Dynamical instability of a dark soliton in a quasi-one-dimensional Bose-Einstein condensate perturbed by an optical lattice

TL;DR

This paper studies how a dark soliton in a quasi-one-dimensional Bose-Einstein condensate becomes dynamically unstable due to harmonic trapping and optical lattice effects, leading to sound emission and destabilization.

Contribution

It reveals the combined impact of harmonic traps and optical lattices on dark soliton stability and characterizes sound emission behavior in this context.

Findings

Harmonic trap induces soliton dynamical instability.

Optical lattice enhances instability and dephases sound waves.

Sound emission power is proportional to the square of soliton acceleration.

Abstract

The motion of a dark soliton is investigated in a one-dimensional dilute Bose-Einstein condensate confined in a harmonic trap and an optical lattice. The harmonic trap induces a dynamical instability of the soliton, culminating in sound emission. The presence of the optical lattice enhances the instability, and in addition, dephases the emitted sound waves, thus preventing stabilisation of the soliton by sound reabsorption. This instability can be probed experimentally by monitoring the soliton oscillations under various lattice configurations, which can be realised by changing the intensity and angle between the laser beams that form the lattice. For short enough times, such that the emitted sound does not reinteract with the soliton, the power emitted by the soliton is found to be proportional to the square of the local soliton acceleration, which is in turn proportional to the deformation of the soliton profile.