  Second-order optical processes lead to a host of applications in classical
and quantum optics. With the enhancement of parametric interactions that arise
due to light confinement, on-chip implementations promise very-large-scale
photonic integration. But as yet there is no route to a device that acts at the
single photon level. Here we exploit the $\chi^{(3)}$ nonlinear response of a
Si$_{3}$N$_{4}$ microring resonator to induce a large effective $\chi^{(2)}$.
Effective second-order upconversion (ESUP) of a seed to an idler can be
achieved with 74,000 %/W efficiency, indicating that single photon nonlinearity
is within reach of current technology. Moreover, we show a nonlinear coupling
rate of seed and idler larger than the energy dissipation rate in the
resonator, indicating a strong coupling regime. Consequently we observe a
Rabi-like splitting, for which we provide a detailed theoretical description.
This yields new insight into the dynamics of ultrastrong effective nonlinear
interactions in microresonators, and access to novel phenomena and applications
in classical and quantum nonlinear optics.
