Manipulation of Feshbach resonances in ultracold atomic collisions using time-dependent magnetic fields

We have calculated the time-dependent dynamics of two ultracold Na atoms in an atom trap where a time-dependent magnetic field $B\left(t\right)\mathrm{}$ moves a Feshbach resonance state across the energy threshold for a binary collision. Our coupled-channel scattering calculations, which reproduce the observed properties of such resonances in sodium atom collisions, can be reduced to an effective two-channel configuration-interaction model for one bound state and one continuum. The model is adapted to describe the time-dependent dynamics induced by $B\left(t\right)\mathrm{}$ for two atoms trapped either in a strongly confining single well of an optical lattice or in an optical potential in the presence of a Bose-Einstein condensate. We show that a simple Landau-Zener curve crossing model gives quantitative agreement with exact calculations of field-induced transition rates. If $B\left(t\right)\mathrm{}$ sweeps the resonance across threshold from above, two atoms in the ground state of the trap potential can be efficiently converted to translationally cold dimer molecules. If the resonance is swept from below, the atoms can be removed from the ground state and placed in hot vibrational levels of the trap. Our calculations reproduce the rapid atom loss rates observed in a Na Bose-Einstein condensate due to sweeping a Feshbach resonance state through the binary collision threshold.