Landau criterion for an anisotropic Bose-Einstein condensate

In this work we discuss the Landau criterion for anisotropic superfluidity. To this end we consider a pointlike impurity moving in a uniform Bose-Einstein condensate with either interparticle dipole-dipole interaction or Raman-induced spin-orbit coupling. In both cases we find that the Landau critical velocity $v_{\mathrm{c}}$ is generally smaller than the sound velocity in the moving direction. Beyond $v_{\mathrm{c}}$, the energy dissipation rate is explicitly calculated via a perturbation approach. In the plane-wave phase of a spin-orbit-coupled Bose gas, the dissipationless motion is suppressed by the Raman coupling even in the direction orthogonal to the recoil momentum. Our predictions can be tested in the experiments with ultracold atoms.

Figure 1

(a) Excitation spectrum $E_{\mathbf{q}}$ of a dipolar BEC as a function of $\mathbf{q}·\widehat{\mathbf{v}}$, where $\widehat{\mathbf{v}}$ is in the direction with ${\theta }_{\mathbf{v}}=\pi /4$ (see the inset). The solid line is for the momentum $\mathbf{q}$ in the direction with ${\theta }_{\mathbf{q}}$ determined by Eq. (10), the dash-dotted line is for ${\theta }_{\mathbf{q}}={\theta }_{\mathbf{v}}$, and the dotted line is tangent to the solid line in the $q\to 0$ limit and its slope is equal to $v_{\mathrm{c}}$. (b) Anisotropic critical velocity as a function of ${\theta }_{\mathbf{v}}$ (solid line). The dashed line shows the sound velocity in the moving direction. For both plots ${\epsilon }_{\mathrm{dd}}=0.8$.

Figure 2

(a) Dissipation rate $P$ of a moving impurity in a polarized dipolar BEC as a function of $v$ and ${\epsilon }_{\mathrm{dd}}$. The dash-dotted line shows the critical velocity and the dashed line shows the sound velocity in the moving direction. (b) Velocity dependence of $P$ for ${\epsilon }_{\mathrm{dd}}=0.8$. For both plots ${\theta }_{\mathbf{v}}=\pi /4$ and $P$ is in units of $U_0^{2}n{m}^3{c}_0^3$.

Figure 3

(a) Lower branch excitation spectrum $E_{\mathbf{q}}$ in the PW phase of a SO-coupled Bose gas as a function of $\mathbf{q}·\widehat{\mathbf{v}}$, where $\widehat{\mathbf{v}}$ is in the direction with ${\theta }_{\mathbf{v}}=\pi /2$ (see the inset). The solid line is for the momentum $\mathbf{q}$ in the direction that $E_{\mathbf{q}}/\left(\mathbf{q}·\widehat{\mathbf{v}}\right)$ reaches the global minimum with ${\theta }_{\mathbf{q}}\simeq 0.91\pi$, the dash-dotted line is for ${\theta }_{\mathbf{q}}={\theta }_{\mathbf{v}}$, and the dotted line is tangent to the solid line at the roton minimum and its slope is equal to $v_{\mathrm{c}}$. (b) Anisotropic critical velocity as a function of ${\theta }_{\mathbf{v}}$ (solid line). The dashed line shows the sound velocity in the moving direction. For both plots $\mathrm{\Omega }=2.5E_{\mathrm{r}}$ and $gn=1E_{\mathrm{r}}$.

Figure 4

(a) Dissipation rate $P$ of a moving impurity in a SO-coupled BEC as a function of $v$ and $\mathrm{\Omega }$. The dash-dotted line shows the critical velocity and the dashed line shows the sound velocity in the moving direction. (b) Velocity dependence of $P$ for $\mathrm{\Omega }=2.5E_{\mathrm{r}}$. For both plots $\widehat{\mathbf{v}}$ is perpendicular to ${\mathbf{k}}_{\mathrm{r}}$ (i.e., ${\theta }_{\mathbf{v}}=\pi /2$), $gn=1E_{\mathrm{r}}$, and $P$ is in units of $U_0^{2}n{m}^3{c}_0^3$.