Learning the Fuzzy Phases of Small Photonic Condensates

Phase transitions, being the ultimate manifestation of collective behaviour, are typically features of many-particle systems only. Here, we describe the experimental observation of collective behaviour in small photonic condensates made up of only a few photons. Moreover, a wide range of both equilibrium and non-equilibrium regimes, including Bose-Einstein condensation or laser-like emission are identified. However, the small photon number and the presence of large relative fluctuations places major difficulties in identifying different phases and phase transitions. We overcome this limitation by employing unsupervised learning and fuzzy clustering algorithms to systematically construct the fuzzy phase diagram of our small photonic condensate. Our results thus demonstrate the rich and complex phase structure of even small collections of photons, making them an ideal platform to investigate equilibrium and non-equilibrium physics at the few particle level.