Few-body ultracold reactions in a Bose-Fermi mixture

The spectrum of two bosons and two fermions in a trap is calculated using a correlated-Gaussian basis throughout the range of a broad Fano-Feshbach resonance. The calculations provide a few-body solution to the magneto-association of fermionic Feshbach molecules. This solution is used to study the time evolution of the system as the scattering length changes, mimicking experiments with Bose-Fermi mixtures near Fano-Feshbach resonances. The structure of avoided crossings in the few-body spectrum enables an interpretation of the dynamics of the system as a sequence of Landau-Zener transitions. The calculated molecule formation rate is compared with experimental observations.