Temporal coherences of atomic chaotic light sources: the Siegert relation and beyond

Light is characterized by its electric field, yet quantum optics has revealed the importance of monitoring photon-photon correlations at all orders. We here present a comparative study of two experimental setups, composed of cold and warm Rubidium atoms, respectively, which allow us to probe and compare photon correlations up to the fourth order. The former operates in the quantum regime where spontaneous emission dominates, whereas the latter exhibits a temperature-limited coherence time. While both setups present almost-chaotic light statistics, we discuss how the access to different orders of photon correlations allows one to better characterize the mechanisms responsible for deviations from those statistics.