  Coherent inter-conversion between an optical and a mechanical excitation in
an optomechanical resonator can be used for the storage of an optical pulse as
an excitation in a mechanical oscillator. This optomechanical light storage is
enabled by external writing and readout pulses at one mechanical frequency
below the optical resonance. In this paper, we expand an earlier experimental
study [Phys. Rev. Lett. 107, 133601 (2011)] on storing an optical pulse as a
radial breathing mode in a silica microsphere. We show that the heterodyne
beating between a readout pulse and the corresponding retrieved pulse features
a periodic oscillation with a well-defined phase and with the beating period
given by the mechanical frequency, demonstrating directly the coherent nature
of the light storage process. The coherent inter-conversion accelerates with
increasing optomechanical coupling rates, providing an effective mechanism for
tailoring the temporal profile of the retrieved pulse. Experimental studies on
both light storage and optomechanically induced transparency under nearly the
same conditions also illustrate the connections between these two
closely-related processes.
