Vortex structures in dipolar condensates

We investigate the properties of single vortices and of the vortex lattice in a rotating dipolar condensate. We show that vortices in this system possess several features induced by the long-range anisotropic dipolar interaction between particles. For example, when the dipoles are polarized along the rotation axis, vortices may display a craterlike structure; when dipoles are polarized orthogonal to the rotation axis, the vortex cores take an elliptical shape and the vortex lattice no longer possesses hexagonal symmetry.

Figure 1

(Color online). Solid lines, function ${\left[f_{\lambda }^z\left(\varrho \right)\right]}^{-1∕3}$ for $\lambda =11$, 100, and 400 in descending order. Dashed line, the asymptote ${\left(2\pi \right)}^{-1∕6}\varrho$.

Figure 2

(Color online) (a) Radial density profile of the single vortex state for $\lambda =100$ and various scattering lengths (in units of Bohr radius $a_B$). (b) The $\lambda$ dependence of critical scattering length (in units of $a_B$). Here ◻ and ▵ denote, respectively, the nonvortex state and the axial vortex state.

Figure 3

(Color online) Density profile of a vortex lattice state for $\lambda =100$, $\Omega =0.4{\omega }_{\perp }$, and $a=-10a_B$. The inset shows the position of the vortices which form a triangular lattice with hexagonal symmetry.

Figure 4

(Color online) Structure of a single vortex state with dipoles polarized along the $x$ axis. The parameters are $\lambda =100$, $a=16a_B$, and $\Omega =0.3{\omega }_{\perp }$. (a) Density profile. The solid curves show the densities along the $x$ and $y$ axes. (b) Density contour plot. Brighter color represents higher density. (c) Contour plot of the phase of the wave function.

Figure 5

(Color online) Density contour plots for $\lambda =100$, $a=18a_B$, and various rotating frequencies. The dots at the lower right corners show the positions of vortices.