the choice of time window). The observed ringdown time $\tau_\text{m} = 5.3$ s corresponds to a mechanical quality factor $Q$ = 4.3 million at 400 mK, though this value varies with thermal cycling (i.e. between 400 mK and 4 K), and typically ranges from $\sim 4-5$ million.

As shown in Fig. \[fig1\]a, two independent Nd-YAG lasers (wavelength $\lambda$ = 1064 nm) provide a total of five beams for driving the cavity and performing the heterodyne detection of the membrane’s motion (described below). To achieve a large optomechanical back action with these lasers, we require a high-finesse optical cavity. The top and bottom mirrors in Fig. \[fig1\]a are designed to have a power reflectivity exceeding 99.98% and 99.998% respectively at $\lambda = 1064$ nm, which would correspond to a cavity finesse of 30,000. Generally these mirrors perform above this specification, however. Figure \[fig1\]c shows the results of a typical cavity ringdown measurement performed by toggling the power of a laser driving the cavity, and collecting the power leaking out of the cavity when the drive is shut off. The measured time constant $\tau_c = $ 1.34 s corresponds to a finesse of $F=37,000$. This value generally depends on the day the 