Fast, robust, and amplified transfer of topological edge modes on a time-varying mechanical chain

We show that it is possible to successfully, rapidly, and robustly transfer a topological vibrational edge mode across a time-varying mechanical chain. The stiffness values of the springs of the chain are arranged in an alternating staggered way such that we obtain a mechanical analog of the quantum Su-Schrieffer-Heeger model, which exhibits a nontrivial topological phase. Using optimal control methods, we are able to design control schemes for driving the stiffness parameters such that the transfer is done with high fidelity, speed, and robustness against disorder as well as energy amplification of the target edge mode.