Abstract
Optical analog experiments have captured a lot of interest in recent years by offering a strategy to test theoretical models and concepts that would be otherwise untestable. The approach relies on the similarity between the mathematical model for light propagation in nonlinear optical media and the model to be mimicked. In particular, the analogy between light and a quantum fluid with superfluidlike properties has been studied extensively. Still, while most of these studies use thermo-optical media to perform these experiments, the possibility of using nematic liquid crystals to perform such optical analog experiments remains to be analyzed. This work explores how this medium can constitute an alternative to materials more commonly used in optical analogs, such as thermo-optical media, and how its tunable properties can be advantageous to explore and better control fluidlike properties of light. Moreover, we explore the analogy between the propagation of light and a quantum fluid, and propose a pump-probe experiment to measure the dispersion relation of the superfluid analog.

Abstract
This work models the propagation of an optical pulse in a four-level atomic system in the electromagnetically induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a continuous-wave control laser beam and an assisting incoherent pump field, it is shown how these media can provide an excellent framework to experimentally explore pulse dynamics in the presence of non-conservative terms, either gain or loss. Furthermore, we explore the existence of stable dissipative soliton solutions, testing the analytical results with computational simulations of both the effective (1+1)-dimensional model and the full Maxwell-Bloch system of equations.

Abstract
The interaction of light with matter in near-to-resonant conditions opens a path for the exploration of nontrivial optical response that can play an important role in future photonics-driven technology. But as the attention shifts towards many-level atomic systems and involving multi-dimensional experimental scenarios, the complexity of the physical systems makes the analytical approach to the semiclassical model of the MaxwellBloch equations impossible without any strongly-limiting approximations. In this context, robust and highperformance computational tools are mandatory. In this work, we describe the development and implementation of a cross-platform Maxwell-Bloch numerical solver that is capable to exploit the different hardware available to tackle efficiently the problems under consideration. Moreover, it is demonstrated that this simulation tool can address a vast class of problems with considerable reduction of simulation time, featuring speedups up to 30 when running in massive parallel GPUs compared with the same codes running on a CPU, showing its potential towards addressing a large class of modern problems in photonics.

Abstract
Solitons are localized wave solutions that appear in nonlinear systems when self-focusing effects balance the usual pulse dispersion of common optical media. Their stability and particle-like behavior make them ideal candidates for applications that range from communication to optical computing, but in real world physical systems, dissipative processes makes these otherwise stable solutions unstable, and true solitons are particularly hard to observe in systems featuring non-negligible dissipation. In these cases a special type of localized stable solutions, called dissipative solitons, are still possible to obtain, if in addition to a balance between diffraction and nonlinearity, an equilibrium between gain and loss is also present. In this work we discuss theoretically how a 4-level atomic system and an incoherent pumping process can be an ideal experimental testbed for studying this interesting class of solutions, featuring tunable optical properties and controllable gain/loss dynamics that allow to study both classes of temporal and spatial dissipative optical solitons.

Abstract
As quantum-driven processes and properties start to shape the future of technology, quantum simulations appear as a crucial piece of the puzzle, acting both as building blocks and catalysts for the improvement of the understanding of unique quantum features. In essence, they can be understood as a class of prototype experiments that allow a study of quantum properties in a controllable environment. In this context, quantum fluids of light are one of the strongest candidates for this role as coherent behavior is easily accessible and not hidden by detrimental thermal noise usually present in more common quantum systems. In this work we explore the underlying theory of quantum fluids of light in propagating geometries through the hydrodynamic interpretation of light, where photons behave as interacting particles in the presence of a nonlinear medium. Exploiting the highly controllable optical properties of atomic systems and their enhanced nonlinear properties related to quantum coherence phenomena, we discuss how they can be used to set a tunable platform for quantum simulations. As examples, we demonstrate a series of quantum features of this light fluid in the form of superfluidic-like behaviors, ranging from the more common and experimentally confirmed suppressed scattering, drag-force cancellation and Bogoliubov-like dispersion relation for the elementary excitations, to other interesting phenomena yet to be explored, such as the case of persistent currents.

Abstract
Although the quantum theory of the optical response of individual atoms to coherent light with frequencies close to electronic transitions and the fluid equations for a gas are well known and understood from first principles, they are developed independently of each other and therefore cannot be applied directly to describe many of the quantum collective and transport phenomena that occur in cold atomic gases, especially in what regards their interaction with optical pulses and beams. Few attempts have been made to derive a consistent formalism and theory that are capable to model this type of systems, and those which exist rely on the adaptation of several ad-hoc hypothesis and simplifications, such as space and time dependent density operators. In this paper we provide the theoretical foundations and establish a formalism capable of paving the way for the development of new simulation tools and to explore new problems in nonlinear optics out of equilibrium.