  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.
