Edge-state instabilities of bosons in a topological band

TL;DR

This paper investigates the dynamical instabilities of bosonic edge states in topological bands, demonstrating that edge modes can become unstable while bulk modes remain stable, leading to rapid edge mode population.

Contribution

It introduces the concept of edge-state instabilities in bosonic topological bands and analyzes their dynamics using the Su-Schrieffer-Heeger model.

Findings

Edge modes can be dynamically unstable while bulk modes are stable.

Rapid population of edge states occurs due to instabilities.

Topological properties influence bosonic dynamical behavior.

Abstract

In this work, we consider the dynamics of bosons in bands with non-trivial topological structure. In particular, we focus on the case where bosons are prepared in a higher-energy band and allowed to evolve. The Bogoliubov theory about the initial state can have a dynamical instability, and we show that it is possible to achieve the interesting situation where the topological edge modes are unstable while all bulk modes are stable. Thus, after the initial preparation, the edge modes will become rapidly populated. We illustrate this with the Su-Schrieffer-Heeger model which can be realized with a double-well optical lattice and is perhaps the simplest model with topological edge states. This work provides a direct physical consequence of topological bands whose properties are often not of immediate relevance for bosonic systems.