  The interaction of optical and mechanical modes in nanoscale optomechanical
systems has been widely studied for applications ranging from sensing to
quantum information science. Here, we develop a platform for cavity
optomechanical circuits in which localized and interacting 1550 nm photons and
2.4 GHz phonons are combined with photonic and phononic waveguides. Working in
GaAs facilitates manipulation of the localized mechanical mode either with a
radio frequency field through the piezo-electric effect, or optically through
the strong photoelastic effect. We use this to demonstrate a novel acoustic
wave interference effect, analogous to coherent population trapping in atomic
systems, in which the coherent mechanical motion induced by the electrical
drive can be completely cancelled out by the optically-driven motion. The
ability to manipulate cavity optomechanical systems with equal facility through
either photonic or phononic channels enables new device and system
architectures for signal transduction between the optical, electrical, and
mechanical domains.
