Dissipation-Driven Superradiant Phase Transition of a Two-Dimensional Bose–Einstein Condensate in a Double Cavity

We study superradiant phase transitions in a hybrid system of a two-dimensional Bose–Einstein condensate of atoms and two cavities arranged with a tilt angle. By adjusting the loss rate of cavities, we map out the phase diagram of steady states within a mean field framework. It is found that when the loss rates of the two cavities are different, superradiant transitions may not occur at the same time in the two cavities. A first-order phase transition is observed between the states with only one cavity in superradiance and both in superradiance. In the case that both cavities are superradiant, a net photon current is observed flowing from the cavity with small decay rate to the one with large decay rate. The photon current shows a non-monotonic dependence on the loss rate difference, owing to the competition of photon number difference and cavity field phase difference. Our findings can be realized and detected in experiments.