  Periodic driving and Floquet engineering have emerged as invaluable tools for
controlling and uncovering novel phenomena in quantum systems. In this study,
we adopt these methods to manipulate nonequilibrium processes within
electronic-vibronic open quantum systems. Through resonance mechanisms and by
focusing on the limit-cycle dynamics and quantum thermodynamic properties, we
illustrate the intricate interplay between the driving field and vibronic
states and its overall influence on the electronic system. Specifically, we
observe an effective decoupling of the electronic system from the periodic
driving at specific frequencies, a phenomenon that is mediated by the
vibrational mode interaction. Additionally, we engineer the driving field to
obtain a partial removal of the Franck-Condon blockade. These insights hold
promise for efficient charge current control. Our results are obtained from
numerically exact calculations of the hierarchical equations of motion and
further analyzed by a time-periodic master equation approach.
