Quantum phase transition of two-level atoms interacting with a finite radiation field

Abstract

We introduce a group-theoretical extension of the Dicke model which describes an ensemble of two-level atoms interacting with a finite radiation field. The later is described by a spin model which exhibits the main properties of the Kerr medium, and whose main feature is that it possesses a maximum number of excitations. We use the energy surface minimization method to demonstrate that the extended Dicke model exhibits a quantum phase transition, and we analyse its dependence upon the maximum number of excitations of the model. Our analysis is carried out via three methods: through mean-field analysis (i.e. by using the tensor product of coherent states), by using parity-preserving symmetry-adapted states (using the critical values obtained in the meanfield analysis and numerically minimizing the energy surface) and by means of the exact quantum solution (i.e. by numerically diagonalizing the Hamiltonian). Possible connections with the qpdeformed algebras are also discussed.