Making Cold Molecules by Time-dependent Feshbach Resonances

TL;DR

This paper presents a simple, adaptable model based on Feshbach resonances and Landau-Zener theory to predict atom-to-molecule conversion efficiencies in cold atomic gases, including Bose-Einstein condensates.

Contribution

It introduces a straightforward, parameterized model for predicting molecule formation via time-dependent Feshbach resonances, applicable to both trapped atoms and condensates.

Findings

Model accurately predicts conversion probabilities for specific atomic species.

Landau-Zener interpretation provides intuitive understanding of the process.

Model is useful for estimating efficiencies in experimental setups.

Abstract

Pairs of trapped atoms can be associated to make a diatomic molecule using a time dependent magnetic field to ramp the energy of a scattering resonance state from above to below the scattering threshold. A relatively simple model, parameterized in terms of the background scattering length and resonance width and magnetic moment, can be used to predict conversion probabilities from atoms to molecules. The model and its Landau-Zener interpretation are described and illustrated by specific calculations for $^{23}$Na, $^{87}$Rb, and $^{133}$Cs resonances. The model can be readily adapted to Bose-Einstein condensates. Comparison with full many-body calculations for the condensate case show that the model is very useful for making simple estimates of molecule conversion efficiencies.