The dynamical structure factor of a fermionic supersolid on an optical lattice

We perform a Quantum Monte Carlo study of a spin-balanced two-dimensional cold Fermi gas on an optical lattice, which can be experimentally 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, in order to characterize the dynamical properties of this supersolid phase. We find evidence of the existence of two collective modes, which we interpret as arising from the two broken symmetries in the system: $s$-wave pairing superfluidity coexists with a non-uniform local density. The mapping $U \to -U$ in the Hubbard model makes these results important for the repulsive model as well. Furthermore, this work paves the way for an investigation of the behavior of the model when we move away from half-filling, either changing the density or introducing a spin polarization.