The Effect of Spin-Orbit Coupling on Spin-Polarized Cold Atomic Fermi Systems in Optical Lattices

Evidence of the stability of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase has recently been presented in Phys. Rev. Lett. 128, 203201 (2022), for dense spin-polarized Fermi atomic gases in optical lattices. Building upon these non-perturbative results, we investigate the effect of additional terms in the Hamiltonian to the FFLO phase, namely spin-orbit coupling and in- and out-of-plane Zeeman fields. Such terms can be engineered experimentally in cold atomic Fermi systems and are expected to open the possibility to observe exotic superfluid states with non-trivial topological properties. Preliminary mean-field results from Hartree-Fock-Bogoliubov (HFB) calculations will be discussed to shed light on the different orders that can emerge in the low-energy landscape of cold atomic systems in optical lattices. These HFB calculations may then be later interfaced with correlated Quantum Monte Carlo methodologies.