Comparing Contact and Dipolar Interactions in a Bose-Einstein Condensate

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 $^{52}\mathrm{Cr}$. 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.