Abstract
In this work we use the concept of paraxial fluids of light to explore quantum turbulence, probing a turbulent regime induced on an optical beam propagating inside a defocusing nonlinear media. For that purpose, we establish a physical analogue of a two-component quantum fluid by making use of orthogonal polarizations and incoherent beam interaction, obtaining a system for which the perturbative excitations follow a modified Bogoliubov-like dispersion relation. This dispersion relation features regions of instability that define an effective range of energy injection and that are easily tuned by manipulating the relative angle of incidence between the two components. Our numerical results support the predictions and show evidence of direct and inverse turbulent cascades expected from weak wave turbulence theories, which may inspire new ways to explore to quantum turbulence with optical analogues.

Abstract
Reservoir computing is a promising framework that facilitates the approach to physical neuromorphic hardware by enabling a given nonlinear physical system to act as a computing platform. In this work, we exploit this paradigm to propose a versatile and robust soliton-based computing system using a discrete soliton chain as a reservoir. By taking advantage of its tunable governing dynamics, we show that sufficiently strong nonlinear dynamics allows our soliton-based solution to perform accurate regression and classification tasks of non-linear separable datasets. At a conceptual level, the results presented pave a way for the physical realization of novel hardware solutions and have the potential to inspire future research on soliton-based computing using various physical platforms, leveraging its ubiquity across multiple fields of science, from nonlinear optical media to quantum systems.

Abstract
In the last three decades, a lot of research has been devoted to the optical response of an atomic media in near-to-resonant conditions and to how nonlinear optical properties are enhanced in these systems. However, as current research turns its attention towards multi-level and multidimensional systems interacting with several electromagnetic fields, the ever-increasing complexity of these problems makes it difficult to treat the semiclassical model of the Maxwell-Bloch equations analytically without any strongly-limiting approximations. Thus, numerical methods and particularly robust and fast computational tools, capable of addressing such class of modern and future problems in photonics, are mandatory. In this paper, we describe the development and implementation of a Maxwell-Bloch numerical solver that exploits the massive parallelism of the GPUs to tackle efficiently problems in multidimensional settings or featuring Doppler broadening effects. This constitutes a simulation tool that is capable of addressing a vast class of problems with considerable reduction of simulation time, featuring speedups up to 15 compared with the same codes running on a CPU.

Abstract
Nonminimally coupled curvature-matter gravity models are an interesting alternative to the theory of general relativity to address the dark energy and dark matter cosmological problems. These models have complex field equations that prevent a full analytical study. Nonetheless, in a particular limit, the behavior of a matter distribution can, in these models, be described by a Schrodinger-Newton system. In nonlinear optics, the Schrodinger-Newton system can be used to tackle a wide variety of relevant situations, and several numerical tools have been developed for this purpose. Interestingly, these methods can be adapted to study general relativity problems as well as its extensions. In this work, we report the use of these numerical tools to study a particular nonminimal coupling model that introduces two new potentials, an attractive Yukawa potential, and a repulsive potential proportional to the energy density. Using the imaginary-time propagation method, we have shown that static solutions arise even at low energy density regimes.

Abstract
The Theory of General Relativity is currently the most accepted model to describe gravity, and although many experiments and observations continue to validate it, recent astrophysical and cosmological observations require to include new forms of matter and energy (dark matter and dark energy), to be consistent. Modified theories of gravity with non-minimal coupling between curvature and matter are extensions of the Theory of General Relativity and have been proposed to address these shortcomings. Interestingly, matter at large scales behaves as a fluid and under certain approximations, the field equations can be approximated to a generalized Schrodinger-Newton system of equations. This model is largely found in the nonlinear optical systems, in particular to describe light propagating in nonlinear and nonlocal optical materials and also as a base model for the development of many optical analogues. Due to this, there are a wide variety of numerical methods developed to tackle this type of mathematical models, and that can be used to study these alternative gravity models. In this work, we explore the application of these numerical techniques based on GPGPU supercomputing, initially developed to study light propagating in nonlinear optical systems, to explore a particular non-minimal coupled gravity model. This model, in the nonrelativistic limit, modifies the hydrodynamic equations with the introduction of an attractive Yukawa potential and a repulsive one proportional to the matter density. We used the Schrodinger-Newton formalism to numerically study this model and, through the imaginary-time propagation method, we found stationary solutions that were sustained by the repulsive potential introduced by the non-minimal coupled model, even in the absence of a pressure term. We developed an analytical study in the Thomas-Fermi approximation and compared the predictions with numerical solutions. Finally, we explored how this gravity model may be emulated in the laboratory as an optical analogue.

Abstract
The last years saw the emergence of nonlinear optical materials, with local and nonlocal nonlinearities, as experimentally accessible systems to implement optical analogues of quantum fluids. In these systems, a light beam propagating in the nonlinear medium can be interpreted as a fluid, where the diffraction in the transverse plane to the propagation gives the effective mass of the fluid and the medium nonlinearity mediates the required interactions between the photons. This fluid interpretation and its application have been extensively studied, from the creation of superfluid-like flows and the study of phenomena associated with this effect to the implementation of gravity analogues. Furthermore, many optical materials have been considered, with a special interest in the ones that offer tunable mechanisms that allow to easily control the system properties to better explore and emulate the different phenomena. Recently, nematic liquid crystals have been proposed as an interesting tunable material capable of supporting superfluids of light. These systems have a nonlocal character and offer external mechanisms that can be used to tailor the nonlinearity to better emulate the desired analogue system. Indeed, through the application of an external electric field perpendicular to the direction of propagation, is it possible to control the nonlocal length of the nonlinearity. This mechanism offers interesting opportunities in the present context. In this work, through numerical methods based on GPGPU supercomputing, we explore the possibility of observing superfluid effects in defocusing nematic liquid crystals. In particular, we explore the possibility of observing the drag force cancellation and the emission of quantized vortices, which are two manifestations of a superfluid flow. Furthermore, we also discuss the possibility of using these systems for creating an analogue of quantum turbulence with these materials. These studies constitute a stepping-stone towards the implementation of gravity analogues with nematic liquid crystals.