The Dynamical Structure Factor of a Fermionic Supersolid on an Optical Lattice

We perform a Quantum Monte Carlo study of a cold Fermi gas on a 2D optical lattice, realized with laser standing waves. The system is modeled with a Hubbard hamiltonian with on-site attractive interaction. At half-filling, when on average one fermion occupies each lattice site, the system displays an intriguing supersolid phase: a superfluid with a checkerboard density modulation. Interfacing unbiased Auxiliary-Field Monte Carlo simulations with state-of-art analytic continuation techniques, we compute the density dynamical structure factor $S({\bf{q}},\omega)$ of the system and the density response function $\chi({\bf{q}})$, in order to characterize this supersolid phase. These results shed light into this interesting physical regime, where $s$-wave pairing superfluidity coexists with a non-uniform local density.