## Superfluid and quantum features in the hydrodynamic flow of a fluid of light

### Pierre-Élie Larré, INO-CNR BEC Center, Dipartimento di Fisica, Università di Trento, Via Sommarive 14, 38123 Povo, Italia

In the presence of a significant Kerr optical nonlinearity, a many-photon light beam can behave as a quantum fluid of interacting bosons. This has opened the way to active experimental and theoretical investigations of many-body hydrodynamic and quantum features in photon-based systems, the research field of the so-called quantum fluids of light. A promising platform to study photon-fluid physics consists in the paraxial propagation of a quasimonochromatic light wave through a nonabsorbing cavityless nonlinear optical medium of Kerr type. In contrast to semiconductor-planar-microcavity architectures where driving and dissipation play a major role in the evolution of the fluid of light, the photon field in a cavityless, propagating, geometry obeys a fully conservative Gross–Pitaevskii-type quantum dynamics. The statistical properties of the photon beam entering the dielectric fix the initial conditions of the problem and the ones of the light exiting the medium determine the final state of the photon field.

The first part of my talk will be dedicated to a review of a very general quantum theory of light propagation in such a configuration. As a first application of the formalism, we will see in a second part that the occurrence of a frictionless flow of superfluid light past a solid dielectric immersed into a nonlinear optical liquid may be revealed from the dramatic suppression of the optomechanical deformation of the object, demonstrating that, in the optical case also, superfluidity is associated with a drop in the force exerted by the fluid on obstacles stymying its flow. In a third part, I will show that the paraxial-propagation geometry constitutes a very simple platform to investigate quantum-quench physics in closed systems of many interacting bosons, including, e.g., the acoustic analog of the dynamical Casimir effect, the light-cone-like spreading of the two-body correlations following a quantum quench, or the emergence of prethermalization features in one-dimensional configurations. Before concluding, I will present ongoing experiments aiming at measuring the Bogoliubov dispersion relation in a one-dimensional nonlinear optical waveguide (in Trento) and at detecting superfluid features in the flow of a photon fluid past a localized optical defect (in Nice and Edinburgh). Finally, I will briefly expose in-progress works carried out in Trento and Trieste, on the study of the strong-interaction, Tonks–Girardeau, regime in one-dimensional cavityless geometries and on the investigation of the relaxation of a quantum-quenched photon gas towards the Bose–Einstein statistics.