Stability and Tunneling Dynamics of a Dark-Bright Soliton Pair in a Harmonic Trap

TL;DR

This paper investigates the stability, bifurcations, and tunneling dynamics of dark-bright soliton pairs in a one-dimensional Bose-Einstein condensate within a harmonic trap, revealing symmetry breaking and Josephson-like behavior.

Contribution

It introduces a detailed analysis of bifurcations and tunneling dynamics of dark-bright solitons, connecting them to Bosonic Josephson Junction physics and exploring beyond the double-well approximation.

Findings

Symmetry breaking bifurcation occurs at a critical particle number.

Dark-bright solitons exhibit Josephson-like tunneling dynamics.

Complex anharmonic and aperiodic motions observed at larger deviations.

Abstract

We consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright (DB) solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a Bosonic Josephson Junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.