Topological Superradiant States in a Degenerate Fermi Gas

We predict the existence of a topological superradiant state in a two-component degenerate Fermi gas in a cavity. The superradiant light generation in the transversely driven cavity mode induces a cavity-assisted spin-orbit coupling and opens a bulk gap at half filling. This mechanism can simultaneously drive a topological phase transition in the system, yielding a topological superradiant state. We map out the steady-state phase diagram in the presence of an effective Zeeman field, and identify a critical tetracritical point beyond which the topological and the conventional superraidiant phase boundaries separate. The topological phase transition can be detected from its signatures in either the momentum distribution of the atoms or the variation of the cavity photon occupation due to the nontrivial feedback of the atoms on the cavity field.