Two-Component 3D Atomic Bose-Einstein Condensates Support Complex Stable Patterns

TL;DR

This paper computationally discovers a variety of complex, stable, topologically charged patterns in three-dimensional two-component Bose-Einstein condensates, demonstrating their potential experimental observability.

Contribution

It introduces a novel computational approach combining deflation techniques with initial guess selection to find diverse stable patterns in multi-component nonlinear wave systems.

Findings

Identified stable vortex structures, rings, and labyrinth patterns in 3D BECs.

Demonstrated spectral stability through Bogolyubov-de Gennes analysis.

Showed potential for experimental realization of complex patterns.

Abstract

We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to two-component atomic Bose-Einstein condensates in parabolic traps, our methods can be broadly applied to high-dimensional, nonlinear systems of partial differential equations. The combination of the so-called deflation technique with a careful selection of initial guesses enables the computation of an unprecedented breadth of patterns, including ones combining vortex lines, rings, stars, and ``vortex labyrinths''. Despite their complexity, they may be dynamically robust and amenable to experimental observation, as confirmed by Bogolyubov-de Gennes spectral analysis and numerical evolution simulations.