Dynamical strong coupling and parametric amplification in mechanical modes of graphene drums

Mechanical resonators are ubiquitous in modern information technology. With the ability to couple them to electromagnetic and plasmonic modes, they hold the promise to be the key building blocks in future quantum information technology. Graphene based resonators are of interest for technological applications due to their high resonant frequencies, multiple mechanical modes, and low mass. The tension mediated non-linear coupling between various modes of the resonator can be excited in a controllable manner. Here, we engineer a graphene resonator to have large frequency tunability at low temperatures resulting in large intermodal coupling strength. We observe the emergence of new eigenmodes and amplification of the coupled modes using red and blue parametric excitation respectively. We demonstrate that the dynamical intermodal coupling is tunable. A cooperativity of 60 between two resonant modes of ~100 MHz is achieved in the strong coupling regime. The ability to dynamically control the coupling between high frequency eigenmodes of a mechanical system opens up possibility for quantum mechanical experiments at low temperatures.