Observation of the kinetic condensation of classical waves

The observation of Bose-Einstein condensation, in which particle interactions lead to a thermodynamic transition into a single, macroscopically populated coherent state, is a triumph of modern physics1-5. It is commonly assumed that this transition is a quantum process, relying on quantum statistics, but recent studies in wave turbulence theory have suggested that classical waves with random phases can condense in a formally identical manner6-9. In complete analogy with gas kinetics, particle velocities map to wavepacket kvectors, collisions are mimicked by four-wave mixing, and entropy principles drive the system towards an equipartition of energy. Here, we use classical light in a self-defocusing photorefractive crystal to give the first observation of classical wave condensation, including the growth of a coherent state, the spectral redistribution towards equilibrium, and the formal reversibility of the interactions. The results confirm fundamental predictions of kinetic wave theory and hold relevance for a variety of fields, ranging from Bose-Einstein condensation to information transfer and imaging.