  The topological superfluids with Majorana zero modes have not yet been
realized in ultracold atoms with Rashba spin-orbit coupling. Here we show that
these phases can be realized with an artificial gauge potential, which can be
regarded as a site-dependent rotating Zeeman field. This potential breaks the
inversion symmetry and plays the same role as Rashba spin-orbit coupling. In
the inverted bands, this model can open a proper parameter regime for
topological superfluids. Strikingly, we find that the interaction near the
Fermi surface is dominated by the dispersion scattering in the same band, thus
can realize topological phase with much weaker attractive interaction, as
compared with the model with Rashba spin-orbit coupling. We find a large regime
for the gapped topological Fulde-Ferrell-Larkin-Ovchinnikov superfluids and
unveil the phase diagram with mean-field theory, which should be credible in
the weak interaction regime. In regarding the negligible heating effect in
realizing this potential in alkaline and rare-earth atoms, our model has the
potential to be the first system to realize the long-sought topological FFLO
phase and the associated Majorana zero modes.
