Effect of cavity-induced long-range interactions between two-component fermions on optical lattices

We study interacting two-component fermions subjected to a periodic optical lattice potential and an optical cavity. In addition to the tunneling interaction and on-site interaction modified by the optical lattice potential, the cavity photons mediate long-range interactions between Fermi atoms. At the steady-state limit of the cavity photon decay, the photon mediated long-range interaction that contains a spin-flip term. After decoupling this spin-flip interaction term using a mean-field theory, we introduce a unitary transformation to convert our Hamiltonian into an effectively site-dependent population-imbalance quasi-fermion system. We then solve our effective Hamiltonian to study the effect of the long-range interactions on physical properties using standard theoretical approaches.