A Generalized Jaynes-Cummings Model: Nonlinear dynamical superalgebra $u(1\mathrm{/}1)$ and Supercoherent states

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