  The non-equilibrium dynamics of small boson ensembles in a one-dimensional
optical lattice is explored upon a sudden quench of an additional harmonic trap
from strong to weak confinement. We find that the competition between the
initial localization and the repulsive interaction leads to a resonant response
of the system for intermediate quench amplitudes, corresponding to avoided
crossings in the many-body eigenspectrum with varying final trap frequency. In
particular, we show that these avoided crossings can be utilized to prepare the
system in a desired state. The dynamical response is shown to depend on both
the interaction strength as well as the number of atoms manifesting the
many-body nature of the tunneling dynamics.
