Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions

摘要

We derive rigorous one- and two-dimensional mean-field equations for cigar-and pancake-shaped dipolar Bose-Einstein condensates with arbitrarypolarization angle. We show how the dipolar interaction modifies the contactinteraction of the strongly confined atoms. In addition, our equationsintroduce a nonlocal potential, which is anisotropic for pancake-shapedcondensates. We propose to observe this anisotropy via measurement of thecondensate aspect ratio. We also derive analytically approximate densityprofiles from our equations. Both the numerical solutions of our reducedmean-field equations and the analytical density profiles agree well withnumerical solutions of the full Gross-Pitaevskii equation while being moreefficient to compute.