Synthetic Mechanical Lattices with Synthetic Interactions

TL;DR

This paper introduces a method to create highly tunable synthetic mechanical lattices using real-time measurement and feedback, enabling exploration of complex phenomena like topology, non-Hermiticity, and nonlinear dynamics in mechanical systems.

Contribution

It demonstrates the experimental engineering of synthetic lattice Hamiltonians with tunable parameters and nonlinear interactions in mechanical metamaterials.

Findings

Successful control over local site energies, loss, gain, and complex hopping.

Implementation of non-reciprocal hopping in mechanical systems.

Introduction of nonlinear interaction terms through feedback control.

Abstract

Metamaterials based on mechanical elements have been developed over the past decade as a powerful platform for exploring analogs of electron transport in exotic regimes that are hard to produce in real materials. In addition to enabling new physics explorations, such developments promise to advance the control over acoustic and mechanical metamaterials, and consequently to enable new capabilities for controlling the transport of sound and energy. Here, we demonstrate the building blocks of highly tunable mechanical metamaterials based on real-time measurement and feedback of modular mechanical elements. We experimentally engineer synthetic lattice Hamiltonians describing the transport of mechanical energy (phonons) in our mechanical system, with control over local site energies and loss and gain as well as control over the complex hopping between oscillators, including a natural extension to non-reciprocal hopping. Beyond linear terms, we experimentally demonstrate how this measurement-based feedback approach opens the window to independently introducing nonlinear interaction terms. Looking forward, synthetic mechanical lattices open the door to exploring phenomena related to topology, non-Hermiticity, and nonlinear dynamics in non-standard geometries, higher dimensions, and with novel multi-body interactions.