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

Abstract

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.