Topological bound states of a quantum walk with cold atoms

TL;DR

This paper proposes a method to engineer topologically non-trivial quantum walks with cold atoms, demonstrating boundary states, phase diagrams, and robustness, with potential mapping to the Creutz ladder.

Contribution

It introduces a novel approach to create and observe topologically protected states in cold atom quantum walks, including phase diagram derivation and experimental identification methods.

Findings

Topologically protected bound states are observable at phase boundaries.

The system's phase diagram shows distinct topological phases.

Mapping to the Creutz ladder reveals additional insights.

Abstract

We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically non-trivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct phases using the finite beam width of the applied lasers. A topologically protected bound state can then be observed, which is pinned to the interface and is robust to perturbations. We show that it is possible to identify this bound state by averaging over spin sensitive measures of the atom's position, based on the spin distribution that these states display. Interestingly, there exists a parameter regime in which our system maps on to the Creutz ladder.