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

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 quasiperiodic 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.