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

Mechanical resonators are ubiquitous in modern information technology. With the possibility of coupling them to electromagnetic and plasmonic modes, they hold promise as 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(1-7). The tension -mediated nonlinear coupling between various modes of the resonator can be excited in a controllable manner(8-11). Here we engineer a graphene resonator with large frequency tunability at low temperatures, resulting in a 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 similar to 100 MHz is achieved in the strong coupling regime. The ability to dynamically control the coupling between the high -frequency eigenmodes of a mechanical system opens up the possibility of quantum mechanical experiments at low temperatures(12,13).