In the present paper, we consider the steady state of Fermi atoms coupled to a shaken cavity field at half filling. This shaking generates a time-dependent dynamical optical lattice with backaction on the atomic degrees of freedom. In the high-frequency limit, the shaken dynamical optical lattice produces interesting cavity-field-dependent long-range hoppings, including the nearest-, next-nearest-, and next-next-nearest-neighbor hoppings. They can change the band structures of the system and thus induce nontrivial topological superradiant phases, especially with a large winding number and four degenerate edge states. We also briefly address possible experimental observations of the predicted topological superradiant phases. Our results provide an alternative way to explore novel many-body physics in cavity quantum electrodynamics systems.

• Received 22 November 2018

DOI:https://doi.org/10.1103/PhysRevA.99.043630