  The nonequilibrium ultracold bosonic quantum dynamics in finite optical
lattices of unit filling following a linear interaction quench from a
superfluid to a Mott insulator state and vice versa is investigated. The
resulting dynamical response consists of various inter and intraband tunneling
modes. We find that the competition between the quench rate and the
interparticle repulsion leads to a resonant dynamical response, at moderate
ramp times, being related to avoided crossings in the many-body eigenspectrum
with varying interaction strength. Crossing the regime of weak to strong
interactions several transport pathways are excited. The higher-band excitation
dynamics is shown to obey an exponential decay possessing two distinct time
scales with varying ramp time. Studying the crossover from shallow to deep
lattices we find that for a diabatic quench the excited band fraction
decreases, while approaching the adiabatic limit it exhibits a non-linear
behavior for increasing height of the potential barrier. The inverse ramping
process from strong to weak interactions leads to a melting of the Mott
insulator and possesses negligible higher-band excitations which follow an
exponential decay for decreasing quench rate. Finally, independently of the
direction that the phase boundary is crossed, we observe a significant
enhancement of the excited to higher-band fraction for increasing system size.
