Quantum Statistics of a Shell-Shaped Bose-Einstein Condensate

The recent development of NASA's Cold Atom Laboratory, a space-based facility for ultracold atoms experiments, allows the routine production of Bose-Einstein condensates in microgravity. The ongoing investigations are focusing on shell-shaped geometries, in which the atoms are confined on a thin ellipsoidal surface with radio frequency-induced adiabatic potentials. We analyze the quantum statistical properties of spherical and ellipsoidal shells, focusing on the phenomena of Bose-Einstein condensation and superfluidity. Moreover, we discuss the physics of topological excitations on a spherical superfluid, which drive the Berezinskii-Kosterlitz-Thouless transition, and their interplay with the curvature of the hosting surface. Our results are a reliable benchmark for the current experimental investigations.