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 $d>d_c$: the stripe phase and phase separation between high and low densities. In 2D, we prove that the stripe phase is always favored for $d\gtrsim d_c$, 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.

Figure 1

(Color online) The stripe phase in 2D dipolar gases. The three dotted arrows mark the $x$, $y$ and $z$ axes. The lighter (darker) regions in the 2D plane represent higher (lower) density. The solid line with an arrow represents the direction of the external field, which aligns the direction of the dipoles.

Figure 2

(Color online) Diagrammatic expansion for ${\Pi }_{2\text{D}}^{1\text{IR}}\left(\vec{q}\right)$. The solid lines are free-fermion propagators and the dashed lines represent the dipolar interaction.

Figure 3

(Color online) One-loop calculation of $\Delta \left(\vec{q}\right)$ in (a) 2D and (b) 3D. In the 2D case, we choose ${\varphi }_{\vec{q}}=\frac{\pi }{2}$ and for the 3D, ${\theta }_{\vec{q}}=\pi /2$. From top to bottom, the dipole momentum for each of the curves are: $d/d_c=0$, 0.9, 1, and 1.1 respectively. The dashed vertical line marks the momentum $2k_F$.