Zak Phase in Discrete-Time Quantum Walks

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.

Some formulas corrected

Cited by in corpus (1)

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