Imaging the Motion of a Graphene Nanomechanical Resonator Network

Programmable networks of nanomechanical resonators offer a potential platform to construct phononic crystals and metamaterials, to simulate quantum phenomena, and to realize neuromorphic computing schemes. A key step in achieving programmability is to measure the coupling between resonators in the network. Typically, the coupling is calculated from spectra of resonant modes, which works well for a single pair of coupled resonators. However, as these networks are made larger in size, matching a given spectral mode splitting to an individual coupled pair in the network becomes increasingly challenging. Here we develop a means to identify which resonators are coupled by imaging the network’s amplitude and phase for each spectral peak with scanning interferometric microscopy (SIM). Together with a simple mechanical model, these images spatially resolve the coupling and energy distribution in the network. Using our technique, we image a network of graphene nanomechanical resonators and identify an isolated region of two strongly coupled resonators and a third weakly coupled resonator. As a tool for future programmable nanomechanical networks, our SIM approach could be used to tune resonators, to illuminate vibrational energy leaks, and to image energy flow in patterned waveguides.