Observation of lump solitons in a photon fluid

Solitons are the cornerstone of nonlinear physics. The integrability of nonlinear equations is the basis of this universal concept. However, most multidimensional systems lack of integrability, a fundamental limitation that challenges the existence of solitons in high dimensions. A groundbreaking exception would be the lump soliton, a two-dimensional solution of the Kadomtsev-Petviashvili (KP) equation with the unique property of propagating unperturbed in three-dimensional space. Due to the difficulty of implementing the KP dynamics in any physical system, lump solitons have never been observed. Here, we report the first experimental observation of a lump soliton. The lump forms in a two-dimensional photon fluid experiencing a defocusing nonlinearity in a photorefractive crystal. We tailor the input field shape and the nonlinearity to realize the hydrodynamic integrable regime of the KP equation. The lump emerges as a self-localized wave that propagates unaltered with a transverse velocity. We confirm its integrable nature by reporting, for the first time, the elastic collision of solitons in two dimensions. As the first experimental evidence of integrable solitons in high dimension, our observation paves the way for a new era in the study of nonlinear systems.