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Single photon-level quantum frequency conversion has recently beendemonstrated using silicon nitride microring resonators. The resonanceenhancement offered by such systems enables high-efficiency translation ofquantum states of light across wide frequency ranges at sub-watt pump powers.Using a quantum-mechanical Hamiltonian formalism, we present a detailedtheoretical analysis of the conversion dynamics in these systems, and show thatthey are capable of converting single- and multi-photon quantum states.Analytic formulas for the conversion efficiency, spectral conversionprobability density, and pump power requirements are derived which are in goodagreement with previous theoretical and experimental results. We show that withonly modest improvement to the state of the art, efficiencies exceeding 95% areachievable using less than 100 mW of pump power. At the critical drivingstrength that yields maximum conversion efficiency, the spectral conversionprobability density is shown to exhibit a flat-topped peak, indicating a rangeof insensitivity to the spectrum of a single photon input. Two alternatetheoretical approaches are presented to study the conversion dynamics: adressed mode approach that yields a better intuitive picture of the conversionprocess, and a study of the temporal dynamics of the participating modes in theresonator, which uncovers a regime of Rabi-like coherent oscillations of singlephotons between two different frequency modes. This oscillatory regime arisesfrom the strong coupling of distinct frequency modes mediated by coherentpumps.

Quantum frequency conversion and strong coupling of photonic modes using four-wave mixing in integrated microresonators