Josephson tunneling of dark solitons in a double-well potential

TL;DR

This paper investigates Josephson tunneling of dark solitons in a double-well Bose-Einstein condensate, revealing stable and unstable tunneling regimes and proposing an experimental setup for observation.

Contribution

It introduces the concept of Josephson tunneling of dark solitons, extending known phenomena from ground states to excited states in a double-well potential.

Findings

Stable tunneling of dark solitons identified

Unstable tunneling regions mapped out

Coupled-mode system accurately models the dynamics

Abstract

We study the dynamics of matter waves in an effectively one-dimensional Bose-Einstein condensate in a double well potential. We consider in particular the case when one of the double wells confines excited states. Similarly to the known ground state oscillations, the states can tunnel between the wells experiencing the physics known for electrons in a Josephson junction, or be self-trapped. As the existence of dark solitons in a harmonic trap are continuations of such non-ground state excitations, one can view the Josephson-like oscillations as tunnelings of dark solitons. Numerical existence and stability analysis based on the full equation is performed, where it is shown that such tunneling can be stable. Through a numerical path following method, unstable tunneling is also obtained in different parameter regions. A coupled-mode system is derived and compared to the numerical observations. Regions of (in)stability of Josephson tunneling are discussed and highlighted. Finally, we outline an experimental scheme designed to explore such dark soliton dynamics in the laboratory.