Stability of gap solitons in a Bose-Einstein condensate

TL;DR

This paper investigates the stability of gap solitons in Bose-Einstein condensates, finding they are stable only in one dimension and unstable in higher dimensions due to transverse excitations, with decay times analyzed.

Contribution

It demonstrates the dimensional dependence of gap soliton stability in Bose-Einstein condensates using numerical methods under realistic conditions.

Findings

Gap solitons are stable only in one-dimensional setups.

Transverse excitations cause instability in higher dimensions.

Decay times are large compared to soliton time scales.

Abstract

We analyze the dynamical stability of gap solitons formed in a quasi one-dimensional Bose-Einstein condensate in an optical lattice. Using two different numerical methods we show that, under realistic assumptions for experimental parameters, a gap soliton is stable only in a truly one-dimensional situation. In two and three dimensions resonant transverse excitations lead to dynamical instability. The time scale of the decay is numerically calculated and shown to be large compared to the characteristic time scale of solitons for realistic physical parameters.