In a dipolar Fermi gas, the dipole-dipole interaction between fermions can be turned into a dipolar Ising interaction between pseudospins in the presence of an ac electric field. When trapped in a two-dimensional optical lattice, this dipolar Fermi gas has a very rich phase diagram at zero temperature, due to the competition between antiferromagnetism and superfluidity. At half-filling, the antiferromagnetic state is the favored ground state. The superfluid state appears as the ground state at a smaller filling factor. In between there is a phase-separated region. The order parameter of the superfluid state can display different symmetries depending on the filling factor and interaction strength, including the d-wave (d), the extended s-wave (xs), or their linear combination (xs + id). Implications for the current experiment are discussed.
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