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Título: The Super-radiant Phase Transition in Entangled N-Atoms System

Resumo: We consider the Dicke spin-boson model composed by a single bosonic  mode and an ensemble of N identical two-level atoms. Assuming that the system is in thermal equilibrium with a reservoir at some temperature we consider the situation where the coupling between the bosonic mode and the atoms generates real and virtual processes. Furthermore we also consider the dipole-dipole interaction, which generates entangled states in the atomic system. The quantum phase transition and the transition from fluorescent to super-radiant phase is investigated in this situation.