We propose a simple experimental scheme to realize simultaneously the one-dimensional spin-orbit coupling and the staggered spin flip in ultracold pseudospin-
1/2 atomic Fermi gases trapped in optical lattices. In the absence of interspecies interactions, the system supports type-I and II Weyl semimetals in three-dimensional and gapped Chern insulators and gapless topological semimetal states in two-dimensional lattices. By turning on the
s-wave interactions, a rich variety of gapped and gapless inhomogeneous topological superfluids can emerge. In particular, a gapped topological Fulde-Ferrell superfluid, which supports the chiral edge states at opposite boundaries with the same chirality, is predicted.
We investigate theoretically nonmagnetic impurity scattering in a one-dimensional atomic topological superfluid in harmonic traps by solving self-consistently the microscopic Bogoliubov-de Gennes equation. In sharp contrast to topologically trivial Bardeen-Cooper-Schrieffer
s-wave superfluid, topological superfluid can host a midgap state that is bound to localized nonmagnetic impurity. For strong impurity scattering, the bound state becomes universal, with nearly zero energy and a wave function that closely follows the symmetry of that of Majorana fermions. We propose that the observation of such a universal bound state could be useful evidence for characterizing the topological nature of topological superfluids. Our prediction is applicable to an ultracold, resonantly interacting Fermi gas of
40K atoms with spin-orbit coupling confined in a two-dimensional optical lattice.
The experimental realizations of artificial spin-orbit coupling (SOC) and non-Hermitian potentials in ultracold atoms provide a versatile platform for exploring their interplay in quantum many-body systems. Here, we investigate a two-component Fermi gas in a three-dimensional cubic lattice with Rashba SOC and a complex-valued interaction arising from two-body loss. Based on a non-Hermitian mean-field theory, this work elucidates the interplay of dissipation and SOC in the pairing behavior of Fermi gases. Dissipation not only drives a phase transition from a superfluid to a normal state and induces a reentrant superfluid but also, synergistically with SOC, significantly expands the stability regions of both the normal and metastable superfluid phases. Moreover, the introduction of a Zeeman field can drive the system into a topological superfluid phase characterized by a nontrivial topological invariant. These results thereby uncover a rich spectrum of pairing phenomena in this dissipative quantum system.