Spontaneous inhomogeneous phases in ultracold dipolar Fermi gases

We study the collapse of ultracold fermionic gases into inhomogeneous states due to strong dipolar interaction in both two-dimensions (2D) and three-dimensions (3D). Depending on the dimensionality, we find that two different types of inhomogeneous states are stabilized once the dipole moment reaches a critical value d>dc: the stripe phase and phase separation between high and low densities. In 2D, we prove that the stripe phase is always favored for d > or approx. dc, regardless of the microscopic details of the system. In 3D, the one-loop perturbative calculation suggests that the same type of instability leads to phase separation. Experimental detection and finite-temperature effects are discussed.