High-gain photon pair generation in a microring resonator with time-dependent non-perturbative effects

In this work, we present a quantum theory for pulsed photon pair generation in a single ring resonator. Our approach combines the Heisenberg picture input-output formalism with the Ikeda mapping from classical nonlinear optics. In doing so, we address the high-gain regime by incorporating non-perturbative effects, including self-phase modulation, cross-phase modulation, and time-ordering, which are roots for significantly different behaviors in the low-gain regime. We also account for optical losses by introducing an auxiliary waveguide, allowing for a more accurate representation of experimentally viable scenarios. Numerical simulations reveal that non-perturbative effects significantly distort transfer functions, making desirable operations challenging without careful optimization. We show that appropriate detuning of the pump frequency can mitigate these issues, leading to enhanced brightness and higher spectral purity in the high-gain regime. We further investigate the performance of a single ring resonator as a two-mode squeezer by analyzing various performance metrics under experimentally relevant optical loss conditions.