Entangled states and superradiant phase transitions

The full Dicke model is composed of a single bosonic mode and an ensemble of N identical two-level atoms. In the model, the coupling between the bosonic mode and the atoms generates resonant and nonresonant processes. We also consider a dipole-dipole interaction between the atoms, which is able to generate entangled states in the atomic system. By assuming thermal equilibrium with a reservoir at temperature β-1, the transition from fluorescent to superradiant phase and the quantum phase transition are investigated. It is shown that the critical behavior of the full Dicke model is not modified by the introduction of the dipole-dipole interaction.