Multiple atomic dark solitons in cigar-shaped Bose-Einstein condensates

TL;DR

This paper investigates the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates, modeling their interactions, stability conditions, and potential experimental realizations.

Contribution

It introduces a particle-like model for soliton interactions and systematically analyzes the stability of multi-soliton states using Bogoliubov-de Gennes analysis.

Findings

Well-separated solitons can be modeled by particle-like equations of motion.

Multiple soliton states can be stable for large atom numbers.

Dynamical instabilities can arise from resonance effects at small atom numbers.

Abstract

We consider the stability and dynamics of multiple dark solitons in cigar-shaped Bose-Einstein condensates (BECs). Our study is motivated by the fact that multiple matter-wave dark solitons may naturally form in such settings as per our recent work [Phys. Rev. Lett. 101, 130401 (2008)]. First, we study the dark soliton interactions and show that the dynamics of well-separated solitons (i.e., ones that undergo a collision with relatively low velocities) can be analyzed by means of particle-like equations of motion. The latter take into regard the repulsion between solitons (via an effective repulsive potential) and the confinement and dimensionality of the system (via an effective parabolic trap for each soliton). Next, based on the fact that stationary, well-separated dark multi-soliton states emerge as a nonlinear continuation of the appropriate excited eigensates of the quantum harmonic oscillator, we use a Bogoliubov-de Gennes analysis to systematically study the stability of such structures. We find that for a sufficiently large number of atoms, multiple soliton states may be dynamically stable, while for a small number of atoms, we predict a dynamical instability emerging from resonance effects between the eigenfrequencies of the soliton modes and the intrinsic excitation frequencies of the condensate. Finally we present experimental realizations of multi-soliton states including a three-soliton state consisting of two solitons oscillating around a stationary one.