Hollow shell geometry and topological change of spherical Bose-Einstein condensates

We present our study [\underline {arXiv:1612.05809}] and recent progress on a spherical BEC undergoing a topological change from a filled sphere to a novel hollow shell geometry. Motivated by the upcoming realization of these hollow systems by NASA's Cold Atom Laboratory, we analyze their equilibrium properties and collective mode (CM) structure. We show that distinctive non-monotonic features in the CM spectrum of a spherical BEC indicate its deformation from a filled to a hollow geometry and the emergence of an inner boundary. This topological change produces the most drastic effect for high angular momentum CMs as they correspond to surface modes localized to condensate boundaries and undergo a redistribution of nodes once an additional boundary is present. Additionally, our numerical simulations show how the CM features can be probed in typical sudden-quench experiments. Finally, we go beyond the micro-gravity regime, discussing how the equilibrium and CM properties are modified as gravity breaks the spherical symmetry.