  Shell-shaped hollow Bose-Einstein condensates (BECs) exhibit behavior
distinct from their filled counterparts and have recently attracted attention
due to their potential realization in microgravity settings. Here we study
distinct features of these hollow structures stemming from vortex physics and
the presence of rotation. We focus on a vortex-antivortex pair as the simplest
configuration allowed by the constraints on superfluid flow imposed by the
closed-surface topology. In the two-dimensional limit of an infinitesimally
thin shell BEC, we characterize the long-range attraction between the
vortex-antivortex pair and find the critical rotation speed that stabilizes the
pair against energetically relaxing towards self-annihilation. In the
three-dimensional case, we contrast the bounds on vortex stability with those
in the two-dimensional limit and the filled sphere BEC, and evaluate the
critical rotation speed as a function of shell thickness. We thus demonstrate
that analyzing vortex stabilization provides a nondestructive means of
characterizing a hollow sphere BEC and distinguishing it from its filled
counterpart.

Quantum Gases