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 Physics Communications

Gazeau-Klauder coherent states in position-deformed Heisenberg algebra

Latévi M. Lawson, Prince K. Osei

Published Aug 1, 2022• 4 citations
Publisher

Abstract

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.

DOI
10.1088/2399-6528/ac8a8a

Related papers

Coherent states of position-dependent mass trapped in an infinite square well

Naila Amir, Shahid Iqbal

We develop generalized coherent states based on the Gazeau–Klauder formalism for a particle with position-dependent mass trapped in an infinite square well. We study the quantum statistical properties of these states by means of the Mandel parameter and the second-order correlation function. Our analysis reveals that the constructed coherent states exhibit sub-Poissonian statistics. Moreover, theoretical investigations of wave packet revivals and fractional revivals for the pertaining system have been performed by means of the autocorrelation function and temporal evolution of probability density.

Journal of Mathematical Physics•Aug 1, 2020•12 citations

Deformed Gazeau-Klauder Schrödinger cat states with modified commutation relations

Chee Leong Ching, Wei Khim Ng

Generalized coherent states under deformed quantum mechanics that exhibit intrinsic minimum length [Phys. Rev. D 86, 064038 (2012)] and maximum momentum [Phys. Rev. D 88, 084009 (2013)] have been well studied following the Gazeau-Klauder approach. In this paper, as an extension to the study of quantum deformation, we investigate the famous Schr\"odinger cat states (SCs) under these two classes of quantum deformation. Following the concept of generalized Gazeau-Klauder Schr\"odinger cat states (GKSCs) in [J. Phys. A 45, 244006 (2012)], we construct the deformed GKSCs for both phenomenological models that exhibit intrinsic minimum length and/or maximum momentum. All comparisons between minimum length and maximum momentum deformations are illustrated and plots are done in even and odd cat states since they are one of the most important classic statistical characteristics of SCs. Probability distribution and entropies are studied. In general, deformed cat states do not possess the original even and odd state statistical properties. Nonclassical properties of the deformed GKSCs are explored in terms of the Mandel $Q$ parameter, quadrature squeezing $(\mathrm{\ensuremath{\Delta}}{X}_{q})\ifmmode\cdot\else\textperiodcentered\fi{}(\mathrm{\ensuremath{\Delta}}{Y}_{q})$, as well as Husimi quasiprobability distribution $\mathcal{Q}$. Some of these distinguishing quantum-gravitational features may possibly be realized qualitatively and even be measured quantitatively in future experiments with the advanced development in quantum atomic and optics technology.

arXiv:1907.04506•Physical review. D/Physical review. D.•Oct 25, 2019•8 citations

Generalized coherent states and their statistical characteristics in power-law potentials

Shahid Iqbal, Farhan Saif

Generalized coherent states based on Gazeau-Klauder formalism are developed for one-dimensional power-law potentials and their quantum statistical characteristics, together with generalized Heisenberg algebra coherent states, are reported. We show that these states exhibit super-Poissonian, Poissonian, or sub-Poissonian distributions as a function of the power-law exponent. The analytical results are supported by numerical calculations. In addition, we explain possible sources of errors in numerical analysis.

Journal of Mathematical Physics•Aug 1, 2011•21 citations

$(q;l,λ)$-deformed Heisenberg algebra: coherent states, their statistics and geometry

Joseph Désiré Bukweli, Mahouton Norbert Hounkonnou

The Heisenberg algebra is deformed with the set of parameters ${q, l,λ}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.

arXiv:1211.3312•Nov 14, 2012•0 citations

Investigating and analysis of the properties of coherent states of a deformed nonlinear harmonic oscillator

Daeimohammad, Mohsen, Nili Ahmadabadi, Mohammad

In this research, we study the coherent states of a deformed nonlinear harmonic oscillator. We use the perturbation theory to compute eigenstates and eigen-values ​​for a deformed nonlinear harmonic oscillator and then define the generalized coherent states based on the Gazeau-Klauder formulation. Then, using the Mandel parameter and the second-order correlation function, we will investigate the statistical properties of the system. The analysis shows that the coherent states for a deformed and non-deformed nonlinear harmonic oscillator follows the sub-Poissonian and super-Poissonian statistics, and exhibits the antibunching and bunching effects, respectively. In addition, we show that the anti-correlation function for a deformed nonlinear oscillator is strongly fluctuating and irregular. Also, the anti-correlation function of a non-deformed nonlinear harmonic oscillator shows the phenomena of collapse and revival of fractional revelations. We also examine the limits of different parameters so that the obtained results are valid.

