Dipolar Bose gas in a weak isotropic speckle disorder

We investigate the properties of a homogeneous dipolar Bose gas in a weak three-dimensional isotropic speckle disorder at finite temperatures. By using the Bogoliubov theory (beyond the mean field), we calculate the condensate and the superfluid fractions as a function of density and strengths of disorder and interaction. The disorder impact on the anomalous density, the chemical potential, and the ground-state energy is also analyzed. We show that the peculiar interplay of the dipole-dipole interaction and weak disorder makes the superfluid fraction and sound velocity anisotropic.

Figure 1

Behavior of the disorder function $h({\epsilon }_{dd},\sigma /\xi )$ from Eq. (18) as a function of $\sigma /\xi$. Black line: ${\epsilon }_{dd}=0$ (pure contact interaction). Blue dashed line: ${\epsilon }_{dd}=0.38$ (Er atoms). Red dotted line: ${\epsilon }_{dd}=0.6$. Green dot-dashed line: ${\epsilon }_{dd}=0.95$. Here, the interaction can be adjusted by means of the Feshbach resonance.

Figure 2

Behavior of the disorder functions (a) $h^{\parallel }({\epsilon }_{dd},\sigma /\xi )$ and (b) $h^{\perp }({\epsilon }_{dd},\sigma /\xi )$ as a function of $\sigma /\xi$. Black line: ${\epsilon }_{dd}=0$. Blue dashed line: ${\epsilon }_{dd}=0.38$. Red dotted line: ${\epsilon }_{dd}=0.6$. Green dot-dashed line: ${\epsilon }_{dd}=0.95$.