Tunable nonlinearity in a Graphene-Silicon Nitride hybrid resonator

Silicon Nitride (SiNx) resonators with high Q have garnered attention due to their strong promise of operation in the quantum regime at room temperature. Simultaneously, graphene resonators with high Young’s modulus leading to large and tunable mechanical nonlinearity, have opened up possibilities of mixing and manipulating frequency modes. Here we propose a hybrid system that integrates high Q of SiNx resonator with nonlinearity of graphene resonator. When both resonator modes are tuned on resonance, the motional backaction of graphene induces nonlinear response in SiNx. The hybrid mode, when driven parametrically at twice the resonant frequency, demonstrates parametric amplification and cascaded four wave mixing. Generated peaks and their dispersion reveal the rich interplay between nonlinear damping and cubic nonlinearity. Observations match well with numerical simulations. Furthermore, in direct analogy with optomechanics, the graphene acts as an auxiliary cavity leading to induced nonlinearity on SiNx at resonance. These results indicate that such a hybrid mechanical system can be an efficient, alternate platform for coherent control of modes, in the growing field of opto and electromechanics.