The ASTON and CNRS teams have begun a detailed study on solitary wave formation in weakly non-integrable models for optical wave turbulence. Using the direct scattering transform as a tool for identifying coherent structures, they have started characterising how solitons are formed and broken down as part of wave turbulence, with work being finalised in the derivation of a semi-local approximation model for wave turbulence in the Schrödinger-Helmholtz equation. This will provide a completely new perspective in how approximations to kinetic wave equations are handled in wave turbulent systems. The ASTON and CNRS teams have studied the dynamics of superfluids described by the nonlinear Schrödinger equation and focussed on out-of-equilibrium states where turbulent cascades carry energy along scales. They have shown the co-existence of a hydrodynamic Kolmogorov turbulent regime and a Kelvin-wave cascade, and have addressed the dynamics of impurities in superfluids, specifically in how thermal waves induce a stochastic motion on the impurity that is well described by an Ornstein-Uhlenbeck process and characterized its friction term by analytical calculations and numerical simulations.
WP2 has so far produced works on a mathematically consistent derivation of a point-vortex model that has been derived from the 2D nonlinear Schrödinger equation providing specific values of self-interaction energies. Subsequently, the point-vortex model has been studied in the context of dipole scattering with a comprehensive characterisation of interactions mapped. Interesting collapse solutions have been identified and likely paths for topological vortex mixing. Further work has started on solitonic turbulence in nonlinear optics using the direct scattering transform in models close to the 1D nonlinear Schrödinger equation to identify coherent structures.
In Nice, the CNRS team has worked on experiments on 2D optical turbulence using hot and cold atomic vapors and photorefractive crystal platforms. In the atomic vapor experiment, they studied the process of snaking instability of a grey soliton leading to the formation of multiple quantized vortices. In photorefractive crystals, they have implemented 2D quantized vortex turbulence by an optical flow passing an array of potentials (“a grid”) to identify an optimal configuration for creating the largest number of quantized vortices.
In USP, the goal was to study the feasibility of implementing a new experimental tool to measure electric field and intensity correlations of the scattered light, a technique already mastered in my cold atom experiment in Nice. Since then, this setup has been implemented in one of the BEC experiments and intensity correlations measurements have already been observed on the light scattered by atoms trapped in a magneto-optical trap.
ASTON and NSU have produced collaborative work on optical turbulence in mode-locked fibre lasers has been carried out. Such lasers do not have limitations for pulse energy and thus are very promising in practice. Due to a large number of longitudinal modes such lasers may demonstrate optical wave turbulence features, making them interesting devices both for practice and fundamental science. It was demonstrated that the mode-lock operation with linear polarization maintenance is possible in a relatively simple fibre laser with naturally occurring nonlinearity management.
