Topologically protected edge gap solitons of interacting Bosons in one-dimensional superlattices

TL;DR

This paper explores topologically protected edge gap solitons in interacting bosons within one-dimensional superlattices, revealing their stability, topological properties, and relation to edge states and adiabatic transport.

Contribution

It introduces the concept of stable edge gap solitons with nonzero topological invariants in 1D bosonic superlattices, linking them to topological and transport phenomena.

Findings

Existence of stable edge gap solitons in 1D superlattices

Edge gap solitons possess nonzero topological invariants

Connection to quantized adiabatic particle transport

Abstract

We comprehensively investigate the nontrivial states of interacting Bose system in one-dimensional optical superlattices under the open boundary condition. Our results show that there exists a kind of stable localized states: edge gap solitons. We argue that the states originate from the eigenstates of independent edge parabolas. In particular, the edge gap solitons exhibit a nonzero topological invariant. The topological nature is due to the connection of the present model to the quantized adiabatic particle transport problem. In addition, the composition relations between the gap solitons and the extend states under the open boundary condition are discussed.