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Europhysics Letters (EPL)

Density matrix approach of the excitation on coherent states of the pseudoharmonic oscillator

Dušan Popov, Nicolina Pop, Ioan Luminosu, Viorel Chiritoiu

Published Aug 1, 2009• 5 citations
Publisher

Abstract

We have examined the excitation on coherent states of the pseudoharmonic oscillator which are obtained by repeated action of the raising operator on the usual coherent states. By using the density matrix approach, we have examined some interesting properties (including the nonclassicality) of these states, both in pure and also in mixed (thermal) cases.

DOI
10.1209/0295-5075/87/44003

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We have examined the excitation on coherent states of the pseudoharmonic oscillator which are obtained by repeated action of the raising operator on the usual coherent states. By using the density matrix approach, we have examined some interesting properties (including the nonclassicality) of these states, both in pure and also in mixed (thermal) cases.
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In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schrödinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is much easier to work with, in comparison to the functional Hilbert space. The SU (1, 1) dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut—Girardello and Gilmore—Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.
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