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We study an optical cavity coupled to a lattice of Rydberg atoms, which can be represented by a generalized Dicke model. We show that the competition between the atom-atom interaction and atom-light coupling induces a rich phase diagram. A novel superradiant solid (SRS) phase is found, where both the superradiance and crystalline orders coexist. Different from the normal second order superradiance transition, here both the solid-1/2 and SRS to SR phase transitions are first order. These results are confirmed by large scale quantum Monte Carlo simulations.
Zhang et al. (Tue,) studied this question.