  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 atomic 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 (SR) transition, here both the Solid-1/2 and SRS to SR
phase transitions are first order. These results are confirmed by the large
scale quantum Monte Carlo simulations.
