Vortices in Rotating Bose-Einstein Condensate Shells

We present a study of superfluid vortices in rotating shell-shaped Bose-Einstein condensates (BECs). Hollow spherical BECs are of interest in connection to ongoing experimental efforts on the International Space Station and they naturally occur in optical lattice systems of ultracold bosons and interiors of neutron stars. Fundamentally, they have interesting geometry (non-zero curvature) and topology (hollow center). When BECs are rotated, discrete vortices are generated in pairs, as a consequence of the quantum coherence and the closed shape of the system. Using a mean-field approach, numerical solutions of the Gross-Pitaevskii equation and insights from classical fluid dynamics, we find that hollow condensates have a lower energy barrier to emergence of vortices than fully filled BECs. Further, we show that the rotation frequency at which nucleation of vortex lines is energetically favorable increases with BEC shell thickness. At this frequency the first vortex line is generated as straight and extends along the rotation axis. We consider the possibility of bent vortex lines (off-axis vortex pairs of opposite circulations in the two-dimensional shell limit) and determine that they are unstable except at fast rotation.