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Tunable phonon cavity coupling in graphene membranes

A major achievement of the past decade has been the realization of macroscopic quantum systems by exploiting interactions between optical cavities and mechanical resonators. In these systems, phonons are coherently annihilated or created in exchange for photons. Similar phenomena have recently been observed through "phonon cavity" coupling -- energy exchange between modes of a single system as mediated by intrinsic material nonlinearity. To date, this has been demonstrated primarily for bulk crystalline, high-quality-factor (Q>100,000) mechanical systems operated at cryogenic temperatures. Here we propose graphene as an ideal candidate for the study of such nonlinear mechanics. The large elastic modulus of this material and capability for spatial symmetry breaking via electrostatic forces is expected to generate a wealth of nonlinear phenomena, including tunable inter-modal coupling. We have fabricated circular graphene membranes and report strong phonon cavity effects at room temperature, despite the modest Q (~100) of this system. We observe both amplification into parametric instability ("mechanical lasing") and cooling of Brownian motion in the fundamental mode through excitation of cavity sidebands. Furthermore, we characterize quenching of these parametric effects at large vibrational amplitudes, offering a window on the all-mechanical analogue of cavity optomechanics, where observation of such effects has proven elusive.