Static and dynamic properties of shell-shaped condensates

TL;DR

This paper provides a comprehensive theoretical and numerical analysis of hollow Bose-Einstein condensates, focusing on their static, dynamic, and topological properties, especially during the transition from filled to hollow structures, with implications for future experiments in microgravity.

Contribution

It offers the first detailed study of equilibrium and collective modes of hollow BECs, including the hollowing transition and effects of gravity, using analytic and numerical methods.

Findings

Identification of signatures of the filled-to-hollow transition in collective modes

Analysis of the effects of gravity and microgravity on shell stability and mode structure

Extension of hollowing signatures from spherical to disk-to-ring geometries

Abstract

Static, dynamic, and topological properties of hollow systems differ from those that are fully filled as a result of the presence of a boundary associated with an inner surface. Hollow Bose-Einstein condensates (BECs) naturally occur in various ultracold atomic systems and possibly within neutron stars but have hitherto not been experimentally realized in isolation on Earth because of gravitational sag. Motivated by the expected first realization of fully closed BEC shells in the microgravity conditions of the Cold Atomic Laboratory aboard the International Space Station, we present a comprehensive study of spherically symmetric hollow BECs as well as the hollowing transition from a filled sphere BEC into a thin shell through central density depletion. We employ complementary analytic and numerical techniques in order to study equilibrium density profiles and the collective mode structures of condensate shells hosted by a range of trapping potentials. We identify concrete and robust signatures of the evolution from filled to hollow structures and the effects of the emergence of an inner boundary, inclusive of a dip in breathing-mode-type collective mode frequencies and a restructuring of surface mode structure across the transition. By extending our analysis to a two-dimensional transition of a disk to a ring, we show that the collective mode signatures are an essential feature of hollowing, independent of the specific geometry. Finally, we relate our work to past and ongoing experimental efforts and consider the influence of gravity on thin condensate shells. We identify the conditions under which gravitational sag is highly destructive and study the mode-mixing effects of microgravity on the collective modes of these shells.