Iranian Journal of Physics Research•Sep 1, 2023•0 citations

KLAUDER–PERELOMOV AND GAZEAU–KLAUDER COHERENT STATES FOR SOME SHAPE INVARIANT POTENTIALS

Alireza Chenaghlou, Hossein Fakhri

Firstly, the solvability of some quantum models like Eckart and Rosen–Morse II are explained on the basis of the shape invariance theory. Then, two generalized types of the Klauder–Perelomov and Gazeau–Klauder coherent states are calculated for the models. By means of calculating the Mandel parameter, it is shown that the weight distribution function of the first type coherent states obeys the Poissonian and super-Poissonian statistics, however, the weight distribution function of the second type coherent states obeys the Poissonian and sub-Poissonian statistics.

Modern Physics Letters A•Aug 30, 2002•27 citations
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.
We develop generalized coherent states based on the Gazeau–Klauder formalism for a particle with position-dependent mass trapped in an infinite square well. We study the quantum statistical properties of these states by means of the Mandel parameter and the second-order correlation function. Our analysis reveals that the constructed coherent states exhibit sub-Poissonian statistics. Moreover, theoretical investigations of wave packet revivals and fractional revivals for the pertaining system have been performed by means of the autocorrelation function and temporal evolution of probability density.
Generalized coherent states under deformed quantum mechanics that exhibit intrinsic minimum length [Phys. Rev. D 86, 064038 (2012)] and maximum momentum [Phys. Rev. D 88, 084009 (2013)] have been well studied following the Gazeau-Klauder approach. In this paper, as an extension to the study of quantum deformation, we investigate the famous Schr\"odinger cat states (SCs) under these two classes of quantum deformation. Following the concept of generalized Gazeau-Klauder Schr\"odinger cat states (GKSCs) in [J. Phys. A 45, 244006 (2012)], we construct the deformed GKSCs for both phenomenological models that exhibit intrinsic minimum length and/or maximum momentum. All comparisons between minimum length and maximum momentum deformations are illustrated and plots are done in even and odd cat states since they are one of the most important classic statistical characteristics of SCs. Probability distribution and entropies are studied. In general, deformed cat states do not possess the original even and odd state statistical properties. Nonclassical properties of the deformed GKSCs are explored in terms of the Mandel QQQ parameter, quadrature squeezing $(\mathrm{\ensuremath{\Delta}}{X}_{q})\ifmmode\cdot\else\textperiodcentered\fi{}(\mathrm{\ensuremath{\Delta}}{Y}_{q})$, as well as Husimi quasiprobability distribution Q\mathcal{Q}Q. Some of these distinguishing quantum-gravitational features may possibly be realized qualitatively and even be measured quantitatively in future experiments with the advanced development in quantum atomic and optics technology.
Generalized coherent states based on Gazeau-Klauder formalism are developed for one-dimensional power-law potentials and their quantum statistical characteristics, together with generalized Heisenberg algebra coherent states, are reported. We show that these states exhibit super-Poissonian, Poissonian, or sub-Poissonian distributions as a function of the power-law exponent. The analytical results are supported by numerical calculations. In addition, we explain possible sources of errors in numerical analysis.
(q;l,λ)(q;l,λ)(q;l,λ)-deformed Heisenberg algebra: coherent states, their statistics and geometry
The Heisenberg algebra is deformed with the set of parameters q,l,λ{q, l,λ}q,l,λ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.
In this research, we study the coherent states of a deformed nonlinear harmonic oscillator. We use the perturbation theory to compute eigenstates and eigen-values ​​for a deformed nonlinear harmonic oscillator and then define the generalized coherent states based on the Gazeau-Klauder formulation. Then, using the Mandel parameter and the second-order correlation function, we will investigate the statistical properties of the system. The analysis shows that the coherent states for a deformed and non-deformed nonlinear harmonic oscillator follows the sub-Poissonian and super-Poissonian statistics, and exhibits the antibunching and bunching effects, respectively. In addition, we show that the anti-correlation function for a deformed nonlinear oscillator is strongly fluctuating and irregular. Also, the anti-correlation function of a non-deformed nonlinear harmonic oscillator shows the phenomena of collapse and revival of fractional revelations. We also examine the limits of different parameters so that the obtained results are valid.
Firstly, the solvability of some quantum models like Eckart and Rosen–Morse II are explained on the basis of the shape invariance theory. Then, two generalized types of the Klauder–Perelomov and Gazeau–Klauder coherent states are calculated for the models. By means of calculating the Mandel parameter, it is shown that the weight distribution function of the first type coherent states obeys the Poissonian and super-Poissonian statistics, however, the weight distribution function of the second type coherent states obeys the Poissonian and sub-Poissonian statistics.