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Topological $p_{x}+ip_{y}$ Superfluid Phase of a Dipolar Fermi Gas in a 2D Optical Lattice

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 $p_{x}+ip_{y}$ superfluid phase can be realized in a single-component dipolar Fermi gas trapped in a 2D square optical lattice with this attractive interaction at low temperatures. The $p_{x}+ip_{y}$ superfluid state has potential applications for topological quantum computing. We obtain the phase diagram of this system at zero temperature. In the weak-coupling limit, the p-wave superfluid phase is stable for all filling factors. As the interaction strength increases, it is stable close to filling factors $n=0$ or $n=1$, and phase separation takes place in between. When the interaction strength is above a threshold, the system is phase separated for any $0<n<1$. The transition temperature of the $p_{x}+ip_{y}$ superfluid state is estimated and the implication for experiments is discussed.