2D Zak Phase Landscape in Photonic Discrete-Time Quantum Walks

TL;DR

This paper explores the 2D Zak phase landscape in photonic discrete-time quantum walks, revealing non-trivial topological properties and proposing a novel method to break time-reversal symmetry without inducing Berry curvature.

Contribution

It introduces numerical analysis of Zak phases in symmetric photonic quantum walks and proposes a new approach to break TRS while maintaining zero Berry curvature.

Findings

Non-trivial Zak phase structures in three DTQW scenarios

A novel method to break TRS without Berry curvature

Analogy to the Aharonov-Bohm effect in photonic systems

Abstract

We present a study of the 2D Zak phase landscape in photonic discrete-time quantum walk (DTQW) protocols. In particular, we report numerical results for three different DTQW scenarios which preserve spatial inversion symmetry (SIS) and time-reversal symmetry (TRS), while presenting a non-trivial Zak phase structure, as a consequence of a non-vanishing Berry connection. Additionally, we propose a novel approach to break TRS in photonic systems, while preserving a vanishing Berry curvature. Our results bear a close analogy to the Aharonov-Bohm effect, stating that in a field-free multiply connected region of space the evolution of the system depends on vector potentials, due to the fact that the underlying canonical formalism cannot be expressed in terms of fields alone.