Stability and dispersion relations of three-dimensional solitary waves in trapped Bose-Einstein condensates

TL;DR

This paper investigates the stability, dispersion relations, and dynamical properties of three-dimensional solitary waves in trapped Bose-Einstein condensates, revealing complex bifurcation scenarios and stability conditions for various soliton structures.

Contribution

It provides the first detailed analysis of the dispersion relations and stability of 3D solitary waves, including Chladni solitons, in cylindrically trapped BECs, based on the Gross-Pitaevskii equation.

Findings

Solitonic vortex is stable for chemical potential over 2.65 times the trap frequency.

Complex Chladni solitons exhibit weaker instabilities than planar dark solitons.

Time-dependent simulations show decay into multiple solitonic vortices.

Abstract

We analyse the dynamical properties of three-dimensional solitary waves in cylindrically trapped Bose-Einstein condensates. Families of solitary waves bifurcate from the planar dark soliton and include the solitonic vortex, the vortex ring and more complex structures of intersecting vortex-line known collectively as Chladni solitons. The particle-like dynamics of these guided solitary waves provides potentially profitable features for their implementation in atomtronic circuits, and play a key role in the generation of metastable loop currents. Based on the time-dependent Gross-Pitaevskii equation we calculate the dispersion relations of moving solitary waves and their modes of dynamical instability. The dispersion relations reveal a complex crossing and bifurcation scenario. For stationary structures we find that for $\mu/\hbar\omega_\perp > 2.65$ the solitonic vortex is the only stable solitary wave. More complex Chladni solitons still have weaker instabilities than planar dark solitons and may be seen as transient structures in experiments. Fully time-dependent simulations illustrate typical decay scenarios, which may result in the generation of multiple separated solitonic vortices.