Eur. Phys. J. D (2013) 67: 179
https://doi.org/10.1140/epjd/e2013-40258-3

Regular Article

Generalized su(1,1) coherent states for pseudo harmonic oscillator and their nonclassical properties

¹ Department of Physics, Azarbaijan Shahid Madani University, P.O. Box 51745 -406, Tabriz, Iran
² Department of Physics, Payame Noor University, P.O. Box 19395 -4697, Tehran, Iran

^a e-mail: bmojaveri@azaruniv.ac.ir

Received: 23 April 2013
Received in final form: 28 May 2013
Published online: 19 August 2013

Abstract

In this paper we define a non-unitary displacement operator, which by acting on the vacuum state of the pseudo harmonic oscillator (PHO), generates new class of generalized coherent states (GCSs). An interesting feature of this approach is that, contrary to the Klauder-Perelomov and Barut-Girardello approaches, it does not require the existence of dynamical symmetries associated with the system under consideration. These states admit a resolution of the identity through positive definite measures on the complex plane. We have shown that the realization of these states for different values of the deformation parameters leads to the well-known Klauder-Perelomov and Barut-Girardello CSs associated with the su(1,1) Lie algebra. This is why we call them the generalized su(1,1) CSs for the PHO. Finally, study of some statistical characters such as squeezing, anti-bunching effect and sub-Poissonian statistics reveals that the constructed GCSs have indeed nonclassical features.