Multiple fluxon analogues and dark solitons in linearly coupled Bose-Einstein condensates

TL;DR

This paper investigates coupled Bose-Einstein condensates using Gross-Pitaevskii equations, focusing on fluxon analogues and dark solitons, and provides a variational method to estimate their oscillation frequencies.

Contribution

It introduces a theoretical approximation for fluxon-like solutions in coupled BECs and analyzes their dynamics with good qualitative agreement.

Findings

Identification of fluxon analogues and dark solitons in coupled BECs

Development of a variational approximation for oscillation frequencies

Qualitative agreement between theory and numerical results

Abstract

Two effectively one-dimensional parallel coupled Bose-Einstein condensates in the presence of external potentials are studied. The system is modelled by linearly coupled Gross-Pitaevskii equations. In particular, the interactions of grey-soliton-like solutions representing analogues of superconducting Josephson fluxons as well as coupled dark solitons are discussed. A theoretical approximation based on variational formulations to calculate the oscillation frequency of the grey-soliton-like solution is derived and a qualitatively good agreement is obtained.