  The out-of-equilibrium dynamics of interaction quenched finite ultracold
bosonic ensembles in periodically driven one-dimensional optical lattices is
investigated. It is shown that periodic driving enforces the bosons in the
outer wells of the finite lattice to exhibit out-of-phase dipole-like modes,
while in the central well the atomic cloud experiences a local breathing mode.
The dynamical behavior is investigated with varying driving frequency,
revealing a resonant-like behavior of the intra-well dynamics. An interaction
quench in the periodically driven lattice gives rise to admixtures of different
excitations in the outer wells, an enhanced breathing in the center and an
amplification of the tunneling dynamics. We observe then multiple resonances
between the inter- and intra-well dynamics at different quench amplitudes, with
the position of the resonances being tunable via the driving frequency. Our
results pave the way for future investigations on the use of combined driving
protocols in order to excite different inter- and intra-well modes and to
subsequently control them.
