Gap solitons and Bloch waves of interacting bosons in one-dimensional optical lattices: From the weak to the strong interaction limits

TL;DR

This paper investigates the properties and stability of gap solitons and nonlinear Bloch waves of interacting bosons in one-dimensional optical lattices across all interaction strengths, revealing their composition relation and stability conditions.

Contribution

It demonstrates the existence of a composition relation between gap solitons and nonlinear Bloch waves for all interaction strengths and analyzes their stability across different regimes.

Findings

Stable gap solitons exist near the bottom of the band gap in weak interactions.

Increasing interaction strength can destabilize gap solitons.

Stable gap solitons are more easily formed in weakly interacting systems.

Abstract

We study the gap solitons and nonlinear Bloch waves of interacting bosons in one-dimensional optical lattices, taking into account the interaction from the weak to the strong limits. It is shown that composition relation between the gap solitons and nonlinear Bloch waves exists for the whole span of the interaction strength. The linear stability analysis indicates that the gap solitons are stable when their energies are near the bottom of the linear Bloch band gap. By increasing the interaction strength, the stable gap solitons can turn into unstable. It is argued that the stable gap solitons can easily be formed in a weakly interacting system with energies near the bottoms of the lower-level linear Bloch band gaps.