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.