Non-equilibrium dynamical phases of the two-atom Dicke model

•We investigate the non-equilibrium dynamical phases of the two-atom Dicke model.•The dynamical phase diagram reveals a new kind of non-equilibrium mixed phase.•A new kind of dynamical phase transition is predicted from mixed phase to the superradiant phase.•In the dynamical phase diagram of the mixed phase, there are regions where the superradiant phase cannot exist.

In this paper, we investigate the non-equilibrium dynamical phases of the two-atom Dicke model, which can be realized in a two species Bose–Einstein condensate interacting with a single light mode in an optical cavity. Apart from the usual non-equilibrium normal and inverted phases, a non-equilibrium mixed phase is possible which is a combination of normal and inverted phase. A new kind of dynamical phase transition is predicted from non-superradiant mixed phase to the superradiant phase which can be achieved by tuning the two different atom–photon couplings. We also show that a dynamical phase transition from the non-superradiant mixed phase to the superradiant phase is forbidden for certain values of the two atom–photon coupling strengths.