Coherent frequency transfer of optical nonlinearities by feedback control of a non-degenerate optical parametric oscillator

Strong, coherent optical nonlinearities, such as those found in atom-cavity QED systems, are key resources for ultra-low-power optical information processing. However, such nonlinearities often arise from resonant effects occurring in a narrow band of frequencies, limiting their utility within heterogeneous networks of optical devices. At the same time, optical parametric oscillators (OPOs) are a robust platform for tunable light generation, converting pump light into signal and idler light at potentially vastly different frequencies. Here, we consider a coherent feedback scheme in which a narrowband nonlinear device, modelled as a Kerr cavity, is connected by an optical feedback loop to the signal port of an non-degenerate OPO below threshold. We use the SLH formalism to derive a rigorous input-output quantum model for this composite device, and we show by numerical simulation that the nonlinear input-output behavior of the Kerr cavity can be transferred to the idler port of the OPO, thus implementing a coherent transfer of the optical nonlinearity from one frequency to another.