Detecting the Fermi surface nesting effect for the fermionic Dicke transition by trap-induced localization

Recently, the statistical effect of fermionic superradiance has been verified by a series of experiments both in free space and in a cavity. The Pauli blocking effect can be visualized by a 1/2 scaling of the Dicke transition critical pumping strength against the particle number $N_{\mathrm{at}}$ for fermions in a trap. However, the evidence for the Fermi surface (FS) nesting effect, which manifests the enhancement of superradiance by Fermi statistics, is still missing. Here we report a scheme for detecting FS nesting with the help of the trap-induced localization on the trap edge. We find two scalings of the critical pumping strength as $N_{\mathrm{at}}^{-1.33}$ and $N_{\mathrm{at}}^{-0.67}$ for a moderate particle number when localization enters and the Pauli blocking scaling $1/3$ (two-dimensional case) in the $N_{\mathrm{at}}\to \infty$ limit is unaffected. Further, we find the scaling of the critical pumping strength against the particle number increases with the ratio between the recoil energy and the trap frequency in the direction orthogonal to the pumping direction $E_R/{\omega }_z$. The scaling larger than 1 can be identified as a result of the Fermi surface nesting effect. Thus, we find a practical experimental scheme for visualizing the long-desired Fermi surface nesting effect with the help of trap-induced localization in a two-dimensional Fermi gas in a cavity.