Strong indirect coupling between graphene-based mechanical resonators via a phonon cavity.

Mechanical resonators are promising systems for storing and manipulating information. To transfer information between mechanical modes, either direct coupling or an interface between these modes is needed. In previous works, strong coupling between different modes in a single mechanical resonator and direct interaction between neighboring mechanical resonators have been demonstrated. However, coupling between distant mechanical resonators, which is a crucial request for long-distance classical and quantum information processing using mechanical devices, remains an experimental challenge. Here, we report the experimental observation of strong indirect coupling between separated mechanical resonators in a graphene-based electromechanical system. The coupling is mediated by a far-off-resonant phonon cavity through virtual excitations via a Raman-like process. By controlling the resonant frequency of the phonon cavity, the indirect coupling can be tuned in a wide range. Our results may lead to the development of gate-controlled all-mechanical devices and open up the possibility of long-distance quantum mechanical experiments.