Making cold molecules by time-dependent Feshbach resonances

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, parametrized 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 Na-23, Rb-87 and Cs-133 resonances. The model can be readily adapted to Bose-Einstein condensates. Comparison with full many-body calculations for the condensate case shows that the model is very useful for making simple estimates of molecule conversion efficiencies.