Pauli Crystal Superradiance.

Pauli crystals are unique geometric structures of noninteracting fermions, resembling crystals, that emerge solely from Fermi statistics and confinement. Unlike genuine quantum crystals that arise from interparticle interactions, Pauli crystals do not break translation symmetry but nonetheless exhibit nontrivial many-body correlations. In this Letter, we explore Pauli crystal formation in a cavity-fermion setup. We analytically show that when coupled to a cavity, degeneracy in Pauli crystals can trigger zero-threshold transitions to superradiance. This superradiance is accompanied by the emergence of a genuine quantum crystalline state, wherein the atomic density is periodically modulated. We substantiate our findings using state-of-the-art numerical simulations. The combined interplay between statistics, confinement geometry, and interactions mediated by light thus facilitates a novel pathway to quantum crystallization.