Zak Phase in Discrete-Time Quantum Walks

TL;DR

This paper introduces a scheme using discrete-time quantum walks to measure the Zak phase, revealing geometric invariants that can be directly detected, advancing understanding of topological properties in quantum systems.

Contribution

It presents a novel method to detect the Zak phase difference in quantum walks, linking geometric invariants to measurable quantities.

Findings

Zak phase difference can be detected between trajectories

Geometric invariants correspond to phase differences of π and 0

Method allows direct measurement of topological invariants

Abstract

We report on a simple scheme that may present a non-trivial geometric Zak phase ($\Phi_{Zak}$) structure, which is based on a discrete-time quantum walk architecture. By detecting the Zak phase difference between two trajectories connecting adjacent Dirac points where the quasi-energy gap closes for opposite values of quasi-momentum ($k$), it is possible to identify geometric invariants. These geometric invariants correspond to $|\Phi_{Zak}^{+(-)}-\Phi_{Zak}^{-(+)}|=\pi$ and $|\Phi_{Zak}^{+(-)}-\Phi_{Zak}^{+(-)}|=0$, we argue that this effect can be directly measured.