Third-order parametric down-conversion (TOPDC) describes a class of nonlinear interactions in which a pump photon is converted into a photon triplet. This process can occur spontaneously, or it can be stimulated by seeding fields. In the former case, one typically has the generation of non-Gaussian states of light. In the latter, the situation is more variegated, for stimulated TOPDC (StTOPDC) can be implemented in many ways, depending on the number and properties of the seeding fields. Here we show that StTOPDC can be exploited for the generation of quantum correlated photon pairs. We examine the peculiar features of this approach when compared with second-order spontaneous parametric down-conversion and spontaneous four-wave mixing. We model StTOPDC in a microring resonator, predicting observable generation rates in a microring engineered for third-harmonic generation. We conclude that if the experimental difficulties associated with implementing StTOPDC can be overcome, it may soon be possible to demonstrate this process in resonant integrated devices.
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