Ground state correlations in spin-polarized attractive fermions on optical lattices

We compute ground state correlations in a system of spin-polarized cold atoms moving on a two-dimensional optical lattice. We focus on the the bulk limit by leveraging an interface between correlated Quantum Monte Carlo techniques and Hartree-Fock-Bogoliubov calculations. Our recent methodological advances allow us to simulate lattices hosting nearly 500 atoms, which helps us minimize finite-size effects. We systematically explore the high density and small spin polarization regime, which is believed to be most favorable to the emergence of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. We find clear evidence of FFLO order, which appears to be part of an intricate coexistence of long-range orders. We also explore the effects of introducing spin-orbit coupling, which opens the possibility to observe topological superfluids, with intriguing connection with Majorana fermions.