Multi-photon correlations from quantum emitters coupled to vibrational environments lie beyond the reach of standard tools such as the quantum regression theorem (QRT). 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 QRT 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.
@article{arxiv.2509.21569,
title = {A Markovian approach to $N$-photon correlations beyond the quantum regression theorem},
author = {Mateusz Salamon and Oliver Dudgeon and Ahsan Nazir and Jake Iles-Smith},
journal= {arXiv preprint arXiv:2509.21569},
year = {2026}
}