Thermodynamics in expanding shell-shaped Bose-Einstein condensates

TL;DR

This paper investigates the thermodynamic properties of shell-shaped Bose-Einstein condensates in a bubble trap, analyzing spectral changes, critical temperatures, and effects of adiabatic expansion, with implications for space-based cold atom experiments.

Contribution

It introduces a spectral analysis approach for shell-shaped BECs, examines thermodynamic behavior during expansion, and assesses the impact of interactions and experimental modeling.

Findings

Spectral separation reveals dimensional crossover to quasi-2D physics.

Critical temperature decreases faster than system cooling during expansion.

Interactions are less significant in thin shells, but vortex phenomena become prominent.

Abstract

Inspired by investigations of Bose-Einstein condensates (BECs) produced in the Cold Atom Laboratory (CAL) aboard the International Space Station, we present a study of thermodynamic properties of shell-shaped BECs. Within the context of a spherically symmetric `bubble trap' potential, we study the evolution of the system from small filled spheres to hollow, large, thin shells via the tuning of trap parameters. We analyze the bubble trap spectrum and states, and track the distinct changes in spectra between radial and angular modes across the evolution. This separation of the excitation spectrum provides a basis for quantifying dimensional cross-over to quasi-2D physics at a given temperature. Using the spectral data, for a range of trap parameters, we compute the critical temperature for a fixed number of particles to form a BEC. For a set of initial temperatures, we also evaluate the change in temperature that would occur in adiabatic expansion from small filled sphere to large thin shell were the trap to be dynamically tuned. We show that the system cools during this expansion but that the decrease in critical temperature occurs more rapidly, thus resulting in depletion of any initial condensate. We contrast our spectral methods with standard semiclassical treatments, which we find must be used with caution in the thin-shell limit. With regards to interactions, using energetic considerations and corroborated through Bogoliubov treatments, we demonstrate that they would be less important for thin shells due to reduced density but vortex physics would become more predominant. Finally, we apply our treatments to traps that realistically model CAL experiments and borrow from the thermodynamic insights found in the idealized bubble case during adiabatic expansion.