data was taken and the orientation of the membrane. It is lower than the value we measured after initially cooling to 400 mK ($\sim 80,000$). We believe this reduction was caused by either gradual condensation of materials on the surfaces over months of operation, or a change in the membrane’s alignment, which can steer the cavity mode away from a high-performance region of the end mirrors (a spatial dependence of cavity-mirror performance was also observed in Ref. [@Sankey2010Strong]). The finesse measured in Fig. \[fig1\]c corresponds to a cavity loss rate of $\kappa/2\pi$ = 120 kHz, meaning the cryogenic optomechanical system operates in the resolved sideband regime, a condition necessary for ground-state cooling [@Rae2007Theory; @Marquardt2007Quantum].

The first purpose of this apparatus is to perform a heterodyne measurement of the membrane’s motion. As shown in Fig. \[fig1\]a, light from the “signal laser” is split into several frequencies before it interacts with the cavity. The inset of Fig. \[fig1\]a shows a summary of the relative magnitudes and frequencies of the laser light landing on the cavity, with dashed lines roughly illustrating the susceptibility of the different cavity resonances. Most of the light serves as a local oscillator tuned far from the cavity resonance; 