Anisotropic collapse in three-dimensional dipolar Bose-Einstein condensates

We study the (3+1)-dimensional Gross-Pitaevskii / Nonlinear Schrödinger equation describing a dipolar Bose-Einstein condensate. Bound states are computed using accurate numerical techniques. When the dipolar strength is negative, the total number of atoms vs. frequency relationship for these bound states is multi-valued and possesses a cusp point, which corresponds to a “candlestick” ground state. Direct simulations of this ground state exhibit strongly-anisotropic collapse of its nucleus, with different contraction rates along the dipole axis and perpendicular to it. We propose an anisotropic self-similar theory to explain this dynamics. The physical implications are discussed.