Thermodynamics in shell-shaped Bose-Einstein condensates*

Inspired by investigations of Bose-Einstein condensates (BECs) produced in the Cold Atom Laboratory (CAL) aboard the International Space Station (ISS), we present a study of thermodynamic properties of shell-shaped BECs. Within the context of a 'bubble-trap potential', we compute the BEC critical temperature and the evolving temperature of the gas during an adiabatic expansion process that leads to the hollowing of a spherically symmetric ultracold atomic gas. We employ multiple theoretical approaches and find that the standard semiclassical approximation breaks down in the quasi-2D limit. We investigate the topological filled-to-hollow sphere transition and the ensuing crossover from 3D to 2D physics. We address the relevance of interactions in shell-shaped geometries and the thermodynamics of the resulting collective excitations. We compare our results with the experimentally realistic situation and identify the parameter regimes and phenomena directly relevant to the CAL setting.