Synthetic mechanical lattices with synthetic interactions

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 real materials. In addition enabling new physics explorations, such developments promise advance control acoustic and metamaterials, consequently enable capabilities controlling sound energy. Here, we demonstrate building blocks highly tunable metamaterials real-time measurement feedback modular elements. We experimentally engineer synthetic lattice Hamiltonians describing energy (phonons) our system, with local site energies loss gain well complex hopping between oscillators, including natural extension nonreciprocal hopping. Beyond linear terms, how this measurement-based approach makes it possible independently introduce nonlinear interaction terms. Looking forward, lattices open door phenomena related topology, non-Hermiticity, dynamics nonstandard geometries, higher dimensions, novel multibody interactions.