Topological px+ipy superfluid phase of a dipolar Fermi gas in a two-dimensional optical lattice

Abstract

In a dipolar Fermi gas, the anisotropic interaction between electric dipoles can be turned into an effectively attractive interaction in the presence of a rotating electric field. We show that the topological ${p}_{x}+i{p}_{y}$ superfluid phase can be realized in a single-component dipolar Fermi gas trapped in a two-dimensional square optical lattice with this attractive interaction at low temperatures. The ${p}_{x}+i{p}_{y}$ superfluid state has potential applications for topological quantum computing. We obtain the phase diagram of this system at zero temperature. When the interaction is weak, the $p$-wave superfluid state is stable for most filling factors except near half filling, where phase separation takes place. In the weak-coupling limit, the phase-separation region vanishes. When the interaction strength is above a threshold, the system is phase separated for any filling factor $0<n<1$. The transition temperature of the ${p}_{x}+i{p}_{y}$ superfluid state is estimated and the implication for experiments is discussed.