Enhanced magnetoassociation of $^6$Li in the quantum degenerate regime

We study magnetic Feshbach resonance of ultracold $^6$Li atoms in a dipole trap close to quantum degeneracy. The experiment is carried out by linearly ramping down the magnetic field from the BCS to the BEC side around the broad resonance at $B_r=834.1$G. The Feshbach molecule formation efficiency depends strongly on the temperature of the atomic gas and the rate at which the magnetic field is ramped across the Feshbach resonance. The molecular association process is well described by the Landau-Zener transition while above the Fermi temperature, such that two-body physics dominates the dynamics. However, we observe an enhancement of the atom-molecule coupling as the Fermionic atoms reach degeneracy, demonstrating the importance of many-body coherence not captured by the conventional Landau-Zener model. We develop a theoretical model that explains the temperature dependence of the atom-molecule coupling. Furthermore, we characterize this dependence experimentally and extract the atom-molecule coupling coefficient as a function of temperature, finding qualitative agreement between our model and experimental results. Accurate measurement of this coupling coefficient is important for both theoretical and experimental studies of atom-molecule association dynamics.