Interactions between light and matter lie at the very fundamental level of our physical world. The introduction of atomic gases into optical cavities opens the prospect of realizing effective long-range interatomic interactions via the mediation of cavity fields. We consider a degenerate Fermi gas placed inside a cavity and study the critical strength of pumping field for driving a superradiance transition, through which a charge density wave order of the Fermi gases emerges. For a single component Fermi gas, we find that Fermi surface nesting effect strongly enhances the superradiance tendency . We further study a two-component Fermi gas in a cavity near a Feshbach resonance. We show that as the two-component Fermi gas passes through the BEC-BCS crossover, the superradiant phase transition undergoes a corresponding crossover from a fermionic behavior on the weakly interacting BCS side, to a bosonic behavior on the molecular BEC side .
 Yu Chen, Zhenhua Yu, and Hui Zhai, Phys. Rev. Lett. 112, 143004 (2014)
 Yu Chen, Hui Zhai, and Zhenhua Yu, Phys. Rev. A 91, 021602 (R) (2015)