Spatial mapping and analysis of graphene nanomechanical resonator networks

Nanoelectromechanical (NEMS) resonator networks have drawn increasing interest due to their potential applications in emergent behavior, sensing, phononics, and mechanical information processing. A challenge toward realizing these large-scale networks is the ability to controllably tune and reconfigure the collective, macroscopic properties of the network, which relies directly on the development of methods to characterize the constituent NEMS resonator building blocks and their coupling. In this work, we demonstrate a scalable optical technique to spatially map graphene NEMS networks and read out the fixed-frequency collective response as a single vector. Using the response vectors, we introduce an efficient algebraic approach to quantify the site-specific elasticity, mass, damping, and coupling parameters of network clusters. We apply this technique to accurately characterize single uncoupled resonators and coupled resonator pairs by sampling them at just two frequencies, and without the use of curve fitting or the associated a priori parameter estimates. Our technique may be applied to a range of classical and quantum resonator systems and fills in a vital gap for programming NEMS networks.