New Frontiers in Multidimensional Self-Trapping of Nonlinear Fields and Matter

TL;DR

This paper reviews recent advances in the creation and stabilization of multidimensional solitons, quantum droplets, and complex topological states in nonlinear optical and atomic systems, highlighting new experimental and theoretical breakthroughs.

Contribution

It summarizes recent progress in stabilizing 2D and 3D solitons using novel nonlinearities, potentials, and spin-orbit coupling, including the first creation of 3D quantum droplets.

Findings

Stable 2D and 3D solitons predicted in systems with spin-orbit coupling.

Creation of 3D quantum droplets stabilized by quantum fluctuations.

Observation of complex topological states like skyrmions and hopfions.

Abstract

We review the state of the art and recently obtained theoretical and experimental results for two- and three-dimensional (2D and 3D) solitons and related states, such as quantum droplets, in optical systems, atomic Bose-Einstein condensates (BECs), and other fields - in particular, liquid crystals. The central challenge is avoiding the trend of 2D and 3D solitary states supported by the ubiquitous cubic nonlinearity to be strongly unstable - a property far less present in one-dimensional systems. Many possibilities for the stabilization of multi-dimensional states have been theoretically proposed over the years. Most strategies involve non-cubic nonlinearities or using different sorts of potentials, including periodic ones. New important avenues have arisen recently in systems based on two-component BEC with spin-orbit coupling, which have been predicted to support stable 2D and metastable 3D solitons. An important recent breakthrough is the creation of 3D quantum droplets. These are self-sustained states existing in two-component BECs, which are stabilized by the presence of Lee-Hung-Yang quantum fluctuations around the underlying mean-field states. By and large, multi-dimensional geometries afford unique opportunities to explore the existence of complex self-sustained states, including topologically rich ones, which by their very nature are not possible in one-dimensional geometries. In addition to vortex solitons, these are hopfions, skyrmions, and hybrid vortex-antivortex complexes, which have been predicted in different models. Here we review recent landmark findings in this field and outline outstanding open challenges.