Dynamical Instability of 3d Stationary and Traveling Planar Dark Solitons

TL;DR

This paper investigates the stability and dynamics of 3D planar dark solitons in Bose-Einstein condensates, combining theoretical, numerical, and experimental approaches to understand their decay into vortices and rings.

Contribution

It provides a comprehensive analysis of the existence, stability, and decay mechanisms of 3D dark solitons, including new traveling solutions and stability thresholds.

Findings

Numerical simulations match experimental observations of solitons and decay products.

Identified exact traveling solutions and their destabilization thresholds.

Quantified how soliton speed affects transverse instability.

Abstract

Here we revisit the topic of stationary and propagating solitonic excitations in self-repulsive three-dimensional Bose-Einstein condensates by quantitatively comparing theoretical analysis and associated numerical computations with our experimental results. Using fully 3d numerical simulations, we explore the existence, stability, and evolution dynamics of planar dark solitons, as well as their instability-induced decay products including solitonic vortices and vortex rings. In the trapped case and with no adjustable parameters, our numerical findings are in correspondence with experimentally observed coherent structures. Without a longitudinal trap, we identify numerically exact traveling solutions and quantify how their transverse destabilization threshold changes as a function of the solitary wave speed.