Bose-Einstein condensation of trapped interacting spin-1 atoms

TL;DR

This paper studies Bose-Einstein condensation in trapped spin-1 atoms with ferromagnetic or antiferromagnetic interactions, revealing different condensation behaviors based on interaction type and conservation constraints.

Contribution

It develops a mean field, semiclassical two-fluid model to analyze condensation patterns in spin-1 atoms with different magnetic interactions.

Findings

Antiferromagnetic interactions prevent condensation in the $|m_F=0>$ state.

Double condensation occurs for antiferromagnetic interactions.

Triple condensation can occur for ferromagnetic interactions.

Abstract

We investigate Bose-Einstein condensation of trapped spin-1 atoms with ferromagnetic or antiferromagnetic two-body contact interactions. We adopt the mean field theory and develop a Hartree-Fock-Popov type approximation in terms of a semiclassical two-fluid model. For antiferromagnetic interactions, our study reveals double condensations as atoms in the $|m_F=0>$ state never seem to condense under the constraints of both the conservation of total atom number $N$ and magnetization $M$. For ferromagnetic interactions, however, triple condensations can occur. Our results can be conveniently understood in terms of the interplay of three factors: (anti) ferromagnetic atom-atom interactions, $M$ conservation, and the miscibilities between and among different condensed components.