Abstract In this paper, we present coherent states à la Gazeau-Klauder for a free particle in square well potential within position-deformed Heisenberg algebra . These states satisfy the Klauder’s mathematical requirement to build coherent states. Some statistical properties such as the probability distribution, the intensity correlation function and the Mandel parameter are calculated and analyzed. We find that these states are sub-Poissonian in nature. We also construct for these coherent states, the even cat states and we evaluate its Wigner function which analyses the quasiprobability distribution of these states. We graphically demonstrate that these states exhibit nonclassical behavior.Abstract In this paper, we present coherent states à la Gazeau-Klauder for a free particle in square well potential within position-deformed Heisenberg algebra . These states satisfy the Klauder’s mathematical requirement to build coherent states. Some statistical properties such as the probability distribution, the intensity correlation function and the Mandel parameter are calculated and analyzed. We find that these states are sub-Poissonian in nature. We also construct for these coherent states, the even cat states and we evaluate its Wigner function which analyses the quasiprobability distribution of these states. We graphically demonstrate that these states exhibit nonclassical behavior.

Journal of Physics CommunicationsAug 1, 20224 citations

Nonlinear Coherent States and Some of Their Properties

J. Récamier, M. Gorayeb, Wolf Luis Mochán +1 more

International Journal of Theoretical PhysicsAug 8, 200733 citations

Coherent States with Complex Functions

K. Thirulogasanthar, G. Honnouvo, G. Honnouvo

arXiv:math-ph/0307054International Journal of Theoretical PhysicsApr 1, 20041 citation

Deformed Weyl–Heisenberg algebra and quantum decoherence effect

Sh. Dehdashti, M. Bagheri Harouni, Ali Mahdifar +1 more

We study the dynamics of a catlike superposition of f-deformed coherent states under dissipative decoherence. For this purpose, we investigate two important categories of f-deformed coherent states: Gazeau–Klauder and displacement-type coherent states. In addition, we consider two deformation functions; one of them describes a harmonic oscillator in an infinite well and another corresponds to a harmonic oscillator in a quantum well with finite depth. The decoherence effects appeared through a dissipative interaction of the environment with the catlike states. In this study, we first show that the Gazeau–Klauder coherent state is more resistant under the decoherence process, in contrast to the displacement-type one, and second, that the potential range of the infinite well and the depth of potential possess a remarkable role in the decoherence process.We study the dynamics of a catlike superposition of f-deformed coherent states under dissipative decoherence. For this purpose, we investigate two important categories of f-deformed coherent states: Gazeau–Klauder and displacement-type coherent states. In addition, we consider two deformation functions; one of them describes a harmonic oscillator in an infinite well and another corresponds to a harmonic oscillator in a quantum well with finite depth. The decoherence effects appeared through a dissipative interaction of the environment with the catlike states. In this study, we first show that the Gazeau–Klauder coherent state is more resistant under the decoherence process, in contrast to the displacement-type one, and second, that the potential range of the infinite well and the depth of potential possess a remarkable role in the decoherence process.

Laser PhysicsApr 15, 20146 citations

$(q;l,λ)-$ deformed Heisenberg algebra: representations, special functions and quantization$(q;l,λ)-$deformed Heisenberg algebra: representations, special functions and quantization

Mahouton Norbert Hounkonnou, Sama Arjika, Ezinvi Baloïtcha

This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements $ρ(z',z)$ , derivedfrom $(q;l,λ)-$ deformed boson coherent states.The induced $ρ(z',z)$ self-reproducing property with the associated self-reproducing kernel $K(z',z)$ is computed and analyzed. An explicit construction of novel classes of generalized continuous $(q;l,λ)-$ Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements $ρ(z',z)$, derivedfrom $(q;l,λ)-$deformed boson coherent states.The induced $ρ(z',z)$ self-reproducing property with the associated self-reproducing kernel $K(z',z)$ is computed and analyzed. An explicit construction of novel classes of generalized continuous $(q;l,λ)-$Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.

arXiv:1301.7028Jan 29, 20130 citations

Truncated exponential polynomials and truncated coherent states

Won Sang Chung, HASSAN HASSANABADI

The European Physical Journal PlusJul 1, 202010 citations

(q;l,λ)-

deformed Heisenberg algebra: representations, special functions and quantization

This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements

ρ(z',z)

, derivedfrom

(q;l,λ)-

deformed boson coherent states.The induced

ρ(z',z)

self-reproducing property with the associated self-reproducing kernel

K(z',z)

is computed and analyzed. An explicit construction of novel classes of generalized continuous

(q;l,λ)-

Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.