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Algebraic structure and analytic solutions of generalized three-levelJaynes-Cummings models

Jie Jie, QLWang, SJWei

Published Jan 1, 1997• 0 citations
OpenAlex

Abstract

A generalized three-level Jaynes-Cummings model (JCM) which includes A generalized three-level Jaynes-Cummings model (JCM) which includes

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A generalized three-level Jaynes - Cummings model (JCM) which includes various ordinary JCMs is shown explicitly to have an SU(3) structure: the Hamiltonian can be treated as a linear function of the generators of the SU(3) group. Based on this algebraic structure, the exact algebraic solutions of the Schrödinger equation, as well as eigenvalues and eigenstates of the Hamiltonian, are obtained by an algebraic method. Thus the three-level JCM is completely solved algebraically. The SU(N) structure of the N-level JCM is also constructed explicitly and can be solved by the same method.
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.