Thermalization of quantum light induced by classical nonlinear wave dynamics

Thermalization of isolated quantum systems is an intriguing phenomenon at the forefront of contemporary physics. In this work, we demonstrate that nonlinear multimode optical platforms can be harnessed to induce effective quantum interactions between photons. Through numerical experiments, we reveal the thermalization of quantum light, specifically single- and two-photon states, propagating alongside classical light within multimode nonlinear optical systems. This thermalization is clearly manifested by the emergence of Rayleigh-Jeans and Boltzmann statistical distributions. Beyond providing a deeper understanding of how classical nonlinearities can be used to investigate quantum many-body dynamics, our findings enable the exploration of a broader range of complex quantum phenomena, including aspects of quantum phase transitions, within readily accessible classical optical settings.