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Excitation on the Coherent States of Pseudoharmonic Oscillator

Dušan Popov, Nicolina Pop, Vjekoslav D. Sajfert, Mădălin O. Bunoiu, Iosif Malaescu

Published Jan 1, 2009• 2 citations

Abstract

In the last decades, much attention has been paid to the excitation on coherent states, especially for coherent states of the harmonic oscillator ([1] and references therein). But an interesting anharmonic oscillator with many potential applications is also the pseudoharmonic oscillator (PHO). So, in the present paper we have defined the excitation on the Klauder‐Perelomov coherent states (E‐KP‐CSs) for the PHO. These states are obtained by repeatedly operating the raising operator K+ on a usual Klauder‐Perelomov coherent state (KP‐CS) of the PHO [2]. We have verified that really, the E‐KP‐CSs fulfill all the properties of the coherent states, as stated by Klauder [3]. We have examined the nonclassical properties of the E‐KP‐CSs, by using the density matrix formalism and examining the dependence of the Mandel parameter Qz,k;m(|z|2) on the |z|2 and on the m. It seems that these states can be used in optical communication field and in the physics of quantum information, as signal beams, due to the fact that in these fields the nonclassicality plays an important role.

DOI: 10.1063/1.3153456

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In the last decades, much attention has been paid to the excitation on coherent states, especially for coherent states of the harmonic oscillator ([1] and references therein). But an interesting anharmonic oscillator with many potential applications is also the pseudoharmonic oscillator (PHO). So, in the present paper we have defined the excitation on the Klauder‐Perelomov coherent states (E‐KP‐CSs) for the PHO. These states are obtained by repeatedly operating the raising operator K+ on a usual Klauder‐Perelomov coherent state (KP‐CS) of the PHO [2]. We have verified that really, the E‐KP‐CSs fulfill all the properties of the coherent states, as stated by Klauder [3]. We have examined the nonclassical properties of the E‐KP‐CSs, by using the density matrix formalism and examining the dependence of the Mandel parameter Qz,k;m(|z|2) on the |z|2 and on the m. It seems that these states can be used in optical communication field and in the physics of quantum information, as signal beams, due to the fact that in these fields the nonclassicality plays an important role.

Photon-added Barut

ndash

Girardello coherent states of the pseudoharmonic oscillator

In a previous paper (Popov D 2001 J. Phys. A: Math. Gen. 34 5283) we have constructed the coherent states (CSs) of the pseudoharmonic oscillator (PHO). These states are of the Barut–Girardello type. In the present paper, we have constructed and investigated some properties of the photon-added Barut–Girardello coherent states (PA-BGCSs) of the PHO. These states are not orthogonal but are normalized and satisfy a unity resolution relation (the completeness relation). We have found the analytical form for the positive weight function in the resolution of unity. By using these states, we have calculated some expectation values (the first two powers of the number operator N ), which have evinced some non-classical properties. In order to examine the statistical properties of a PHO gas, which obeys the quantum canonical distribution, the diagonal P -representation of the density operator ρ ( m ) is constructed and the thermal expectation values are calculated. All these quantities are expressed in terms of Meijer G -functions, and so the PA-BGCSs are a new field of application for these functions. Also, the time dependence of the PA-BGCSs is examined. If in the obtained results we put m = 0, we recover all the results from our previous paper.

In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schro¨dinger 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.

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 very 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.

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.