The fate of Fulde-Ferrell-Larkin-Ovchinnikov order in spin-orbit coupled cold atomic Fermi systems

This work will build on the recent non-perturbative results in Phys. Rev. Lett. 128, 203201

(2022), where a robust numerical evidence of the stability of the Fulde-Ferrell-Larkin-

Ovchinnikov (FFLO) phase of dense spin-polarized Fermi atomic gases in optical lattices was

presented. We are now poised to explore the effects of other terms in the Hamiltonian, like 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 and possible connections with

Majorana fermions. The long-term plan is to interface state-of-the-art Hartree-Fock-Bogoliubov

calculations with correlated Quantum Monte Carlo methodologies. In this presentation, we will

discuss preliminary results, mostly at the mean-field level, to shed light into the different orders

that can emerge in the low-energy landscape of cold atomic systems in optical lattices.