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.

• Received 1 May 2011

DOI:https://doi.org/10.1103/PhysRevA.84.043630