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We show that pairing in an ultracold Fermi gas underspin-orbital-angular-momentum coupling (SOAMC) can acquire topologicalcharacters encoded in the quantized angular degrees of freedom. The resultingtopological superfluid is the angular analog of its counterpart in aone-dimensional Fermi gas with spin-orbit coupling, but characterized by a Zakphase defined in the angular-momentum space. Upon tuning the SOAMC parameters,a topological phase transition occurs, which is accompanied by the closing ofthe quasiparticle excitation gap. Remarkably, a topological vortex state canalso be stabilized by deforming the Fermi surface, which is topologicallynon-trivial in both the coordinate and angular-momentum space, offeringinteresting potentials for applications in quantum information and quantumcontrol. We discuss how the topological phase transition and the exotic vortexstate can be detected experimentally.

Angular topological superfluid and topological vortex in an ultracold Fermi gas