Observation of the kinetic condensation of classical waves

Bose–Einstein condensation is usually considered to be an inherently quantum mechanical phenomenon. An observation of the condensation in a classical system of light waves in a nonlinear crystal demonstrates that it is a general wave-mechanical phenomenon. 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 physics 1 , 2 , 3 , 4 , 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 manner 6 , 7 , 8 , 9 . In complete analogy with gas kinetics, particle velocities map to wavepacket k -vectors, 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.