Learning the Fuzzy Phases of Small Photonic Condensates

TL;DR

This paper reports the experimental observation of collective behaviour and phase transitions in small photonic condensates with only a few photons, using machine learning techniques to analyze their complex phase structure.

Contribution

It introduces the use of unsupervised learning and fuzzy clustering to identify phases in small photon systems, revealing rich phase behavior at the few-particle level.

Findings

Observation of collective behaviour in small photonic condensates

Identification of equilibrium and non-equilibrium phases

Construction of a fuzzy phase diagram for few-photon systems

Abstract

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.