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arXiv:hep-th/0007167 · International Journal of Modern Physics B

A GENERALIZED JAYNES–CUMMINGS MODEL: NONLINEAR DYNAMICAL SUPERALGEBRA u(1/1) AND SUPERCOHERENT STATES

Mohammed Daoud A, Jamila Douari

Published May 10, 2003• 12 citations
arXivHTMLPDF

Abstract

The generalization of the Jaynes–Cummings (GJC) Model is proposed. In this model, the electromagnetic radiation is described by a Hamiltonian which generalizes the harmonic oscillator to take into account some nonlinear effects which can occur in the experimental situations. The dynamical superalgebra and supercoherent states of the related model are explicitly constructed. Relevant quantities (total number of particles, energy and atomic inversion) are computed.

DOI
10.1142/s0217979203018302

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The unitary transformation method is utilized for the closed form solution of the nonlinear generalization of the Jaynes–Cummings (JC) model, which includes arbitrary multiphoton and intensity-dependent interactions between radiation and matter. Specifically, the unitary transformation leading to the diagonalization of the relevant Hamiltonian is established and energy levels and eigenstates are derived. It is also shown that the results for the JC model can be extended to the anti-Jaynes–Cummings (AJC) model through the map between the two models.