Engineering electro-optics in SiGe/Si waveguides for quantum transduction

High efficiency microwave-optical transduction for quantum state transfer remains an outstanding technical challenge. Resonant electro-optic transduction via three-wave mixing is an attractive solution, with a simple operating principle that does not rely on intermediate quantum states. However, intrinsic optical and microwave losses in electro-optic materials with large Pockels coefficients have limited the conversion efficiency of existing devices. Here, we show that an optimal conversion efficiency can be achieved with a relatively weak linear electro-optic material, as long as both the optical and microwave quality factors are high. We then specifically discuss designs for electro-optic quantum transducers based on superconducting microwave resonators coupled to SiGe/Si ring resonators. We theoretically show that applying an electric field to the SiGe/Si waveguides induces an effective Pockels effect, allowing three-wave mixing without introducing loss. Together with its excellent compatibility with superconducting qubit fabrication, the SiGe/Si platform promises to be an exciting avenue for quantum-state frequency conversion.