Extended Data Fig. 5: Demodulation efficiency and timing.
a, Calculated intracavity phonon and output photon flux versus time of the transducer with one initial phonon using coupled-mode theory. b, Calculated microwave measurement efficiency using different demodulation waveforms. Matched waveform gives the highest possible efficiency and is limited by device internal loss. c, Added noise in the microwave photon. The temporal heating is a theory fit to the time-domain heating measurement, assuming a bath with exponentially decaying thermal noise excited by the laser pulse. The temporal mode of the single photon is shown in comparison. The measured temporal heating is shown as grey dots. d, Measurement of the best demodulation timing for different demodulation waveforms. Efficiency of the demodulation is measured by the relative variance of post-selected state IQ data from single photon detection events versus the thermal state IQ, explained in detail in Methods. Black curves are control calculations using randomly selected IQ data instead of post-selected. Error bars are the standard deviation over 8 sets of measurements with data points being the mean values. e, Microwave Sμμ with no optical pump. 50 measurements, taken in quick succession of each other are plotted (blue) where one of them is highlighted for clarity (blue dots). The red curve shows the fit result from coupled-mode theory. For some traces the mechanical mode is undercoupled while for others it is overcoupled due to fluctuations of the intrinsic mechanical loss rate. The frequency is also stochastically jumping around. When the optical pump is turned on, the mechanical mode becomes more stable and its linewidth increases to ~ 1 MHz. These effects are possibly due to two-level systems (TLS).
