# Topological quantum walks in momentum space with a Bose-Einstein condensate

## TL;DR

This paper demonstrates the experimental realization of topological quantum walks using a Bose-Einstein condensate in momentum space, revealing topological phase transitions and interaction-induced localization effects.

## Contribution

It introduces a novel method to implement discrete-time topological quantum walks with cold atoms and measures topological invariants directly in an experimental setting.

## Key findings

- Observation of topological phase transitions
- Measurement of topological invariants via mean chiral displacements
- Detection of interaction-induced localization phenomena

## Abstract

We report the experimental implementation of discrete-time topological quantum walks of a Bose-Einstein condensate in momentum space. Introducing stroboscopic driving sequences to the generation of a momentum lattice, we show that the dynamics of atoms along the lattice is effectively governed by a periodically driven Su-Schrieffer-Heeger model, which is equivalent to a discrete-time topological quantum walk. We directly measure the underlying topological invariants through time-averaged mean chiral displacements, which are consistent with our experimental observation of topological phase transitions. We then observe interaction-induced localization in the quantum-walk dynamics, where atoms tend to populate a single momentum-lattice site under interactions that are non-local in momentum space. Our experiment opens up the avenue of investigating discrete-time topological quantum walks using cold atoms, where the many-body environment and tunable interactions offer exciting new possibilities.