  We study the process of production of ultracold molecules from ultracold
atoms using a sinusoidally oscillating magnetic field modulation. When the
magnetic field is resonant roughly with the molecular binding energy,
Shapiro-like resonances are observed. Their resonance profiles are well fitted
by the Lorentzian functions. The line widths depend on both the amplitude and
the duration of the applied modulations, and are found to be dramatically
broadened by thermal dephasing effect. The resonance centers shift due to both
many-body effect and finite temperature effect. Our theory is consistent with
recent experiment (S. T. Thompson, E. Hodby, and C. E. Wieman, Phys. Rev. Lett.
95, 190404 (2005)). Our model predicts a 1/3 ceiling for the molecular
production yield in uncondensed ultracold atomic clouds for a long coupling
time, while for the condensed atoms the optimal conversion yield could be
beyond the limit.
