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, and obtained analytic expressions relating the thermal correlation function to the single emitter photon statistics.