Tailoring edge-to-edge pumping via adiabatic transformations and non-Hermitian shortcuts

We propose a systematic way to achieve superfast edge-to-edge transformations in modulated mechanical lattices. According to the bulk-edge correspondence principle, the occurrence of localized edge states in dynamical systems is inherently linked with the topological characteristics of the band structure. Such states can be either localized at the left or the right boundary of the structure depending on a relevant modulation parameter which, in the case at hand, is the phase of the modulation. When the phase, or phason, is varied in an adiabatic fashion, there is the opportunity to trigger a modal transformation that drives the energy transfer between the boundaries of the lattice. We show that there is a limiting speed for this transformation to successfully occur and, given a number of damping and anti-damping elements placed along the lattice, we demonstrate that edge-to-edge transitions can be achieved with faster (non-adiabatic) propagation rates. This work opens new opportunities in the context of controllable waveguides and investigates the energy transfer capabilities of such a specific family of non-Hermitian structures.