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The temporal modulation of a relevant parameter can be employed to inducemodal transformations in Hermitian elastic lattices. When this is combined witha proper excitation mechanism, it allows to drive the energy transfer acrossthe lattice with tunable propagation rates. Such a modal transformation,however, is limited by the adiabaticity of the process, which dictates an upperbound for the modulation speed. In this manuscript, we employ a non-Hermitianshortcut by way of a tailored gain and loss to violate the adiabatic limit and,therefore, to achieve superfast modal transformations. A quantitative conditionfor adiabaticity is firstly derived and numerically verified for a pair ofweakly coupled time-dependent mechanical oscillators, which can be interpretedin the light of modal interaction between crossing states. It is shown that forsufficiently slow time-modulation, the elastic energy can be transferred fromone oscillator to the other. A non-Hermitian shortcut is later induced to breakthe modal coupling and, therefore, to speed-up the modal transformation. Thestrategy is then generalized to elastic lattices supporting topological edgestates. We show that the requirements for a complete edge-to-edge energytransfer are lifted from the adiabatic limit toward higher modulationvelocities, opening up new opportunities in the context of wave manipulationand control.

Adiabatic edge-to-edge transformations in time-modulated elastic lattices and non-Hermitian shortcuts