Direct Probe of Topological Invariants Using Bloch Oscillating Quantum Walks

TL;DR

This paper introduces a method using Bloch-oscillating quantum walks to directly measure topological invariants in quantum systems, linking theoretical concepts with a practical circuit QED experimental protocol.

Contribution

It presents a novel approach to directly probe topological invariants via quantum walks, including a detailed measurement strategy and an experimental implementation proposal.

Findings

Demonstrated connection between quantum walk phases and topological invariants

Proposed an experimental protocol in circuit QED architecture

Outlined a method to disentangle dynamical and geometric phases

Abstract

The topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a simple time-dependent, Bloch-oscillating quantum walk enables the direct measurement of topological invariants. We consider two classes of one-dimensional quantum walks and connect the global phase imprinted on the walker with its refocusing behavior. By disentangling the dynamical and geometric contributions to this phase we describe a general strategy to measure the topological invariant in these quantum walks. As an example, we propose an experimental protocol in a circuit QED architecture where a superconducting transmon qubit plays the role of the coin, while the quantum walk takes place in the phase space of a cavity.