Anisotropic Superfluid Behavior of a Dipolar Bose-Einstein Condensate

We present transport measurements on a dipolar superfluid using a Bose-Einstein condensate of ${}^{162}\mathrm{Dy}$ with strong magnetic dipole-dipole interactions. By moving an attractive laser beam through the condensate we observe an anisotropy in superfluid flow. This observation is compatible with an anisotropic critical velocity for the breakdown of dissipationless flow, which, in the spirit of the Landau criterion, can directly be connected to the anisotropy of the underlying dipolar excitation spectrum. In addition, the heating rate above this critical velocity reflects the same anisotropy. Our observations are in excellent agreement with simulations based on the Gross-Pitaevskii equation and highlight the effect of dipolar interactions on macroscopic transport properties, rendering dissipation anisotropic.

Figure 1

Probing anisotropic critical velocity. (a) Excitation spectrum of a homogeneous dipolar Bose gas. The speed of sound $v_s$ depends on the direction of the excitation $\mathit{k}$ with respect to the dipole polarization $\mathit{B}$, denoted by the angle $\alpha$. (b) The critical velocity $v_c$ (solid), as given by Eq. (2), becomes anisotropic and is in general lower than $v_s$ (dashed). (c) Schematic of the experiment. We drag an attractive laser beam through a dipolar condensate perpendicular ($\alpha =90°$, blue) and parallel ($\alpha =0°$, red) to the magnetic field direction.

Figure 2

Temperature of the dBEC after stirring for (a) the isotropic case with $\mathit{B}\parallel \widehat{\mathit{z}}$ and (b) the anisotropic case with $\mathit{B}\parallel \widehat{\mathit{x}}$ in an almost cylindrical trap. In (c) the trap is additionally reshaped to invert the cloud aspect ratio. The stirring beam is moved along the $x$ (red squares) or $y$ (blue circles) axis, as illustrated in the insets with example in situ images. Critical velocities are extracted by a linear fit (dashed) and marked with arrows. In (a) the response is isotropic with $v_x=0.20(5)$ and $v_y=0.20(7)\mathrm{mm}/\mathrm{s}$, while we observe a clear difference in (b) with $v_{\perp }=0.16(2)\mathrm{mm}/\mathrm{s}$ along $\widehat{\mathit{y}}$ and $v_{\parallel }=0.36(3)\mathrm{mm}/\mathrm{s}$ along $\widehat{\mathit{x}}$. In (c) we extract $v_{\perp }=0.12(3)$ and $v_{\parallel }=0.26(4)\mathrm{mm}/\mathrm{s}$ proving that the observed anisotropy remains even when inverting the anisotropy of the atomic cloud. Data points with stirring frequency matching the trapping frequencies (gray) are excluded from the analysis. Simulations of the eGPE for a single stirring cycle (solid lines) show excellent agreement with the experiment. See text for further parameters.