  The correlated non-equilibrium quantum dynamics following a multiple
interaction quench protocol for few-bosonic ensembles confined in finite
optical lattices is investigated. The quenches give rise to an interwell
tunneling and excite the cradle and a breathing mode. Several tunneling
pathways open during the time interval of increased interactions, while only a
few occur when the system is quenched back to its original interaction
strength. The cradle mode, however, persists during and in between the
quenches, while the breathing mode possesses dinstinct frequencies. The
occupation of excited bands is explored in detail revealing a monotonic
behavior with increasing quench amplitude and a non-linear dependence on the
duration of the application of the quenched interaction strength. Finally, a
periodic population transfer between momenta for quenches of increasing
interaction is observed, with a power-law frequency dependence on the quench
amplitude. Our results open the possibility to dynamically manipulate various
excited modes of the bosonic system.
