  Using pulsed optical excitation and read-out along with single phonon
counting techniques, we measure the transient back-action, heating, and damping
dynamics of a nanoscale silicon optomechanical crystal cavity mounted in a
dilution refrigerator at a base temperature of 11mK. In addition to observing a
slow (~740ns) turn-on time for the optical-absorption-induced hot phonon bath,
we measure for the 5.6GHz `breathing' acoustic mode of the cavity an initial
phonon occupancy as low as 0.021 +- 0.007 (mode temperature = 70mK) and an
intrinsic mechanical decay rate of 328 +- 14 Hz (mechanical Q-factor =
1.7x10^7). These measurements demonstrate the feasibility of using short pulsed
measurements for a variety of quantum optomechanical applications despite the
presence of steady-state optical heating.
