  We theoretically propose and experimentally demonstrate coherent wavelength
conversion of optical photons using photon-phonon translation in a
cavity-optomechanical system. For an engineered silicon optomechanical crystal
nanocavity supporting a 4 GHz localized phonon mode, optical signals in a 1.5
MHz bandwidth are coherently converted over a 11.2 THz frequency span between
one cavity mode at wavelength 1460 nm and a second cavity mode at 1545 nm with
a 93% internal (2% external) peak efficiency. The thermal and quantum limiting
noise involved in the conversion process is also analyzed, and in terms of an
equivalent photon number signal level are found to correspond to an internal
noise level of only 6 and 4x10-3 quanta, respectively.
