  We study the effect of a many-body interaction on inter-band oscillations in
a two-band Bose-Hubbard model with external Stark force. Weak and strong
inter-band oscillations are observed, where the latter arise from a resonant
coupling of the bands. These oscillations collapse and revive due to a weak
two-body interaction between the atoms. Effective models for oscillations in
and out of resonance are introduced that provide predictions for the system's
behaviour, particularly for the time-scales for the collapse and revival of the
resonant inter-band oscillations.
