The exact solution of generalized Dicke models via Susskind–Glogower operators
B. M. Rodríguez-Lara, H. M. Moya-Cessa · 2016
Abstract. 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. PACS numbers: 02.30.Ik,03.65.Fd,42.50.Pq