We investigate the vortex formation properties of a three-dimensional (3D) dipolar Bose-Einstein condensate (BEC) of 52 Cr atoms in an optical lattice potential through numerical simulations of the time-dependent Gross-Pitaevskii equation with a dissipation term. The mechanisms that influence the dipole-dipole interaction and the repulsive contact interaction between atoms during vortex formation are analyzed. We find that the stability of the vortices weakens with increasing attractive dipolar strength and that the repulsive contact interaction between atoms can increase the number of vortices.
We have measured the relative strength ${\ensuremath{\epsilon}}_{dd}$ of the magnetic dipole-dipole interaction compared with the contact interaction in a dipolar chromium Bose-Einstein condensate. We analyze the asymptotic velocities of expansion of the condensate with different orientations of the atomic magnetic moments. By comparing the experimental results with numerical solutions of the hydrodynamic equations for dipolar condensates, we obtain ${\ensuremath{\epsilon}}_{dd}=0.159\ifmmode\pm\else\textpm\fi{}0.034$. We use this result to determine the
s-wave scattering length $a=(5.08\ifmmode\pm\else\textpm\fi{}1.06\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9})\text{ }\mathrm{m}=(96\ifmmode\pm\else\textpm\fi{}20)\text{ }{a}_{0}$ of
52Cr. This is fully consistent with our previous measurements on the basis of Feshbach resonances and therefore confirms the validity of the theoretical approach used to describe the dipolar Bose-Einstein condensate.
We study the influence of dipole–dipole interaction on the formation of vortices in a rotating dipolar Bose–Einstein condensate (BEC) of 52 Cr and 164 Dy atoms in quasi two-dimensional geometry. By numerically solving the corresponding time-dependent mean-field Gross–Pitaevskii equation, we show that the dipolar interaction enhances the number of vortices, while a repulsive contact interaction increases the stability of the vortices. Furthermore, an ordered vortex lattice of a relatively large number of vortices is found in a strongly dipolar BEC.