Production efficiency of Feshbach molecules in fermion systems

We present a consistent nonequilibrium theory for the production of molecular dimers from a two-component quantum-degenerate fermion atomic gas, via a linear downward sweep of the magnetic field across a Feshbach resonance. This problem raises interest because it is presently unclear as to why deviations from the universal Landau-Zener formula for the transition probability at two-level crossing are observed in the experimentally measured production efficiencies. We show that the molecular conversion efficiency is represented by a power series in terms of a dimensionless parameter which, in the zero-temperature limit, depends solely on the initial gas density and the Landau-Zener parameter. Our result reveals a hindrance of the canonical Landau-Zener transition probability due to many-body effects, and presents an explanation for the experimentally observed deviations [K.E. Strecker \textit{et al.}, Phys. Rev. Lett. {\bf 91}, 080406 (2003)].