  Graphene is an attractive material for nanomechanical devices because it
allows for exceptional properties, such as high frequencies and quality
factors, and low mass. An outstanding challenge, however, has been to obtain
large coupling between the motion and external systems for efficient readout
and manipulation. Here, we report on a novel approach, in which we capacitively
couple a high-Q graphene mechanical resonator ($Q \sim 10^5$) to a
superconducting microwave cavity. The initial devices exhibit a large
single-photon coupling of $\sim 10$ Hz. Remarkably, we can electrostatically
change the graphene equilibrium position and thereby tune the single photon
coupling, the mechanical resonance frequency and the sign and magnitude of the
observed Duffing nonlinearity. The strong tunability opens up new
possibilities, such as the tuning of the optomechanical coupling strength on a
time scale faster than the inverse of the cavity linewidth. With realistic
improvements, it should be possible to enter the regime of quantum
optomechanics.
