  We reveal the existence of high-density Feshbach resonances in the collision
between the ground and metastable states of $^{171}$Yb and coherently produce
the associated Feshbach molecules by photoassociation. The extremely small
transition rate is overcome by the enhanced Franck-Condon factor of the weakly
bound Feshbach molecule, allowing us to observe Rabi oscillations with long
decay time between an atom pair and a molecule in an optical lattice. We also
perform the precision measurement of the binding energies, which characterizes
the observed resonances. The ultra-narrow photoassociation will be a basis for
practical implementation of optical Feshbach resonances.
