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

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.

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Cited by in corpus (6)

• Elastic Temporal Waveguiding
• A multiple scattering formulation for elastic wave propagation in space-time modulated metamaterials
• Harnessing $\mathcal{P}\mathcal{T}$-symmetry in non-Hermitian stiffness-modulated waveguides
• Optimal design of fast topological pumping
• Non-Local Elastic Lattices with $\mathcal{P}\mathcal{T}$-Symmetry and Time Modulation: From Perfect Trapping to the Wave Boomerang Effect
• Differences between quantum and classical adiabatic evolution