Observation of Two-Dimensional Dam Break Flow and a Gaseous Phase of Solitons in a Photon Fluid

We report the observation of a two-dimensional (2D) dam break flow of a photon fluid in a nonlinear optical crystal. By precisely shaping the amplitude and phase of the input wave, we investigate the transition from one-dimensional (1D) to 2D nonlinear dynamics. We observe wave breaking in both transverse spatial dimensions with characteristic timescales determined by the aspect ratio of the input box-shaped field. The interaction of dispersive shock waves propagating in orthogonal directions gives rise to a 2D ensemble of solitons. Depending on the box size, we report the evidence of a dynamic phase characterized by a constant number of solitons, resembling a 1D soliton gas in integrable systems. We measure the statistical features of this gaslike phase. Our findings pave the way to the investigation of collective solitonic phenomena in two dimensions, demonstrating that the loss of integrability does not disrupt the dominant phenomenology.