The Yrast Line of a Rapidly Rotating Bose Gas: Gross-Pitaevskii Regime

Abstract

We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functional accurately describes the ground state energy of the corresponding $N$-body Hamiltonian with contact interaction provided the total angular momentum $L$ is much less than $N^2$. While the Gross-Pitaevskii energy is always an obvious variational upper bound to the ground state energy, a more refined analysis is needed to establish it as an exact lower bound. We also discuss the question of Bose-Einstein condensation in the parameter range considered. Coherent states together with inequalities in spaces of analytic functions are the main technical tools.