The Single Particle Excitation Spectrum of Degenerate Fermi gases in a ring cavity

By considering a spin-$\frac{1}{2}$ degenerate Fermi gases in a ring cavity where strong interaction between atoms and light gives rise to a superradiance, we find the cavity dissipation could cause a severe broadening in some special cases, breaking down the quasi-particle picture which was constantly assumed in mean field theory studies. This broadening happens when the band gap resonant with polariton excitation energy. Interestingly enough, this broadening is highly spin selective depending on how the fermions are filled and the spectrum becomes asymmetric due to dissipation. Further, a non-monotonous dependence of the maximal broadening of the spectrum against cavity decay rate $\kappa$ is found and the largest broadening emerges at $\kappa$ comparable to recoil energy.