Revivals in Quantum Walks with quasi-periodically time-dependent coin

Abstract

We provide an explanation of recent experimental results of Xue et al., where full revivals in a time-dependent quantum walk model with a periodically changing coin are found. Using methods originally developed for "electric" walks with a space-dependent, rather than a time-dependent coin, we provide a full explanation of the observations of Xue et al. We extend the analysis from periodic time-dependence to quasi-periodic behaviour with periods incommensurate to the step size. Spectral analysis, one of the principal tools for the study of electric walks, fails for time-dependent systems, but we find qualitative propagation behaviour of the time-dependent system in close analogy to the electric case.

6 pages, 3 figures

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• Spectral Characteristics of the Unitary Critical Almost-Mathieu Operator
• Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility
• Induced on-demand revival in coined quantum walks on infinite $d$-dimensional lattices
• Phase transitions in non-Hermitian superlattices
• Revivals in One-dimensional Quantum Walks with a Time and Spin-dependent Phase Shift
• Spectral Magnetization Ratchets with Discrete Time Quantum Walks
• Resolvent Methods for Quantum Walks with an Application to a Thue-Morse Quantum Walk
• Quantum Walks in Weak Stochastic Gauge Fields
• Theoretical Studies on Quantum Walks with a Time-varying Coin
• Complementarity in quantum walks