  Making use of a generalized quantum theory of paraxial light propagation
where the radiation-axis and the temporal coordinates play exchanged roles, we
discuss the potential of bulk nonlinear optical media in cavityless
configurations for quantum statistical mechanics studies of the conservative
many-body dynamics of a gas of interacting photons. To illustrate the general
features of this point of view, we investigate the response of the fluid of
light to the quantum quenches in the photon-photon interaction constant
experienced at the front and the back faces of a finite slab of weakly
nonlinear material. Extending the standard Bogoliubov theory of dilute
Bose-Einstein condensates, peculiar features are predicted for the statistical
properties of the light emerging from the nonlinear medium.
