Reconstruction of the environmental correlation function from single-emitter photon statistics: A non-Markovian approach

We consider the two-level system approximation of a single emitter driven by a continuous laser pump and simultaneously coupled to the electromagnetic vacuum and to a thermal reservoir beyond the Markovian approximation. We discuss the connection between a rigorous microscopic theory and the phenomenological spectral diffusion approach used to model the interaction of the emitter with the thermal bath. We obtain analytic expressions making it possible to deduce the thermal correlation function from the measured single-emitter photon statistics.