In the presence of a significant optical nonlinearity, a beam of light may behave as an interacting quantum fluid. One speaks of « quantum fluid of light, » following the terminology used in Ref. . The ease of access to local observables and of probing out-of-equilibrium phenomena in these many-body photonic systems make them especially promising for a variety of investigations ranging from basic quantum physics to quantum simulation. An optical platform that presently attracts a growing interest within the quantum-fluid-of-light community consists in a paraxial beam of quasimonochromatic light propagating in a nonlinear optical medium.
The first part of the talk will be dedicated to a review of a general quantum theory of light propagation in such a configuration . As a first application of this formalism, we will then see that the occurrence of a frictionless flow of superfluid light may be revealed from the dramatic suppression of the optomechanical deformation of an elastic solid immersed into a nonlinear liquid . In a third part, we will show that the propagating geometry constitutes a simple platform to investigate the quantum dynamics of many-body systems launched out of equilibrium after an interaction quench , including phenomena like the light-cone effect  and prethermalization .
Finally, a mechanism of evaporative cooling allowing a Bose-Einstein condensation of a quantum fluid of light will be presented . After concluding, if time permits, an in-progress experiment aiming to measure the Bogoliubov dispersion relation of a fluid of light [6, 7] and a theoretical study of the postquench dynamics of a quantum fluid of light in a disordered landscape will be sketched out.
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