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

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.