Pair dynamics in the formation of molecules in a Bose-Einstein condensate

TL;DR

This paper develops a two-channel model incorporating pair dynamics for a Bose-Einstein condensate, showing that individual atomic dynamics are minor and validating traditional rate equations in photoassociation experiments.

Contribution

It generalizes existing mean-field models by explicitly including pair wave functions and derives conditions under which simplified Gross-Pitaevskii equations are valid.

Findings

Pair dynamics can be reduced to coupled Gross-Pitaevskii equations under certain time scale conditions.

Individual atomic dynamics are negligible compared to pair dynamics in typical experiments.

Traditional rate models are validated for photoassociation in Bose-Einstein condensates.

Abstract

We revisit the mean-field treatment of photoassociation and Feshbach resonances in a Bose-Einstein condensate previously used by various authors. Generalizing the Cherny and Shanenko approach (Phys. Rev. E 62, 1646-59 (2000) ) where the finite size of the potentials is explicitly introduced, we develop a two-channel model for a mixed atomic-molecular condensate. Besides the individual dynamics of the condensed and non-condensed atoms, the model also takes into account their pair dynamics by means of pair wave functions. We show that the resulting set of coupled equations can be reduced to the usual coupled Gross-Pitaevskii equations when the time scale of the pair dynamics is short compared to that of the individual dynamics. Such time scales are discussed in the case of typical photoassociation experiments with cw lasers. We show that the individual dynamics plays a minor role, demonstrating the validity of the rates predicted by the usual models describing photoassociation in a nondegenerate gas.