Characterizing Networks of Graphene Nanomechanical Resonators

Programmable nanomechanical networks have a wide range of potential applications, from phononic circuits to quantum simulation. To realize these networks in the lab, it is essential to characterize the network's resonator nodes and connectivity. While spectroscopy is commonly used to characterize small assemblies—like a pair of coupled resonators—it does not provide spatially resolved, node-specific information and readily fails to detect weak coupling. To overcome this challenge, we use scanning interference microscopy (SIM) to spatially image the amplitude and phase of hybridized vibrational modes in an array of suspended graphene nanomechanical resonators. We use these SIM measurements to algebraically characterize the network's complete mechanical parameters including node elasticity, mass, and damping in addition to nearest-neighbor coupling constants. In combination with existing methods to tune resonators, our diagnostic tool and resonator array form a viable programmable nanomechanical network platform and may be used to pattern acoustic waveguides and lattices or to realize dynamic phononic metamaterials.