Solitons and vortices in an evolving Bose-Einstein condensate

TL;DR

This paper investigates the dynamic behavior of a Bose-Einstein condensate, revealing the formation of solitons and vortices through numerical simulation of the Gross-Pitaevskii equation, highlighting complex interference patterns and topological excitations.

Contribution

It provides a detailed numerical analysis of soliton and vortex formation in a confined Bose-Einstein condensate during its evolution.

Findings

Spiral atomic density profiles form due to self-interference.

Dark solitons are identified as density notches with large phase gradients.

Vortex-antivortex pairs are spontaneously created and annihilated, conserving total vorticity.

Abstract

Spatiotemporal evolution of a confined Bose-Einstein condensate is studied by numerically integrating the time-dependent Gross-Pitaevskii equation. Self-interference between the successively expanding and reflecting nonlinear matter waves results in spiral atomic density profile, which subsequently degenerates into an embedding structure: The inner part preserves memory of the initial states while the outer part forms a sequence of necklacelike rings. The phase plot reveals a series of discrete concentric belts. The large gradients between adjacent belts indicate that the ring density notches are dark solitons. In the dynamical process, a scenario of vortex-antivortex pairs are spontaneously created and annihilated, whereas the total vorticity keeps invariant.