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

Mateusz Salamon*, Oliver Dudgeon, and Ahsan Nazir†

Jake Iles-Smith‡

  • *Contact author: mateusz.salamon@manchester.ac.uk
  • †Contact author: ahsan.nazir@manchester.ac.uk
  • ‡Contact author: jake.iles-smith@sheffield.ac.uk
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Phys. Rev. Lett. 136, 080401 – Published 24 February, 2026

DOI: https://doi.org/10.1103/pgk3-b57l

Abstract

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.

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Phys. Rev. Lett. 136, 080401– Published 24 February, 2026
  • Received 3 October 2025
  • Accepted 22 January 2026
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