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 A Mathematical and General

Gazeau-Klauder coherent states in one-mode systems with periodic potential

J M Hollingworth, A. Konstadopoulou, Spiros Chountasis, Apostol Vourdas, Nigel B. Backhouse

Published Oct 31, 2001• 13 citations
Publisher

Abstract

Gazeau-Klauder coherent states for a one-mode system with sinusoidal potential, are introduced. Their quantum statistical properties and their uncertainties are studied. The effect of dissipation on these states is estimated. The evolution of the ordinary (Glauber) coherent states in this system, is also studied. It is shown that these states evolve into superpositions of many macroscopically distinguishable states (`multi-Schrödinger cats').

DOI
10.1088/0305-4470/34/44/308

Related papers

Gazeau–Klauder cat states

Jerzy Dajka, J. Łuczka

Generalization of single-mode Schrödinger cat states is proposed, and their construction in terms of superposition of Gazeau–Klauder coherent states is presented. A comparative analysis of selected properties of this novel states for a nonlinear Kerr oscillator and the ‘traditional’ Schrödinger cats is given with emphasis on the photon statistics and the properties of non-cyclic geometric phase. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.

Journal of Physics A Mathematical and Theoretical•May 30, 2012•5 citations

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.

Laser Physics•Apr 15, 2014•6 citations

Gazeau-Klauder coherent states in position-deformed Heisenberg algebra

Latévi M. Lawson, Prince K. Osei

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 Communications•Aug 1, 2022•4 citations

Wave packet dynamics of nonlinear Gazeau-Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

F. B. Migueu, M. Vubangsi, Martin Tchoffo +1 more

A D = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.

Chinese Physics B•Jan 4, 2021•0 citations

Generation of Glauber Coherent State Superpositions via Unitary Transformations

ANTONINO MESSINA, Benedetto Militello, Anna Napoli

Since their introduction by Glauber in 1963 [1], coherent states have been deeply studied [2] due to the fact that, in some sense, the statistical properties related to the first momenta of their Fock distribution exhibit features interpretable in the realm of classical probability theory. Of course the quantum nature of a coherent state, and ultimately the granularity of the energy of a quantum harmonic oscillator, becomes more and more evident when higher momenta of the Fock distribution are considered. It is of relevance that coherent states of both a mechanical quantum oscillator or a quantized mode of an electromagnetic resonator may be currently proposed in accordance with well-defined protocols. Even more interesting is the fact that they provide the effective possibility of realizing interesting experiments able to bring to the light peculiarities of quantum mechanics. In particular, the very famous gedanken Schrodinger Cat State (SCS) experiment [3] consisting in entangling a microscopic quantum object (an atom) with a macroscopic one (a cat) has been realized. No unfortunate feline has been tortured! Trapped ions have been indeed exploited. In fact, such systems provide the possibility of testing fundamental quantum physics aspects giving at experimentalist’s disposal compound quantum systems consisting of a few-level atomic part and a tri-dimensional harmonic oscillator describing the center of mass motion of an ion confined into a Paul trap. Suitably acting upon the system with Raman lasers it is possible to engineer the Schrodinger Cat-like state [4, 5]

•Jan 1, 2004•2 citations

Gazeau–Klauder coherent states for trigonometric Rosen–Morse potential

Alireza Chenaghlou, Omid Faizy

The Gazeau–Klauder coherent states for the trigonometric Rosen–Morse potential are constructed. It is shown that the resolution of unity, temporal stability, and action identity conditions are satisfied for the coherent states. The Mandel parameter is also calculated for the weighting distribution function corresponding to the coherent states.

Journal of Mathematical Physics•Feb 1, 2008•13 citations
Gazeau-Klauder coherent states for a one-mode system with sinusoidal potential, are introduced. Their quantum statistical properties and their uncertainties are studied. The effect of dissipation on these states is estimated. The evolution of the ordinary (Glauber) coherent states in this system, is also studied. It is shown that these states evolve into superpositions of many macroscopically distinguishable states (`multi-Schrödinger cats').
Generalization of single-mode Schrödinger cat states is proposed, and their construction in terms of superposition of Gazeau–Klauder coherent states is presented. A comparative analysis of selected properties of this novel states for a nonlinear Kerr oscillator and the ‘traditional’ Schrödinger cats is given with emphasis on the photon statistics and the properties of non-cyclic geometric phase. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’.
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.
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.
Since their introduction by Glauber in 1963 [1], coherent states have been deeply studied [2] due to the fact that, in some sense, the statistical properties related to the first momenta of their Fock distribution exhibit features interpretable in the realm of classical probability theory. Of course the quantum nature of a coherent state, and ultimately the granularity of the energy of a quantum harmonic oscillator, becomes more and more evident when higher momenta of the Fock distribution are considered. It is of relevance that coherent states of both a mechanical quantum oscillator or a quantized mode of an electromagnetic resonator may be currently proposed in accordance with well-defined protocols. Even more interesting is the fact that they provide the effective possibility of realizing interesting experiments able to bring to the light peculiarities of quantum mechanics. In particular, the very famous gedanken Schrodinger Cat State (SCS) experiment [3] consisting in entangling a microscopic quantum object (an atom) with a macroscopic one (a cat) has been realized. No unfortunate feline has been tortured! Trapped ions have been indeed exploited. In fact, such systems provide the possibility of testing fundamental quantum physics aspects giving at experimentalist’s disposal compound quantum systems consisting of a few-level atomic part and a tri-dimensional harmonic oscillator describing the center of mass motion of an ion confined into a Paul trap. Suitably acting upon the system with Raman lasers it is possible to engineer the Schrodinger Cat-like state [4, 5]