Angular topological superfluid and topological vortex in an ultracold Fermi gas

We show that pairing in an ultracold Fermi gas under spin-orbital-angular-momentum coupling (SOAMC) can acquire topological characters encoded in the quantized angular degrees of freedom. The resulting topological superfluid is the angular analog of its counterpart in a one-dimensional Fermi gas with spin-orbit coupling, but characterized by a Zak phase defined in the angular-momentum space. Upon tuning the SOAMC parameters, a topological phase transition occurs, which is accompanied by the closing of the quasiparticle excitation gap. Remarkably, a topological vortex state can also be stabilized by deforming the Fermi surface, which is topologically non-trivial in both the coordinate and angular-momentum space, offering interesting potentials for applications in quantum information and quantum control. We discuss how the topological phase transition and the exotic vortex state can be detected experimentally.