Vortex stability near the surface of a Bose-Einstein condensate

The energy functional of a rotating Bose-Einstein condensate was written in terms of variables local to its surface. Using a variational ansatz, the energy of a single vortex moving at the surface of the condensate was calculated. This energy was used to investigate the energetic stability of the vortex in terms of the rotation frequency of the confining potential. Upon increasing the rotation frequency, the vortex approached the surface of the condensate. At a critical rotation frequency, the vortex crossed the surface of the condensate and entered it. The local-density approximation was used to simplify the calculations and lead to analytical results in the Thomas-Fermi limit.