Extended Data Fig. 4: Simulated effect of cladding thickness on g_eo and Q_m.

(a) Schematic of the structure in the simulation. The cladding thickness t_clad is used as the variable. (b) The simulated single-photon coupling rate g_eo at different thickness. (c) The simulated piezoelectric-limited microwave quality factor Q_m at different thickness. The simulation is performed by using the COMSOL piezoelectricity module⁵⁰. (d) The transduction efficiency is \(\eta \propto {g}_{{\rm{eo}}}^{2}{Q}_{{\rm{m}}}\). We thus use \({g}_{{\rm{eo}}}^{2}{{\rm{Q}}}_{{\rm{m}}}\) as the figure of merit to investigate the effect of cladding thickness on the transduction efficiency. It can be seen that \({g}_{{\rm{eo}}}^{2}{{\rm{Q}}}_{{\rm{m}}}\) does not drop substantially when cladding thickness increases. However, the thermal added noise can be well suppressed when the distance between superconductors and optical rings is larger. Therefore, using a larger cladding thickness can in principle reduce thermal added noise without compromising efficiency.