We study the correlation of intensity fluctuations in random electromagnetic beams, the Hanbury Brown-Twiss effect. Not just the state of coherence of the source, but also its state of polarization has a strong influence.
In 1956, Hanbury Brown and Twiss performed their famous intensity-correlation experiment with two 'coherent' beams of light from a thermal source. They argued that such intensity-correlation must entail an excess of photon arrival-time coincidences over chance ones for the two beams, and went on (with Little) to demonstrate this in an experiment (Twiss, Little and Hanbury Brown 1957). About the same time, Brannen and Ferguson (1956) performed a photon-coincidence experiment with coherent thermal light, and obtained a null result (due to lack of sensitivity).
In spite of the predilections of the authors, the work of Hanbury Brown and Twiss on intensity interferometry may have had a more powerful impact on quantum optics than on astronomy. That it could have such an impact on quantum optics is even more surprising when one considers that the their results are more easily explained in the context of classical optics than quantum optics. Nevertheless for more than 50 years, quantum optics has been inspired by intensity interferometry and continues to add new variations and insights. I will discuss experiments using cold atoms, both bosons and fermions, and from sources both coherent and incoherent. The observations yield useful information concerning what happens in atomic systems both when they interact with each other and when they interact with light.