Generalized Matching Condition for Efficient N-Stage Quantum Transduction

Coherently converting quantum states between distinct elements via quantum transducers remains a crucial yet challenging task in quantum science. Especially in demand is quantum transduction between optical frequencies, which are ideal for low-loss transmission across long distances, and microwave frequencies, which admits high-fidelity quantum operations. We present a generic formalism for N-stage quantum transduction that covers all the leading microwave-to-optical linear conversion approaches such as electro-optics, electro-optomechanics, optomagnonics, and atomic ensembles. We then identify a generalized matching condition for achieving maximum conversion efficiency. The generalized matching condition requires resistance matching as well as frequency matching beyond the usual resonant assumption, with simple impedance matched transmission interpretation. Our formalism provides a universal toolbox for determining experimental parameters to realize efficient quantum transduction that can fulfill various practical requirements, and suggests new regimes of non-resonant conversions that can outperform all-resonant ones.