  Electromagnetically induced transparency has great theoretical and
experimental importance in many physics subjects, such as atomic physics,
quantum optics, and more recent cavity optomechanics. Optical delay is the most
prominent feature of electromagnetically induced transparency, and in cavity
optomechanics optical delay is limited by mechanical dissipation rate of
sideband-resolved mechanical modes. Here we demonstrate a cascaded optical
transparency scheme by leveraging the parametric phonon-phonon coupling in a
multimode optomechanical system, where a low damping mechanical mode in the
unresolved-sideband regime is made to couple to an intermediate, high frequency
mechanical mode in the resolved-sideband regime of an optical cavity. Extended
optical delay and higher transmission, as well as optical advancing are
demonstrated. These results provide a route to realize ultra-long optical
delay, indicating a significant step toward integrated classical and quantum
information storage devices.
