The role of particle interactions in a many-body model of Feshbach molecular formation in bosonic systems

In this paper, we investigate the atom-molecule conversion dynamics of a generalized many-body model that includes the atom-atom, atom-molecule, and molecule-molecule interactions, emphasizing the efficiency of the Feshbach molecular formation. We show that the picture of two-body molecular production depicted by the Landau-Zener model is significantly altered: The energy levels are dramatically distorted and the conversion efficiency is suppressed by the particle interactions. According to the rule of constant action and with the help of phase-space analysis, we derive an analytical expression for the conversion efficiency in the adiabatic limit. It shows a ceiling for the conversion efficiency when the interaction strength is larger than a critical value. We further derive a closed equation for the conversion efficiency with the stationary phase approximation. In the sudden limit, the conversion efficiency is twice that predicted by the two-body Landau-Zener formula. Our analytical formula has been confirmed by numerical calculations.