Optomechanical coupling enhanced by quantum reactance in Josephson junction devices*

Graphene mechanical resonators promises to provide a unique platform in the field of cavity optomechanics combined with superconducting microwave cavities. If a suspended graphene Josephson junction mediates the coupling between microwave cavity and mechanical motion of the graphene resonator, strong optomechanical coupling can be achieved owing to the large influence of gate charge tunable Josephson inductance, leading to phonon or photon detection. Furthermore, we have also investigated a scheme to enhance the optomechanical coupling by embedding a Josephson junction Cooper Pair Box (CPB) into the cavity. The CPB is coupled to the cavity via a movable capacitance and the optomechanical interaction is enhanced six-seven orders of magnitude by tuning its charge-dependent Josephson capacitance, facilitating access to ultra-strong coupling regime with properly chosen parameters.