Shell-shaped Bose-Einstein condensates: Dynamics, excitations, and thermodynamics

TL;DR

This paper provides a comprehensive analysis of shell-shaped Bose-Einstein condensates, covering their dynamics, excitations, vortex behavior, thermodynamics, and recent experimental realizations, highlighting their unique properties in hollow geometries.

Contribution

It synthesizes two decades of theoretical work with recent experimental advances, offering new insights into the evolution, excitations, vortex physics, and thermodynamics of shell-shaped BECs.

Findings

Universal dip in frequency spectra signals hollowing transition

Vortex-antivortex pairs stabilized by rotation in shells

Adiabatic expansion causes condensate depletion

Abstract

Shell-shaped Bose-Einstein condensates (BECs) represent a paradigmatic instance of quantum fluids in hollow geometries exhibiting phenomena that bridge from ultracold atomic to astrophysical realms. In this work, we present a comprehensive survey of the dynamics, thermodynamics, and collective excitations of shell-shaped BECs, synthesizing two decades of our group's theoretical work in light of recent experimental breakthroughs. We begin by analyzing the evolution of a BEC from filled-sphere to hollow-shell geometries, illustrating the necessity of microgravity conditions to avoid gravitational sag. We then analyze the collective mode structure across this evolution and pinpoint a universal dip in the frequency spectra as well as mode reconfiguration due to inner-surface excitations as robust signatures of the hollowing-out transition. Turning to vortex physics, we show that the closed-surface topology enforces vortex-antivortex configurations in shell-shaped BECs and that the natural annihilation of these pairs can be stabilized by rotation, with the critical rotation rate depending on shell thickness. In the thermodynamic domain, we investigate the interplay between shell inflation and the BEC phase transition, where adiabatic expansions lead to condensate depletion. This behavior motivates a study of the nonequilibrium dynamics of shell-shaped BECs; we perform such a study by constructing a time-dependent dynamic technique that can capture the evolution in both adiabatic and non-adiabatic regimes. Finally, we review recent experimental realizations of shell-shaped BECs, including the landmark creation of ultracold shells aboard the International Space Station, and outline prospects for exploring quantum fluids in curved geometries.