Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal Of Modern Research Physics

Photon –added Barut –Girardello coherent states for non-linear harmonic oscillator

Sodabe Rezaei, Ardeshir Rabeie

Published Aug 1, 2024• 0 citations
Publisher

Abstract

In this paper, we introduce the generalized coherent states and Photon-added coherent states in the sence of Barut-Girardello for the nonlinear harmonic oscillator with position dependent effective mass.The study of the resolution of the unity as the fundamental property of coherent states, is done in Meijer Gfunction.Also, the non-classical features of these two states are calculated and analyized by using the probability distribution function and Mandel parameter.

DOI
10.61882/jmrph.9.1.35

Related papers

Photon-added Barut$ndash$Girardello coherent states of the pseudoharmonic oscillator

Du$scheck$an Popov

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.

Journal of Physics A Mathematical and General•Aug 7, 2002•49 citations

Barut—Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass

Naila Amir, Shahid Iqbal

Abstract Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.

arXiv:1606.05791•Communications in Theoretical Physics•Jul 1, 2016•24 citations

Barut–Girardello Coherent States for Nonlinear Oscillator with Position-Dependent Mass

Naila, Amir, Shahid +1 more

Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut–Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover,it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.

理论物理通讯:英文版•Jan 1, 2016•0 citations

A set of nonlinear coherent states for the pseudoharmonic oscillator

Khalid Ahbli, Hamidou Kassogué, Patrick K. Kayupe +1 more

We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients $z^n/\sqrt{n!}$ of the canonical coherent states by a specific generalized factorial $x_n^{γ,σ}!$ where parameters $γ$ and $σ$ satisfy some conditions for which the normalization condition and the resolution of identity are verified. The obtained family is a generalization of the Barut-Girardello coherent states and those of the philophase states. In the particular case of parameters $γ$ and $σ$, we attache these states to the pseudo-harmonic oscillator depending on two parameters $α,β> 0$. The obtained nonlinear coherent states are superposition of eigenstates of this oscillator. The associated Bargmann-type transform is defined and we derive some results.

arXiv:1907.08881•Jul 20, 2019•0 citations

New class of generalized photon-added coherent states and some of their non-classical properties

B. Mojaveri, Alireza Dehghani, S Mahmoodi

In this paper, we construct a new class of generalized photon added coherent states (GPACSs), by excitations on a newly introduced family of generalized coherent states (GCSs) (A Dehghani and B Mojaveri 2012 J. Phys. A: Math. Theor. 45 095304 ), obtained via generalized hypergeometric type displacement operators acting on the vacuum state of the simple harmonic oscillator. We show that these states realize resolution of the identity property through positive definite measures on the complex plane. Meanwhile, we demonstrate that the introduced states can also be interpreted as nonlinear coherent states (NLCSs), with a spacial nonlinearity function. Finally, some of their non-classical features as well as their quantum statistical properties are compared with Agarwalʼs photon-added coherent states (PACSs),

Physica Scripta•Jun 24, 2014•15 citations

On the construction of the coherent states of the semiconfined harmonic oscillator with a position-dependent effective mass

Sh. M. Nagiyev, E. I. Jafarov

Abstract We present details of the method for constructing the coherent states of the quantum harmonic oscillator model that exhibits the semiconfinement effect due to a specific change of its mass by position. Its energy spectrum completely overlaps with the Hermite oscillator energy spectrum, whereas the wavefunctions of the stationary states are expressed via the generalized Laguerre polynomials. Two different methods have been applied to compute the coherent states. They are generalized and Barut-Girardello coherent states methods. In both cases, the exact expressions have been obtained. We also analyzed some limit cases, under which the constructed coherent states completely recover the coherent states of the Hermite oscillator.

Journal of Physics Conference Series•Dec 1, 2024•0 citations
In this paper, we introduce the generalized coherent states and Photon-added coherent states in the sence of Barut-Girardello for the nonlinear harmonic oscillator with position dependent effective mass.The study of the resolution of the unity as the fundamental property of coherent states, is done in Meijer Gfunction.Also, the non-classical features of these two states are calculated and analyized by using the probability distribution function and Mandel parameter.
Photon-added BarutndashndashndashGirardello 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.
Abstract Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut—Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover, it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
Using ladder operators for the non-linear oscillator with position-dependent effective mass, realization of the dynamic group SU(1,1) is presented. Keeping in view the algebraic structure of the non-linear oscillator, coherent states are constructed using Barut–Girardello formalism and their basic properties are discussed. Furthermore, the statistical properties of these states are investigated by means of Mandel parameter and second order correlation function. Moreover,it is shown that in the harmonic limit, all the results obtained for the non-linear oscillator with spatially varying mass reduce to corresponding results of the linear oscillator with constant mass.
We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients zn/n!z^n/\sqrt{n!}zn/n!​ of the canonical coherent states by a specific generalized factorial xnγ,σ!x_n^{γ,σ}!xnγ,σ​! where parameters γγγ and σσσ satisfy some conditions for which the normalization condition and the resolution of identity are verified. The obtained family is a generalization of the Barut-Girardello coherent states and those of the philophase states. In the particular case of parameters γγγ and σσσ, we attache these states to the pseudo-harmonic oscillator depending on two parameters α,β>0α,β> 0α,β>0. The obtained nonlinear coherent states are superposition of eigenstates of this oscillator. The associated Bargmann-type transform is defined and we derive some results.
In this paper, we construct a new class of generalized photon added coherent states (GPACSs), by excitations on a newly introduced family of generalized coherent states (GCSs) (A Dehghani and B Mojaveri 2012 J. Phys. A: Math. Theor. 45 095304 ), obtained via generalized hypergeometric type displacement operators acting on the vacuum state of the simple harmonic oscillator. We show that these states realize resolution of the identity property through positive definite measures on the complex plane. Meanwhile, we demonstrate that the introduced states can also be interpreted as nonlinear coherent states (NLCSs), with a spacial nonlinearity function. Finally, some of their non-classical features as well as their quantum statistical properties are compared with Agarwalʼs photon-added coherent states (PACSs),
Abstract We present details of the method for constructing the coherent states of the quantum harmonic oscillator model that exhibits the semiconfinement effect due to a specific change of its mass by position. Its energy spectrum completely overlaps with the Hermite oscillator energy spectrum, whereas the wavefunctions of the stationary states are expressed via the generalized Laguerre polynomials. Two different methods have been applied to compute the coherent states. They are generalized and Barut-Girardello coherent states methods. In both cases, the exact expressions have been obtained. We also analyzed some limit cases, under which the constructed coherent states completely recover the coherent states of the Hermite oscillator.