Ultracold Fermionic Atoms in Square and Triangular Optical Lattices with Non-Abelian Gauge Fields and Out-of-Plane Zeeman Field

The single-band negative-U Hubbard model is applied to investigate ultracold Fermi atoms loaded into square and triangular optical lattices subjected to an effective non-Abelian gauge field and an out-of-plane Zeeman field. The mean-field approximation along with the generalized random phase approximation is used to numerically calculate important and experimentally relevant physical quantities, such as the chemical potential, the pairing gap, the singlet and the triplet condensate fractions, and the slope of the Goldstone sound mode. We found that the Gaussian approximation significantly overestimates the speed of the Goldstone sound mode (by around 30%-40%), and unlike the case of a synthetic Rashba spin-orbit coupling which exhibits sharp changes of the slope of the sound mode across the topological phase transition points, in the presence of both non-Abelian gauge field and out-of-plane Zeeman field the slope of the sound mode is a relatively smooth function.