Matter-wave dark solitons in a double-well potential

TL;DR

This paper investigates the stability and dynamics of matter-wave dark solitons in a double-well potential within Bose-Einstein condensates, identifying critical conditions for instability and simulating their oscillatory behavior.

Contribution

It provides a detailed analysis of the stability of the $ ext{pi}$-state and dark solitons, including the critical barrier height and dynamical evolution via simulations.

Findings

Critical barrier height decreases with increasing atom number.

Dynamical instability causes the dark soliton to oscillate and move away from the trap center.

The $ ext{pi}$-state becomes unstable beyond a certain barrier height.

Abstract

We study stability of the first excited state of quasi-one-dimensional Bose-Einstein condensates in a double-well potential, which is called "$\pi$-state". The density notch in the $\pi$-state can be regarded as a standing dark soliton. From the excitation spectrum, we determine the critical barrier height, above which the $\pi$-state is dynamically unstable. We find that the critical barrier height decreases monotonically as the number of condensate atoms increases. We also simulate the dynamics of the $\pi$-state by solving the time-dependent Gross-Pitaevskii equation. We show that due to the dynamical instability the dark soliton starts to move away from the trap center and exhibits a large-amplitude oscillation.