Five decades ago, Hanbury Brown and Twiss (HBT) demonstrated that the angular size of stars can be measured by correlating the intensity fluctuations measured by two detectors at two different locations. Since then, non-local correlation measurements have become ubiquitous in many areas of physics and have also been applied, beyond photons, to electrons, matter waves and subatomic particles. An important assumption in HBT interferometry is that the particles do not interact on their way from the source to the detectors. However, this assumption is not always valid. Here, we study the effects of interactions on HBT interferometry by considering the propagation of light fields in a nonlinear medium that induces interactions between the photons. We show that interactions affect multipath interference, limiting the ability to extract information on the source. Nevertheless, we find that proper analysis of the intensity fluctuations can recover the size of the source, even in the presence of interactions.
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The authors would like to thank A. Natan, O. Katz and M. Covo for invaluable help. Financial support by the Crown Centre of Photonics is gratefully acknowledged. Y.L. is supported by the Adams fellowship of the Israeli Academy of Science and Humanities.