ar X iv : 0 90 9 . 17 25 v 1 [ qu an t - ph ] 9 S ep 2 00 9 Entangled States and Super - radiant Phase Transition

The Dicke spin-boson model is composed by a single bosonic mode and an ensemble of N identical two-level atoms. Assuming thermal equilibrium with a reservoir at temperature β, we consider the situation where the coupling between the bosonic mode and the atoms generates resonant and non-resonant processes. The thermodynamic of the model is investigated. Next we introduce dipole-dipole interaction between the atoms. We investigate the transition from fluorescent to super-radiant phase and the quantum phase transition in a situation where the dipole-dipole interaction between the atoms generates entangled states in the atomic system. We proved that, the critical behavior is not modified by the introduction of the dipole-dipole interaction. PACS numbers: 42.50.Nn, 05.30.Jp, 73.43.Nq e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]