Transport of dipolar Bose-Einstein condensates in a one-dimensional optical lattice

We show that magnetic dipolar interactions can stabilize superfluidity in atomic gases, but the dipole alignment direction required to achieve this varies depending on whether the flow is oscillatory or continuous. If a condensate is made to oscillate through a lattice, damping of the oscillations can be reduced by aligning the dipoles perpendicular to the direction of motion. However, if a lattice is driven continuously through the condensate, superfluid behavior is best preserved when the dipoles are aligned parallel to the direction of motion. We explain these results in terms of the formation of topological excitations and tunnel barrier heights between lattice sites.

Figure 1

Sketch of the model system for oscillatory flow. The trap is displaced a distance $\Delta x$ in the $x$ direction to trigger a center-of-mass oscillation. The colored oval represents the BEC, the gray line shows the trap before the displacement, the black line the trap after displacement and the oscillating dark red line the optical lattice. Black arrows indicate the axes with $r$ the radial direction.

Figure 2

Expectation value of BEC position along the $x$ direction for the three configurations: without dipolar interactions (red solid curve), with dipoles polarized parallel to the direction of motion (green dashed curve), and with dipoles polarized perpendicular to the direction of motion (blue dotted curve).

Figure 3

Cross sections through the $z=0$ plane of the atom density distribution in the course of oscillatory flow simulations. Panel (o) shows the starting profile without dipolar interactions. Panels (a)-(c) show the profile after $t=0.08\mathrm{s}$ for (a) the configuration without dipolar interactions, (b) with the dipoles polarized parallel to the direction of motion, and (c) with the dipoles aligned perpendicular to the direction of motion.

Figure 4

Sketch of model system for continuous flow. The colored oval represents the BEC. The optical lattice is dragged along the $x$ axis through the cloud at constant velocity. The black line shows the harmonic trap, the oscillating gray curve shows the optical lattice at $t=0.0$ and the oscillating dark red curve shows the shifted lattice. Black arrows indicate the axes with $r$ the radial direction.

Figure 5

Total energy per atom as a function of time for lattice velocities (a) $0.75\mathrm{mm}{\mathrm{s}}^{-1}$, (b) $0.98\mathrm{mm}{\mathrm{s}}^{-1}$, (c) $1.06\mathrm{mm}{\mathrm{s}}^{-1}$, and (d) $1.13\mathrm{mm}{\mathrm{s}}^{-1}$. The red solid curves show the configuration without dipolar interactions, the green dashed curves show the configuration with the dipoles aligned parallel to the direction of motion, and the blue dotted curves show the configuration with the dipoles aligned perpendicular to the direction of motion.

Figure 6

Cross sections through the $z=0$ plane of the atom density distribution in the course of continuous flow simulations. Panel (o) shows the starting profile without dipolar interactions. Panels (a)-(c) show the profile after $t=0.04\mathrm{s}$ for (a) the configuration without dipolar interactions, (b) with the dipoles polarized parallel to the direction of motion, and (c) with the dipoles aligned perpendicular to the direction of motion. The lattice velocity is $v=1.13\mathrm{mm}{\mathrm{s}}^{-1}$.

Figure 7

Total energy per atom at $t=0.02\mathrm{s}$ as a function of $v$ for the three configurations: without dipolar interactions (red dots), with the dipoles polarized parallel to the direction of motion (green diamonds), and with the dipoles polarized perpendicular to the direction of motion (blue squares). Vertical gray lines show the thresholds for the energetic instability (dashed curve) and the dynamical instability (dot-dashed cure).