The mechanical properties of light have found widespread use in the manipulation of gas-phase atoms and ions, helping create new states of matter and realize complex quantum interactions. The field of cavity-optomechanics strives to scale this interaction to much larger, even human-sized mechanical objects. Going beyond the canonical Fabry-Perot cavity with a movable mirror, here we explore a new paradigm in which multiple cavity-optomechanical elements are wired together to form optomechanical circuits. Using a pair of optomechanical cavities coupled together via a phonon waveguide we demonstrate a tunable delay and filter for microwave-over-optical signal processing. In addition, we realize a tight-binding form of mechanical coupling between distant optomechanical cavities, leading to direct phonon exchange without dissipation in the waveguide. These measurements indicate the feasibility of phonon-routing based information processing in optomechanical crystal circuitry, and further, to the possibility of realizing topological phases of photons and phonons in optomechanical cavity lattices.
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