  The association process of Feshbach molecules is well described by a
Landau-Zener (LZ) transition above the Fermi temperature, such that two-body
physics dominates the dynamics. However, using $^6$Li atoms and the associated
Feshbach resonance at $B_r=834.1$ G, 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 LZ
model. In the experiment, we apply a linear association ramp ranging from
adiabatic to non-equilibrium molecule association for various temperatures. 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. In addition, we simulate the dynamics of molecular
association during a nonlinear field ramp. We find that, in the non-equilibrium
regime, molecular association efficiency can be enhanced by sweeping the
magnetic field cubically with time. Accurate measurement of the atom-molecule
coupling coefficient is important for both theoretical and experimental studies
of molecular association and many-body collective dynamics.
