A Complex Chemical Potential: Signature of Decay in a Bose-Einstein Condensate

TL;DR

This paper investigates the static properties of a Bose-Einstein condensate coupled to molecules via Feshbach resonance, revealing a decay mechanism characterized by a complex chemical potential and specific density and scattering length dependencies.

Contribution

It introduces a variational approach to analyze the coupled condensate system, highlighting the decay process through the imaginary part of the chemical potential and its measurable dependencies.

Findings

Collapse of the ground state at critical density

Decay rate scales with density as $ ho^{3/2}$

Decay rate scales with scattering length as $a^{5/2}$

Abstract

We explore the zero-temperature statics of an atomic Bose-Einstein condensate in which a Feshbach resonance creates a coupling to a second condensate component of quasi-bound molecules. Using a variational procedure to find the equation of state, the appearance of this binding is manifest in a collapsing ground state, where only the molecular condensate is present up to some critical density. Further, an excited state is seen to reproduce the usual low-density atomic condensate behavior in this system, but the molecular component is found to produce an underlying decay, quantified by the imaginary part of the chemical potential. Most importantly, the unique decay rate dependencies on density ($\sim \rho ^{3/2}$) and on scattering length ($\sim a^{5/2}$) can be measured in experimental tests of this theory.