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Communications in Theoretical Physics

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

Published Jun 15, 1994• 0 citations
Publisher

Abstract

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 .
DOI
10.1088/0253-6102/21/4/441

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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.