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. [1]. 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 [2]. 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 [3]. 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 [2], including phenomena like the light-cone effect [2] and prethermalization [4]. Finally, a mechanism of evaporative cooling allowing a Bose-Einstein condensation of a quantum fluid of light will be presented [5]. 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.

[1] Carusotto and Ciuti, Rev. Mod. Phys. 85, 299 (2013)
[2] Larré and Carusotto, Phys. Rev. A 92, 043802 (2015)
[3] Larré and Carusotto, Phys. Rev. A 91, 053809 (2015)
[4] Larré and Carusotto, Eur. Phys. J. D 70, 45 (2016)
[5] Chiocchetta et al., EPL 115, 24002 (2016)
[6] Ramiro-Manzano et al., MRS Advances 1, 3281 (2016)
[7] Larré et al., arXiv:1612.07485 (2017)