  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.
