  The combination of large per-photon optical force and small motional mass
attainable in nanocavity optomechanical systems results in strong dynamical
back-action between mechanical motion and the cavity light field. In this work
we study the optical control of mechanical motion within two different
nanocavity structures, a zipper nanobeam photonic crystal cavity and a
double-microdisk whispering-gallery resonator. The strong optical gradient
force within these cavities is shown to introduce signifcant optical rigidity
into the structure, with the dressed mechanical states renormalized into
optically-bright and optically-dark modes of motion. With the addition of
internal mechanical coupling between mechanical modes, a form of
optically-controlled mechanical transparency is demonstrated in analogy to
electromagnetically induced transparency of three-level atomic media. Based
upon these measurements, a proposal for coherently transferring RF/microwave
signals between the optical field and a long-lived dark mechanical state is
described.
