Markovian Approach to N-Photon Correlations beyond the Quantum Regression Theorem

Multiphoton correlations from quantum emitters coupled to vibrational environments lie beyond the reach of standard tools such as the quantum regression theorem. Here, we introduce a Markovian framework for computing frequency-resolved N-photon correlation functions that overcomes this limitation. Applying our approach to a driven semiconductor quantum dot provides a tractable description of phonon effects on fluorescence beyond the single-photon spectrum. Our method accurately captures the emergence of the phonon sideband, missed by conventional quantum regression theorem treatments, and reveals rich phonon-induced structure in the filtered two-photon spectrum. Strikingly, we find that photons emitted via the phonon sideband inherit second-order coherence properties of the Mollow triplet.