Vibrational mechanics in higher dimension: Tuning potential landscapes

This work extends the domain of vibrational mechanics to higher dimensions, with fast vibrations applied to different directions. In particular, the presented analysis considers the case of a split biharmonic drive, where harmonics of frequency $\ensuremath{\omega}$ and $2\ensuremath{\omega}$ are applied to orthogonal directions in a two-dimensional setting. It is shown, both numerically and with analytic calculations, that this determines a highly tunable effective potential with the same symmetry as the original one. The driving allows one not only to tune the amplitude of the potential, but also to introduce an arbitrary spatial translation in the direction corresponding to the $2\ensuremath{\omega}$ driving. The setup allows for generalization to implement translations in an arbitrary direction within the two-dimensional landscapes. The same principles also apply to three-dimensional periodic potentials.