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

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 ${\mathrm{\sigma }}_3$ 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‖1${)}_{\mathit{q}}$, while its relaxation extends the dynamical algebra to the osp(2‖2${)}_{\mathit{q}}$ quantum superalgebra.