  This Habilitation manuscript describes the work done at JQI-NIST and
LKB-ENS-Sorbonne University since 2010. After a brief introduction of the
needed concepts for non-linear and quantum optics in optically dense atomic
medium, I review several experiments about the Gradient Echo Memory protocol in
warm atomic vapors and in cold atomic clouds, and especially the multi-mode
properties of this memory. In the next chapter I describe two experiments of
quantum optics in dense atomic medium : the possibility to image using quantum
noise and the propagation of quantum mutual information in a fast-light medium.
In chapter 4 I study two recents experiments about hydrodynamics of light in
exciton-polariton systems and in warm atomic vapor. Finally I present the
future project of my group at LKB.
  The main goal of this manuscript is to provide the tools to connect
non-linear and quantum optics to quantum fluids of light. Because the physics
of matter quantum fluids and fluids of light has long been the territory of
condensed matter physicists, it is uncommon to find textbooks which draw the
analogies with quantum optics. I have taken the reverse trajectory, being
trained as a quantum optician and moving progressively to quantum gases and
quantum fluids of light. Naturally, I try to use the concepts and resources
developed by the quantum optics community to improve experiment about fluids of
light, but I also reverse the approach and ask a very simple question: what
does the concept of fluid of light bring to our understanding of non-linear and
quantum optics ? It can be rephrased as an operational question: which new
effects can we predict (and possibly observe) using the photon fluid formalism
?
