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We consider a gas of ultracold two-level atoms confined in a cavity, takinginto account for atomic center-of-mass motion and cavity mode variations. Weuse the generalized Dicke model, and analyze separately the cases of aGaussian, and a standing wave mode shape. Owing to the interplay betweenexternal motional energies of the atoms and internal atomic and field energies,the phase-diagrams exhibit novel features not encountered in the standard Dickemodel, such as the existence of first and second order phase transitionsbetween normal and superradiant phases. Due to the quantum description ofatomic motion, internal and external atomic degrees of freedom are highlycorrelated leading to modified normal and superradiant phases.

Dilute gas of ultracold two-level atoms inside a cavity; generalized Dicke model