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 Optics

U(1/1)qq-coherent states and theq-deformed Jaynes-Cummings Model

Le‐Man Kuang

Published Mar 1, 1994• 14 citations
Publisher

Abstract

A q-coherent state for the quantum superalgebra U(1/1) is introduced. A path integral formalism for the q-coherent state is constructed and applied to the q-deformed Jaynes-Cummings model (q-JCM) with the Uq(1/1) dynamical supersymmetry. The complete energy spectrum of the q-JCM is obtained for both the cases when the interaction constants are C-valued and when they are Grassmann valued.

DOI
10.1080/09500349414550501

Related papers

U(1/1) q q -Coherent States and Path Integrals for the q -Deformed Jaynes-Cummings Model

Le‐Man Kuang, Fa-Bo Wang, Gao-Jian Zeng

The q -coherent states for the quantum superalgebra U(1/1) q , are introduced. Path integrals in the q -coherent state representations of the U(1/1) q , are constructed and applied to the q -deformed Jaynes-Cummings model whose dynamical superalgebra is the quantum super-algebra U(1/1) q .

Communications in Theoretical Physics•Jun 15, 1994•0 citations

A two-parameter deformation of the Jaynes-Cummings model: path integral representation

R. Chakrabarti, R. Jagannathan

A two-parameter (p, q) deformation of the Jaynes-Cummings model is obtained using a recently developed (p, q)-deformed oscillator. In the rotating wave approximation (RWA) the dynamical symmetry of the model is the quantum superalgebra u p,q (1 mod 1). The partition function of the model is obtained as a path integral over generalized Perelomov coherent states corresponding to the quantum algebra U p.q (1 mod 1). The complete spectrum of the model is extracted for both the case when the coupling constants are Grassman valued and when they are c-number valued. It is noted that a relaxation of the RWA extends the dynamical symmetry to the quantum superalgebra osp p,q (2 mod 2).

Journal of Physics A Mathematical and General•Dec 7, 1992•12 citations

U(1/1) coherent states and a path integral for the Jaynes-Cummings model

E. A. Kochetov

The path integral over the coherent states of the U(1/1) superalgebra is constructed. It is applied to the Jaynes-Cummings model whose dynamical group is U(1/1).

Journal of Physics A Mathematical and General•Jan 21, 1992•10 citations

Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model

Масуд Чайчиан, Demosthenes Ellinas, P. P. Kulish

The q-deformations of the quantum harmonic oscillator are used for to describe the generalized Jaynes-Cummings model (JCM) by using the q-analog of the Holstein-Primakoff realization of the su(1,1). The corresponding dynamical symmetry is described by a quantum algebra. The q-analogs of the Barut-Girardello and the Perelomov coherent states are introduced and the expectation value of ${\mathrm{\ensuremath{\sigma}}}_{3}$ is calculated. The periodic revivals of the generalized JCM are destroyed for increasing deformation parameter q. The deformed original JCM in the rotating-wave approximation can be described by the u(1\ensuremath{\Vert}1${)}_{\mathit{q}}$, while its relaxation extends the dynamical algebra to the osp(2\ensuremath{\Vert}2${)}_{\mathit{q}}$ quantum superalgebra.

Physical Review Letters•Aug 20, 1990•346 citations

The f-deformed Jaynes–Cummings model and its nonlinear coherent states

O de los Santos-Sánchez, J. Récamier

Based on the f-oscillator formalism, we introduce a nonlinear Jaynes–Cummings model (NJCM) which is constructed from the standard JCM by deforming the single-mode field operators. Such a generalization of the JCM describes the interaction of a two-level atom with a single mode of the electromagnetic field in the presence of a nonlinear Kerr-like medium. Since the medium is modelled as an f-oscillator, it is possible to consider the field f-coherent states (nonlinear coherent states) and their evolution.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 9, 2011•69 citations

The q-deformed Jaynes-Cummings Model and its q-Supercoherent States

Hao San-Ru, Wang, Lu-Ya

In this paper, we have proposed a q-deformed Jaynes-Cummings(JC) model and constructed the q-SuperCoherent States(q-SCSs) for the q-deformed JC model. We have also discussed the properties of the q-supercoherent states and given the completeness relation expression. The representation of the q-supercoherent states for the q-deformed JC model is studied as well. PACS number(s): 03.65.Nk Key Works: q-deformed JC model, q-supercoherent states,q-SCSs representation.

arXiv:quant-ph/0112175•Dec 30, 2001•0 citations
A q-coherent state for the quantum superalgebra U(1/1) is introduced. A path integral formalism for the q-coherent state is constructed and applied to the q-deformed Jaynes-Cummings model (q-JCM) with the Uq(1/1) dynamical supersymmetry. The complete energy spectrum of the q-JCM is obtained for both the cases when the interaction constants are C-valued and when they are Grassmann valued.
A two-parameter (p, q) deformation of the Jaynes-Cummings model is obtained using a recently developed (p, q)-deformed oscillator. In the rotating wave approximation (RWA) the dynamical symmetry of the model is the quantum superalgebra u p,q (1 mod 1). The partition function of the model is obtained as a path integral over generalized Perelomov coherent states corresponding to the quantum algebra U p.q (1 mod 1). The complete spectrum of the model is extracted for both the case when the coupling constants are Grassman valued and when they are c-number valued. It is noted that a relaxation of the RWA extends the dynamical symmetry to the quantum superalgebra osp p,q (2 mod 2).
The q-deformations of the quantum harmonic oscillator are used for to describe the generalized Jaynes-Cummings model (JCM) by using the q-analog of the Holstein-Primakoff realization of the su(1,1). The corresponding dynamical symmetry is described by a quantum algebra. The q-analogs of the Barut-Girardello and the Perelomov coherent states are introduced and the expectation value of ${\mathrm{\ensuremath{\sigma}}}_{3}$ is calculated. The periodic revivals of the generalized JCM are destroyed for increasing deformation parameter q. The deformed original JCM in the rotating-wave approximation can be described by the u(1\ensuremath{\Vert}1)q{)}_{\mathit{q}})q​, while its relaxation extends the dynamical algebra to the osp(2\ensuremath{\Vert}2)q{)}_{\mathit{q}})q​ quantum superalgebra.
Based on the f-oscillator formalism, we introduce a nonlinear Jaynes–Cummings model (NJCM) which is constructed from the standard JCM by deforming the single-mode field operators. Such a generalization of the JCM describes the interaction of a two-level atom with a single mode of the electromagnetic field in the presence of a nonlinear Kerr-like medium. Since the medium is modelled as an f-oscillator, it is possible to consider the field f-coherent states (nonlinear coherent states) and their evolution.