  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.
