this power $P_{\text{lo}}$ simply bounces off the first cavity mirror and returns to a “signal” photodiode (SPD). A small fraction of this light is shifted by [$\omega_{\text{if}}/2\pi$]{} = 80 MHz using an acousto-optical modulator (AOM) and is used to both lock the laser near the cavity resonance and record the membrane’s motion. Locking is achieved via the Pound-Drever-Hall technique [@Black2001Introduction] with 15 MHz sidebands generated by an electro-optical modulator (EOM). A sampler directs $\sim 5$% of these beams’ power into the cryostat and cavity. We use the remaining 95% (sent to a “reference” photodiode RPD) to monitor the laser’s phase and power. The sampler then passes $\sim 95$% of the light escaping the cryostat through to the signal photodiode. This signal is demodulated at the beat note [$\omega_{\text{if}}/2\pi$]{} = 80 MHz in order to simultaneously detect the two sidebands generated by the membrane’s thermal motion.

Figure \[fig1\]d shows a typical power spectral density of these sidebands. A peak appears at the membrane’s fundamental mechanical frequency $\omega_\text{m}/2\pi \approx 261.1$ kHz as expected. The sidebands are identical, as expected for an interferometric measurement in which the laser noise contributes a negligible amount of force noise compared to the thermal bath and the 