Non-adiabatic time-optimal edge mode transfer on mechanical topological chain

We show that it is possible to successfully transfer topologically protected edge modes across a mechanical chain, with non-adiabatic optimal control schemes, in a time even shorter than their own period. The proposed protocols vastly outperform the adiabatic ones, both in time-scales and in robustness against disorder. Our control schemes possess non-adiabatic time intervals during which driving frequencies exceed characteristic frequencies of the system, shift the value of adiabatic invariant, and exchange a great amount of energy. As a bonus feature and in contrast with quantum chains, ultrafast pumping in classical chains is accompanied with amplification of the edge mode. Introducing non-adiabatic pumping of topologically protected states aims to challenge common approaches in this emerging field.