Cat-states in the framework of Wigner-Heisenberg algebra

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• 作者：A. Dehghani^a ; ^{a_dehghani@tabrizu.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; ^{alireza.dehghani@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; B. Mojaveri^b ; ^{bmojaveri@azaruniv.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; ^{bmojaveri@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; S. Shirin^a ; ^{siminshirin2000@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; M. Saedi^c ; ^{m_saedi@pnu.ac.ir" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Pseudo harmonic oscillator ; Pseudo Gaussian oscillator ; Calogero&ndash ; Sutherland model ; Sub-Poissonian statistics ; Squeezing effect ; Wigner cat states
• 刊名：Annals of Physics
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：362
• 期：Complete
• 页码：659-670
• 全文大小：545 K

文摘

A one-parameter generalized Wigner–Heisenberg algebra (WHA) is reviewed in detail. It is shown that WHA verifies the deformed commutation rule $[\hat{x},{\hat{p}}_{\lambda }]=i(1+2\lambda \hat{R})$ and also highlights the dynamical symmetries of the pseudo-harmonic oscillator (PHO). The present article is devoted to the study of new cat-states built from λ$\lambda$-deformed Schrödinger coherent states, which according to the Barut–Girardello scheme are defined as the eigenstates of the generalized annihilation operator. Particular attention is devoted to the limiting case where the Schrödinger cat states are obtained. Nonclassical features and quantum statistical properties of these states are studied by evaluation of Mandel’s parameter and quadrature squeezing with respect to the λ$\lambda$-deformed canonical pairs $(\hat{x},{\hat{p}}_{\lambda })$. It is shown that these states minimize the uncertainty relations of each pair of the su(1,1)$su(1,1)$ components.