Paired phases and Bose-Einstein condensation of spin-one bosons with attractive interaction

TL;DR

This paper investigates paired phases and Bose-Einstein condensation in spin-one bosons with attractive interactions, deriving mean-field equations and classifying solutions based on symmetry, revealing conditions for stability of different condensate phases.

Contribution

It introduces a mean-field framework for spin-one bosons with attractive interactions, identifying conditions for BCS and BEC phases and their stability criteria.

Findings

Self-consistent equations resemble those for scalar bosons.

Singlet phase can exhibit BCS or BEC pairing.

Repulsive interaction in the quintet channel stabilizes condensates.

Abstract

We analyze paired phases of cold bosonic atoms with the hyper spin S=1 and with an attractive interaction. We derive mean-field self-consistent equations for the matrix order parameter describing such paired bosons on an optical lattice. The possible solutions are classified according to their symmetries. In particular, we find that the self-consistent equations for the SO(3) symmetric phase are of the same form as those for the scalar bosons with the attractive interaction. This singlet phase may exhibit either the BCS type pairing instability (BCS phase) or the BEC quasiparticle condensation together with the BCS type pairing (BEC phase) for an arbitrary attraction U_0 in the singlet channel of the two body interaction. We show that both condensate phases become stable if a repulsion U_2 in the quintet channel is above a critical value, which depends on U_0 and other thermodynamic parameters.