Superradiant Transition to a Fermionic Quasicrystal in a Cavity

Abstract: Recently, the steady state superradiance in degenerate Fermi gases has been realized in a cavity, following the previous discovery of the Dicke transition in Bose gases. The most prominent signature of fermionic Dicke transition is its density dependence, which is manifested as the Fermi surface nesting effect and the Pauli blocking effect. We study the superradiant transition in one-dimensional Fermi gases in a cavity with the presence of an incommensurate dipolar lattice. We find a first-order Dicke transition induced by indirect resonance effect, which is a resonance between two atomic levels by the level repulsion from a third level, and causes extra gap opening. By formulating a phenomenological theory, we find that the critical pumping strength for this first-order Dicke transition shows a linear V-shape kink near a particular indirect resonance modified filling $\nu_{\rm IRM}$. The presence and the unique density dependence of this transition manifest the fermionic nature and verify the mechanism of the quasicrystal superradiant transition.