Direct observations of thermalization to a Rayleigh–Jeans distribution in multimode optical fibres

Nonlinear multimode optical systems support a host of intriguing effects that are impossible in single-mode settings. Although nonlinearity can provide a rich environment where the chaotic power exchange among thousands of modes can lead to novel behaviours, understanding and harnessing these processes to our advantage is challenging. Over the years, statistical models have been developed to macroscopically describe the response of these complex systems. One of the cornerstones of these theoretical formalisms is the prediction of a photon–photon-mediated thermalization process that leads to a Rayleigh–Jeans distribution of mode occupations. Here we report the use of mode-resolved measurement techniques to directly observe the thermalization to a Rayleigh–Jeans power distribution in a multimode optical fibre. We experimentally demonstrate that the underlying system Hamiltonian remains invariant during propagation, whereas power equipartition takes place among degenerate groups of modes—all in full accordance with theoretical predictions. Our results may pave the way towards a new generation of high-power optical sources whose brightness and modal content can be controlled using principles from thermodynamics and statistical mechanics.