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

TL;DR

This paper demonstrates how non-Hermitian gain and loss can be used to achieve superfast edge-to-edge modal transformations in elastic lattices, surpassing the adiabatic limit and enabling rapid wave control.

Contribution

It introduces a non-Hermitian shortcut method to violate adiabaticity in elastic lattices, allowing faster modal transformations and energy transfer beyond traditional limits.

Findings

Derived a quantitative adiabaticity condition for mechanical oscillators

Showed superfast modal transformations using gain and loss

Extended the approach to topological elastic lattices

Abstract

The temporal modulation of a relevant parameter can be employed to induce modal transformations in Hermitian elastic lattices. When this is combined with a proper excitation mechanism, it allows to drive the energy transfer across the lattice with tunable propagation rates. Such a modal transformation, however, is limited by the adiabaticity of the process, which dictates an upper bound for the modulation speed. In this manuscript, we employ a non-Hermitian shortcut by way of a tailored gain and loss to violate the adiabatic limit and, therefore, to achieve superfast modal transformations. A quantitative condition for adiabaticity is firstly derived and numerically verified for a pair of weakly coupled time-dependent mechanical oscillators, which can be interpreted in the light of modal interaction between crossing states. It is shown that for sufficiently slow time-modulation, the elastic energy can be transferred from one oscillator to the other. A non-Hermitian shortcut is later induced to break the modal coupling and, therefore, to speed-up the modal transformation. The strategy is then generalized to elastic lattices supporting topological edge states. We show that the requirements for a complete edge-to-edge energy transfer are lifted from the adiabatic limit toward higher modulation velocities, opening up new opportunities in the context of wave manipulation and control.