Dark solitons in cigar-shaped Bose-Einstein condensates in double-well potentials

TL;DR

This paper investigates the static and dynamic properties of dark solitons in cigar-shaped Bose-Einstein condensates within double-well potentials, revealing new soliton states and their stability characteristics across dimensional regimes.

Contribution

It introduces a mean-field model with non-cubic nonlinearity for the dimensional crossover and identifies novel dark soliton states without linear counterparts, analyzing their stability and excitation spectra.

Findings

Existence of dark soliton states without linear counterparts

Connection between anomalous mode frequencies and soliton dynamics

Impact of barrier height on soliton stability and bifurcations

Abstract

We study the statics and dynamics of dark solitons in a cigar-shaped Bose-Einstein condensate confined in a double-well potential. Using a mean-field model with a non-cubic nonlinearity, appropriate to describe the dimensionality crossover regime from one to three dimensional, we obtain branches of solutions in the form of single- and multiple-dark soliton states, and study their bifurcations and stability. It is demonstrated that there exist dark soliton states which do not have a linear counterpart and we highlight the role of anomalous modes in the excitation spectra. Particularly, we show that anomalous mode eigenfrequencies are closely connected to the characteristic soliton frequencies as found from the solitons' equations of motion, and how anomalous modes are related to the emergence of instabilities. We also analyze in detail the role of the height of the barrier in the double well setting, which may lead to instabilities or decouple multiple dark soliton states.