Fulde-Ferrell-Larkin-Ovchinnikov Phase and Beyond in the Ground State of Spin-Polarized Cold Atoms in Optical Lattices

We study the ground state of spin-polarized cold atoms in a two-dimensional optical lattice in the bulk limit by interfacing state-of-the-art Hartree-Fock-Bogoliubov calculations with cutting-edge correlated Quantum Monte Carlo techniques. Leveraging recent methodological advances, we are able to systematically study large lattice sizes, hosting nearly 500 atoms, which allows us to minimize finite-size effects and to provide robust results in the thermodynamic limit. We focus on 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, significantly different from the standard mean-field description. We also explore the effects of introducing spin-orbit coupling, which opens the possibility to observe topological superfluids, with fascinating connection with Majorana fermions.