Thermalization of quantum light induced by classical nonlinear wave dynamics

Abstract

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 where quantum beams propagate alongside classical light within multimode nonlinear optical systems, we reveal the thermalization of fundamental quantum light states--specifically single- and two-photon states. 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 will enable the exploration of a broader range of complex quantum phenomena, including aspects of quantum phase transitions, within readily accessible classical optical settings.

Figures (3)

• Figure 1: Conceptual sketch of nonlinearity-induced thermalization of quantum light. (Left) Classical and quantum light simultaneously injected into nonlinear multimode coupled systems. Each field enters the system with a well defined mode distribution or mode occupancy. (Center) Nonlinear evolution of classical light induces chaotic fluctuations in the effective refractive index. (Right) Boltzmann and Rayleigh-Jeans output mode occupancies for two-photon and single-photon light, respectively.
• Figure 2: Thermalization of classical and single-photon light beams in nonlinear waveguides and a 3D cavity array. a Nonlinear classical and single-photon thermalization computed for a $J_x$ array after a propagation distance $z=5\times 10^4$ and the analytically computed RJ distribution predicting a temperature $T=0.3$ and chemical potential $\mu=-7.98$. b The same as in a for a nonlinear two-dimensional waveguide array after a propagation distance $z=1.5 \times 10^6$. The corresponding analytical RJ distribution is predicted to have temperature $T=-0.08$ and chemical potential $\mu=1.57$. c Nonlinear classical and single-photon thermalization computed for a three-dimensional cavity system after a propagation time $z=8\times 10^5$ and the corresponding RJ distribution with temperature $T=0.05$ and chemical potential $\mu=-1.44$. In all three cases the continuous line represents the analytically obtained RJ distribution, the dot-dashed and cross-dashed lines correspond to the numerically obtained single-photon and classical light distributions, respectively.
• Figure 3: Thermalization of two-photon light in nonlinear waveguide arrays and a cavity array. a Two-photon thermalization computed for a $J_x$ array after a propagation distance $z=5\times 10^4$ and corresponding analytically computed Boltzmann distribution with temperature $T=4.91$. b The same as in a for a two-dimensional waveguide array after a propagation distance $z=1.5\times 10^6$. The corresponding Boltzmann distribution is predicted to exhibit a temperature $T=-1.31$.distribution. c Two-photon thermalization corresponding to the three-dimensional cavity array after a propagation distance $z=8\times 10^5$ and characterized by a Boltzmann distribution with temperature $T=1.44$. In all three cases the insets depict the input two-photon mode distributions.