The Dynamical Structure Factor of a Fermionic Super-solid on an Optical Lattice

We perform a Quantum Monte Carlo simulation and study of a cold atomic Fermi gas on a 2D optical lattice. This system is modeled with a Hubbard hamiltonian with on-site attractive interaction. At half-filling, when on average one fermion occupies each lattice site, with equal numbers of fermions spin up and spin down, the system displays an interesting supersolid phase: a superfluid with a checkerboard density modulation. Combining unbiased Auxiliary-Field Monte Carlo simulations with state-of-art analytic continuation techniques, we compute the density dynamical structure factor S(q,ω) of the system and the density response function χ(q), in order to characterize this supersolid phase. These results shed light on this interesting physical regime, where s-wave pairing superfluidity coexists with a non-uniform local density.