Measurement network diagram and calibrations
============================================

Fig. \[diagram\] shows a detailed schematic of the measurement network.

Data acquistion
---------------

Data acquisition is performed with a Zurich Instruments HF2LI lock-in amplifier. Scattering parameters are measured by sweeping an output tone and demodulator frequency, and spectra can be measured by taking a time trace and computing the Fourier transform. The converter is operated at the base temperature of a dilution refrigerator with optical access, and a cryogenic HEMT amplifier is used for microwave measurements. Microwave signals are measured by demodulating with an I/Q mixer, remodulating at a frequency of 10 MHz, then feeding into the HF2LI. The demodulate-remodulate procedure allows both microwave quadratures to be measured by a single physical channel, and makes the signal processing functions performed by the HF2LI symmetric between the microwave and optical domains. Optical signals are measured by combining the beam exiting the cavity with an LO on a beam splitter and reading out the difference port of a balanced heterodyne detector.

When computing spectra, an incident signal $s(t)$ is demodulated at a frequency $f_\mathrm{d} = f_\mathrm{c} + f_\mathrm{m}$, where $f_\mathrm{c}$ is the carrier frequency: $f_\mathrm{c}=10~\mathrm{MHz}$ for microwave measurements and $f_\mathrm{c}=12~\mathrm{MHz}$ for optical measurements. The resulting quadratures, 