Nonlinear optics processes lie at the heart of photonics and quantum optics for their indispensable role in light sources and information processing. During the past decades, the three- and four-wave mixing (χ(2) and χ(3)) effects have been extensively studied, especially in the micro-/nano-structures by which the photon-photon interaction strength is greatly enhanced. So far, the high-order nonlinearity beyond the χ(3) has rarely been studied in dielectric materials due to their weak intrinsic nonlinear susceptibility, even in high-quality microcavities. Here, an effective five-wave mixing process (χ(4)) is synthesized by incorporating χ(2) and χ(3) processes in a single microcavity. The coherence of the synthetic χ(4) is verified by generating time-energy entangled visible-telecom photon pairs, which requires only one drive laser at the telecom waveband. The photon-pair generation rate from the synthetic process shows an estimated enhancement factor over 500 times upon intrinsic five-wave mixing. Our work demonstrates a universal approach of nonlinear synthesis via photonic structure engineering at the mesoscopic scale rather than material engineering, and thus opens a new avenue for realizing high-order optical nonlinearities and exploring functional photonic devices.

Mean‐field treatment (MFT) is frequently applied to approximately predict the dynamics of quantum optics systems. It simplifies the system Hamiltonian by neglecting the quantum statistics of certain modes that are driven strongly by lasers or couple weakly with other modes. However, the neglected quantum correlations between different modes result in unanticipated quantum effects and might lead to significantly distinct system dynamics. Here, a general and systematic theoretical framework based on perturbation theory in company with MFT is provided to capture these quantum effects. The form of nonlinear dissipation and parasitic Hamiltonian as well as their relationship to the nonlinear coupling rate are predicted. Furthermore, the indicator is also proposed as a measure of the accuracy of mean‐field treatment. As an example, this theory is applied to quantum frequency conversion, in which mean‐field treatment is commonly applied, to test its limitation under strong pump and large coupling strength. The analytical results show excellent agreement with the numerical simulations. This work clearly reveals the residual quantum effects neglected by MFT and provides a more precise theoretical framework for nonlinear optics and quantum optics.

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