Quantum phases of spinful Fermi gases in optical cavities

We explore the quantum phases emerging from the interplay between spin and motional degrees of freedom of a one-dimensional quantum fluid of spinful fermionic atoms, effectively interacting via a photon-mediating mechanism with tunable sign and strength g, as it can be realized in present-day experiments with optical cavities. We find the emergence, in the very same system, of spin- and atomic-density wave ordering, accompanied by the occurrence of superfluidity for g > 0, while cavity photons are seen to drive strong correlations at all g values, with fermionic character for g > 0, and bosonic character for g < 0. Due to the long-range nature of interactions, to infer these results we combine mean-field and exact diagonalization methods supported by bosonization analysis.