Conversion Efficiencies of Heteronuclear Feshbach Molecules

We study the conversion efficiency of heteronuclear Feshbach molecules in population imbalanced atomic gases formed by ramping the magnetic field adiabatically. We extend the recent work [J. E. Williams et al., New J. Phys., 8, 150 (2006)] on the theory of Feshbach molecule formations to various combinations of quantum statistics of each atomic component. A simple calculation for a harmonically trapped ideal gas is in good agreement with the recent experiment [S. B. Papp and C. E. Wieman, Phys. Rev. Lett., 97, 180404 (2006)] without any fitting parameters. We also give the conversion efficiency as an explicit function of initial peak phase space density of the majority species for population imbalanced gases. In the low-density region where Bose-Einstein condensation does not appear, the conversion efficiency is a monotonic function of the initial peak phase space density, but independent of statistics of a minority component. The quantum statistics of majority atoms has a significant effect on the conversion efficiency. In addition, Bose-Einstein condensation of an atomic component is the key element determining the maximum conversion efficiency.