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

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.