Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit

TL;DR

This paper investigates how finite-size effects influence vortex states in rotating Bose-Einstein condensates and compares exact small-system results with the thermodynamic limit described by mean-field theory.

Contribution

It links exact many-body solutions for small systems to mean-field results in the thermodynamic limit, highlighting finite-size effects and their disappearance as N grows.

Findings

Finite-size systems exhibit quasi-periodic oscillations in yrast states.

Finite-size effects vanish in the thermodynamic limit, where mean-field theory becomes accurate.

Exact states show structures not captured by mean-field approximations.

Abstract

For a weakly-interacting Bose gas rotating in a harmonic trap we relate the yrast states of small systems (that can be treated exactly) to the thermodynamic limit (derived within the mean-field approximation). For a few dozens of atoms, the yrast line shows distinct quasi-periodic oscillations with increasing angular momentum that originate from the internal structure of the exact many-body states. These finite-size effects disappear in the thermodynamic limit, where the Gross-Pitaevskii approximation provides the exact energy to leading order in the number of particles N. However, the exact yrast states reveal significant structure not captured by the mean-field approximation: Even in the limit of large N, the corresponding mean-field solution accounts for only a fraction of the total weight of the exact quantum state.