Periodic Reporting for period 2 - HALT (Hydrodynamical approach to light turbulence)
Période du rapport: 2022-10-01 au 2024-09-30
The overarching purpose of HALT (Hydrodynamic Approach to Light Turbulence) is to form a coherent research and training network of world-leading institutions in the multidisciplinary fields of nonlinear optics, hydrodynamic turbulence, and statistical physics to probe and enhance our understanding of one of the most important unsolved problems in physics: the structure of turbulence.
The objective of HALT is to collaboratively develop new pathways in the understanding of complex turbulent behaviours of waves and coherent structures in light propagation through nonlinear optical media and atomic vapours in both one-dimensional (1D) and two-dimensional (2D) systems and draw connections to classical hydrodynamics. At the most fundamental level, developing a universal theoretical treatment of such problems will bring together the fields of nonlinear optics, condensed-matter fluids, and hydrodynamic turbulence into one. This is a truly pioneering project that will unify the approach to turbulence and cross the boundaries of wave-particle duality.
The HALT project will produce a new generation of innovative, skilled and entrepreneurial researchers, many of whom will become future leaders in academia and industry and will make greater contributions to the knowledge-based economy and society.
The objective of HALT is to collaboratively develop new pathways in the understanding of complex turbulent behaviours of waves and coherent structures in light propagation through nonlinear optical media and atomic vapours in both one-dimensional (1D) and two-dimensional (2D) systems and draw connections to classical hydrodynamics. At the most fundamental level, developing a universal theoretical treatment of such problems will bring together the fields of nonlinear optics, condensed-matter fluids, and hydrodynamic turbulence into one. This is a truly pioneering project that will unify the approach to turbulence and cross the boundaries of wave-particle duality.
The HALT project will produce a new generation of innovative, skilled and entrepreneurial researchers, many of whom will become future leaders in academia and industry and will make greater contributions to the knowledge-based economy and society.
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.
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.
The HALT project has developed several new theoretical methods for studying waves and coherent structures in the context of optical and atomic BECs as well as new experimental configurations. Through the heavy publication of research papers, international conference presentations, and invited talks, this project has produced a large impact on many aspects. As a consortium, we are rapidly contributing to the field of optical turbulence and the study of weak non-integrability of solitons and vortices in related systems. Key results that have so far gone beyond the state of the art include:
• 1D optical wave turbulence using kinetic-wave equations and direct scattering transforms to study wave and soliton interactions.
• 2D Schrödinger-Helmholtz systems with derivations of a semi-local approximation model for a more realistic kinetic-wave description.
• A new framework for weak and strong gravitational wave turbulence in the early universe.
• Characterisation of point-vortex dipole scattering with topological mapping of coherent vortex clusters.
• Interactions of optical and quantum BEC vortices with acoustic backgrounds.
• Study of soliton-soliton interaction in the models for 1D optical wave turbulence using frequency-wavenumber plots and direct scattering transform
• Sequence of bifurcation approach to nonlinear uniform condensate of defocussing 1D Nonlinear Schrodinger equation.
• Stability analysis of multi-soliton solutions of the 1D NLS and non-integrable optical wave turbulence equations.
The potential industrial impacts from HALT are planned towards the end of the project due to the project focussing on developing new theories and experimental techniques that will only be matured by the end. To this end, the experimental teams in the HALT consortium are in regular discussion with potential industrial partners but we have yet to prioritise industrial impact at this point in the project.
With the development of new technical and transferrable skills through training, the staff members of this project have enhanced career perspectives. They become more integral to the international research networks in their own and complementary fields related to optical turbulence through networking, training, and collaboration. The research collaboration and knowledge-sharing activities are greatly increasing the quality and impact of the researchers’ academic outputs. This can be evidenced by the publication of more than 20 research papers from the HALT researchers during the 1st periodic reporting period. The HALT project has contributed to the success of several researchers in gaining PhDs, new academic positions, or promotions.
• 1D optical wave turbulence using kinetic-wave equations and direct scattering transforms to study wave and soliton interactions.
• 2D Schrödinger-Helmholtz systems with derivations of a semi-local approximation model for a more realistic kinetic-wave description.
• A new framework for weak and strong gravitational wave turbulence in the early universe.
• Characterisation of point-vortex dipole scattering with topological mapping of coherent vortex clusters.
• Interactions of optical and quantum BEC vortices with acoustic backgrounds.
• Study of soliton-soliton interaction in the models for 1D optical wave turbulence using frequency-wavenumber plots and direct scattering transform
• Sequence of bifurcation approach to nonlinear uniform condensate of defocussing 1D Nonlinear Schrodinger equation.
• Stability analysis of multi-soliton solutions of the 1D NLS and non-integrable optical wave turbulence equations.
The potential industrial impacts from HALT are planned towards the end of the project due to the project focussing on developing new theories and experimental techniques that will only be matured by the end. To this end, the experimental teams in the HALT consortium are in regular discussion with potential industrial partners but we have yet to prioritise industrial impact at this point in the project.
With the development of new technical and transferrable skills through training, the staff members of this project have enhanced career perspectives. They become more integral to the international research networks in their own and complementary fields related to optical turbulence through networking, training, and collaboration. The research collaboration and knowledge-sharing activities are greatly increasing the quality and impact of the researchers’ academic outputs. This can be evidenced by the publication of more than 20 research papers from the HALT researchers during the 1st periodic reporting period. The HALT project has contributed to the success of several researchers in gaining PhDs, new academic positions, or promotions.