Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity

The combination of low mass density, high frequency, and high quality-factor of mechanical resonators made of two-dimensional crystals such as graphene make them attractive for applications in force sensing/mass sensing, and exploring the quantum regime of mechanical motion. Microwave optomechanics with superconducting cavities offers exquisite position sensitivity and enables the preparation and detection of mechanical systems in the quantum ground state. Here, we demonstrate coupling between a multilayer graphene resonator with quality factors up to 220,000 and a high-$\textit{Q}$ superconducting cavity. Using thermo-mechanical noise as calibration, we achieve a displacement sensitivity of 17 fm/$\sqrt{\text{Hz}}$. Optomechanical coupling is demonstrated by optomechanically induced reflection (OMIR) and absorption (OMIA) of microwave photons. We observe 17 dB of mechanical microwave amplification and signatures of strong optomechanical backaction. We extract the cooperativity $C$, a characterization of coupling strength, quantitatively from the measurement with no free parameters and find $C=8$, promising for the quantum regime of graphene motion.