Few-body ultracold reactions in a Bose-Fermi mixtures*

This project investigates the properties of fermionic molecule $^{87}\mbox{Rb} ^{40}\mbox{K}$, including (i) its formation from a mixed gas of bosonic $^{87}\mbox{Rb}$ and fermionic $^{40}\mbox{K}$ through magnetic field ramping and (ii) its scattering properties after formation. This has been approached mainly from the few body perspective: the spectrum of two bosons($^{87}\mbox{Rb}$) and two fermions($^{40}\mbox{K}$) is first calculated in a harmonic trap using correlated-Gaussian basis throughout the range of a broad Fano-Feshbach resonance. This provides a few-body solution to the magneto-association of fermionic Feshbach molecules, subsequently used to study the time-evolution of the system as the scattering length changes, mimicking experiments with Bose-Fermi mixture 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. Molecule-atom and molecule-molecule scattering properties are also discussed.