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

M. Chaichian; D. Ellinas; P. Kulish

doi:10.1103/PhysRevLett.65.980

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

M. Chaichian, D. Ellinas, and P. Kulish

Phys. Rev. Lett. 65, 980 – Published 20 August 1990

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 $σ_{3}$ 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 $)_{q}$ , while its relaxation extends the dynamical algebra to the osp(2‖2 $)_{q}$ quantum superalgebra.

Received 13 April 1990

DOI:https://doi.org/10.1103/PhysRevLett.65.980

Authors & Affiliations

M. Chaichian, D. Ellinas, and P. Kulish

Department of High Energy Physics, University of Helsinki, Siltavuorenpenger 20 C, SF-00170 Helsinki, Finland
Department of Theoretical Physics, University of Helsinki, Siltavuorenpenger 20 C, SF-00170 Helsinki, Finland
Research Institute for Theoretical Physics, University of Helsinki, Siltavuorenpenger 20 C, SF-00170 Helsinki, Finland