Non-Markovian features in semiconductor quantum optics: Quantifying the role of phonons in experiment and theory

We discuss phonon-induced non-Markovian and Markovian features in QD-based optics. We cover lineshapes in linear absorption experiments, phonon-induced incoherence in the Heitler regime, and memory correlations in two-photon coherences. To quantitatively and qualitatively understand the underlying physics, we present several theoretical models which model the non-Markovian properties of the electron-phonon interaction accurately in different regimes. Examples are the Heisenberg equation of motion approach, the polaron master equation, and Liouville-propagator techniques in the independent boson limit and beyond via the path-integral method. Phenomenological modeling overestimates typically the dephasing due to the finite memory kernel of phonons and we give instructive examples of phonon-mediated coherence such as phonon-dressed anticrossings in Mollow physics, robust quantum state preparation, cavity-feeding and the stabilization of the collapse and revival phenomenon in the strong coupling limit.