The exact solution of generalized Dicke models via Susskind-Glogower operators

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. This tridiagonal Hamiltonian 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 Dicke-Kerr model.