# Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices

## TL;DR

This paper presents a scheme to realize topological insulators and quantized magnon pumps using strongly-interacting ultracold atoms in optical superlattices, enabling the exploration of magnonic topological phases and transport.

## Contribution

It introduces a method to engineer topological models for magnons with ultracold atoms and proposes experimental protocols to detect their topological properties.

## Key findings

- Engineered Su-Schrieffer-Heeger and Rice-Mele models for magnons.
- Proposed detection of topological winding numbers via magnon dynamics.
- Demonstrated realization of topological (quantized) magnon pumps.

## Abstract

We propose a scheme realizing topological insulators and quantized pumps for magnon excitations, based on strongly-interacting two-component ultracold atoms trapped in optical superlattices. Specifically, we show how to engineer the Su-Schrieffer-Heeger model for magnons using state-independent superlattices, and the Rice-Mele model using state-dependent superlattices. We describe realistic experimental protocols to detect the topological signatures of magnon excitations in these two models. In particular, we show that the non-equilibrium dynamics of a single magnon can be exploited to directly detect topological winding numbers and phase transitions. We also describe how topological (quantized) pumps can be realized with magnons, and study how this phenomenon depends on the initial magnon state preparation. Our study opens a new avenue for exploring magnonic topological phases of matter and their potential applications in the context of topological magnon transport.