Do attractive bosons condense?

TL;DR

This paper investigates the behavior of attractive bosons in traps, revealing that under rotation, they form uncondensed, fragmented states with angular momentum absorbed by the center of mass, contrasting with repulsive cases.

Contribution

It provides exact solutions for attractive boson models under rotation, showing the emergence of fragmented condensates and center of mass angular momentum absorption.

Findings

Attractive bosons do not form vortices but absorb angular momentum via center of mass motion.

The ground state is uncondensed and fragmented, unlike repulsive bosons.

Repulsive bosons are fully condensed in the thermodynamic limit.

Abstract

Motivated by experiments on bose atoms in traps which have attractive interactions (e.g. ^7Li), we consider two models which may be solved exactly. We construct the ground states subject to the constraint that the system is rotating with angular momentum proportional to the number of atoms. In a conventional system this would lead to quantised vortices; here, for attractive interactions, we find that the angular momentum is absorbed by the centre of mass motion. Moreover, the state is uncondensed and is an example of a `fragmented' condensate discussed by Nozi\`eres and Saint James. The same models with repulsive interactions are fully condensed in the thermodynamic limit.