We study tunneling dynamics of atomic pairs in Bose-Einstein condensates wi
th Feshbach resonances. It is shown that the tunneling of the atomic pairs
depends on not only the tunneling coupling between the atomic condensate an
d the molecular condensate, but also the interatomic nonlinear interactions
and the initial number of atoms in these condensates. It is found that in
addition to oscillating tunneling current between the atomic condensate and
the molecular condensate, the nonlinear atomic-pair tunneling dynamics sus
tains a self-locked population imbalance: a macroscopic quantum self-trappi
ng effect. The influence of decoherence induced by noncondensate atoms on t
he tunneling dynamics is investigated. It is shown that decoherence suppres
ses atomic-pair tunneling.