Multidimensional fluids of light in nonlinear physics: bridging theory and experiment in integrable and non-integrable regimes

Abstract The nonlinear Schrödinger equation (NLS) plays a central role in nonlinear physics, bridging classical and quantum frameworks through a unified mathematical model. While the integrability of the one-dimensional (1D) NLS has yielded profound insights and exact analytical solutions, such as solitons and breathers, the dynamics of the non-integrable two-dimensional (2D) NLS remain largely unexplored, both theoretically and experimentally. This thesis investigates the 2D NLS from an experimental perspective, in a 2D fluid of light realized by propagating a laser beam in a photorefractive nonlinear crystal. We have developed an innovative experimental platform for the investigation of 2D fluids of light, whose main key points are a holographic method for the precise shape of the optical wavefront and the tunability of the nonlinear response of the crystal. By precisely shaping the optical wavefront and tuning the nonlinear response of the medium, we explore both self-focusing and self-defocusing regimes with controlled initial conditions. Two main experiments are presented. The first explores the evolution of a non-analytical initial condition, the 2D dam-break problem, in the focusing regime. By comparing with the integrable 1D dynamics, we reveal that the phenomenology is partially conserved and new features unique to higher-dimensional systems emerge. The second experiment demonstrates the emergence of an integrable regime within a non-integrable system, confirmed by the observation of a 2D lump soliton, an exact solution of the Kadomtsev–Petviashvili (KP) equation. This discovery shows that under specific conditions, integrable-like behavior can be observed even in a 2D nonintegrable system. Beyond fundamental insights into nonlinear wave dynamics, the thesis also explores the potential of nonlinear systems for neuromorphic computing. In particular, we present a platform based on exciton-polaritons as a quantum fluid of light, and discuss its application for implementing reservoir computing architectures aimed at quantum state reconstruction. This opens avenues toward the use of wave-based nonlinear systems as fast and efficient physical neural networks.