Cavity-mediated coupling of mechanical oscillators limited by quantum back-action

A complex quantum system can be constructed by coupling simple elements. For example, trapped-ion(1,2) or superconducting(3) quantum bits may be coupled by Coulomb interactions, mediated by the exchange of virtual photons. Alternatively, quantum objects can be made to emit and exchange real photons, providing either unidirectional coupling in cascaded geometries(4-6), or bidirectional coupling that is particularly strong when both objects are placed within a common electromagnetic resonator(7). However, in such an open system, the capacity of a coupling channel to convey quantum information or generate entanglement may be compromised by photon loss(8). Here, we realize phase-coherent interactions between two addressable, spatially separated, near-groundstate mechanical oscillators within a driven optical cavity. We observe the quantum back-action noise imparted by the optical coupling resulting in correlated mechanical fluctuations of the two oscillators. Our results illustrate challenges and opportunities of coupling quantum objects with light for applications of quantum cavity optomechanics(8-14).