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

• Published in: New journal of physics Vol. 23; no. 9; pp. 93008 - 93023
• Main Authors: Riva, Emanuele, Castaldini, Gianmaria, Braghin, Francesco
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01-09-2021
• Subjects: Adiabatic flow; adiabatic pumping; Behavior; Electromagnetism; Energy; Energy transfer; Mechanical oscillators; Mechanics; Modulation; non-Hermitian; Oscillators; phononic crystal; Physics; Time dependence; topological lattice; Transformations; Upper bounds
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ac1ed4

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.