Revivals in quantum walks with a quasiperiodically-time-dependent coin
Christopher Cedzich, Reinhard F. Werner · Physical Review A · 2016
We provide an explanation of recent experimental results of Xue et al. [P. Xue, R. Zhang, H. Qin, X. Zhan, Z. H. Bian, J. Li, and B. C. Sanders, Phys. Rev. Lett. 114, 140502 (2015)], 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 quasiperiodic behavior 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 behavior of the time-dependent system in close analogy to the electric case.