Stability of Bosonic atomic and molecular condensates near a Feshbach resonance

TL;DR

This paper investigates the stability and phase transitions of atomic and molecular Bose condensates near a Feshbach resonance, highlighting the roles of scattering interactions and potential instabilities.

Contribution

It demonstrates that without molecule-molecule interactions, atomic condensates are unstable or energetically unfavorable compared to molecular condensates, and shows how repulsive interactions can stabilize atomic condensates.

Findings

Atomic condensate is either unstable or energetically higher than molecular condensate without molecule-molecule scattering.

Repulsive molecule-molecule scattering can stabilize dense atomic condensates.

A phase transition between atomic and molecular condensates is possible but may be suppressed by 3-body processes.

Abstract

We explore the Bose condensed phases of an atomic gas on the molecular side of a Feshbach resonance. In the absence of atom-molecule and molecule-molecule scattering, we show that the atomic condensate is either a saddle point of the free energy with energy always exceeding that of the molecular condensate, or has a negative compressibility (hence unstable to density fluctuations). Therefore no phase transition occurs between the atomic and molecular condensates. We also show that a repulsive molecule-molecule scattering can stabilize a sufficiently dense atomic condensate, leading to the possibility of a phase transition. We caution that 3-body processes may render this transition unobservable.