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The topological superfluids with Majorana zero modes have not yet beenrealized in ultracold atoms with Rashba spin-orbit coupling. Here we show thatthese phases can be realized with an artificial gauge potential, which can beregarded as a site-dependent rotating Zeeman field. This potential breaks theinversion symmetry and plays the same role as Rashba spin-orbit coupling. Inthe inverted bands, this model can open a proper parameter regime fortopological superfluids. Strikingly, we find that the interaction near theFermi surface is dominated by the dispersion scattering in the same band, thuscan realize topological phase with much weaker attractive interaction, ascompared with the model with Rashba spin-orbit coupling. We find a large regimefor the gapped topological Fulde-Ferrell-Larkin-Ovchinnikov superfluids andunveil the phase diagram with mean-field theory, which should be credible inthe weak interaction regime. In regarding the negligible heating effect inrealizing this potential in alkaline and rare-earth atoms, our model has thepotential to be the first system to realize the long-sought topological FFLOphase and the associated Majorana zero modes.

Gapped topological Fulde-Ferrell-Larkin-Ovchinnikov superfluids with artificial gauge potential and weak interaction