Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions

TL;DR

This paper explores how to bridge the gap between exact quantum solutions and mean-field approximations in rotating Bose-Einstein condensates, especially for vortex states, by analyzing the separation of the Hilbert space into primary and complementary parts.

Contribution

It introduces a method to connect exact solutions with mean-field results in vortex states of Bose-Einstein condensates, applicable from few-atom systems to the thermodynamic limit.

Findings

Hilbert space separates into primary and complementary parts.

Method effectively bridges exact and mean-field solutions.

Applicable to weakly-interacting Bose-Einstein condensates.

Abstract

When a Bose-Einstein condensed cloud of atoms is given some angular momentum, it forms vortices arranged in structures with a discrete rotational symmetry. For these vortex states, the Hilbert space of the exact solution separates into a "primary" space related to the mean-field Gross-Pitaevskii solution and a "complementary" space including the corrections beyond mean-field. Considering a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we demonstrate how this separation can be used to close the conceptual gap between exact solutions for systems with only a few atoms and the thermodynamic limit for which the mean-field is the correct leading-order approximation. Although we illustrate this approach for the case of weak interactions, it is expected to be more generally valid.