3, they have the Nth-order quantum squeezing for N=mk+k/2 (m=0,1,2, . . .) and even k, but no Nth-order quantum squeezing for other values of N and k; (4) for k\ensuremath{\ge}3, all of them exhibit the lowest- and higher-order quantum antibunching.
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.