B. M. Rodríguez-Lara, H. M. Moya-Cessa
We show a right unitary transformation approach based on Susskind-Glogower operators that diagonalizes a generalized Dicke Hamiltonian in the field basis and delivers a tridiagonal Hamiltonian in the Dicke basis that is diagonalized by a set of orthogonal polynomials satisfying a three-term recurrence relation. Our result is used to deliver a closed form analytic time evolution for the case of a Jaynes-Cummings-Kerr model and to study the time evolution of the population inversion, reduced field entropy and Husimi's Q-function of the field for ensembles of interacting two-level systems under a Jaynes-Cummings-Kerr model.
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http://arxiv.org/abs/1207.6551
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