  A complex quantum system can be constructed by coupling simple quantum
elements to one another. For example, trapped-ion or superconducting quantum
bits may be coupled by Coulomb interactions, mediated by the exchange of
virtual photons. Alternatively quantum objects can be coupled by the exchange
of real photons, particularly when driven within resonators that amplify
interactions with a single electro-magnetic mode. However, in such an open
system, the capacity of a coupling channel to convey quantum information or
generate entanglement may be compromised. Here, we realize phase-coherent
interactions between two spatially separated, near-ground-state mechanical
oscillators within a driven optical cavity. We observe also the noise imparted
by the optical coupling, which results in correlated mechanical fluctuations of
the two oscillators. Achieving the quantum backaction dominated regime opens
the door to numerous applications of cavity optomechanics with a complex
mechanical system. Our results thereby illustrate the potential, and also the
challenge, of coupling quantum objects with light.
