Nonlinear dynamics in quantum fluids of light
Solitons, quantum droplets, hot vapour
The propagation of light in nonlinear media is well described by a $2$D nonlinear Schrödinger equation (NLSE)
within the paraxial approximation, which is equivalent to the Gross-Pitaevskii equation (GPE), the mean-field description for
the dynamics of Bose-Einstein condensates (BECs). As a product of this similarity, we can establish the figure of a quantum
fluid of light. Quantum fluids of light have been used for theoretical and experimental investigations of phenomena already
studied and realised in BECs. In this thesis, we describe the mechanisms that make the conception of a quantum fluid of light
possible for different experimental platforms. Furthermore, we present a study on the formation of self-bound droplets of light
in hot atomic vapours, our chosen nonlinear medium, in an attempt to obtain a mapping between experimental parameters
typically used in BEC experiments and those needed to observe the analogous phenomenon in atomic vapours. We investigate
the static properties of the system, providing a phase diagram for the different and possible solutions for the optical regimes of
interest. Finally, we systematically study droplet dynamics, focusing on the behaviour of the collective monopole excitation
and the dynamic formation of these objects under realistic experimental conditions.