2016/09/30 by G. Puentes · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.3390/cryst7050122
published as Crystals MDPI 7, 122 (2017) · Invited contribution
arxiv created 2017/01/06 · arxiv updated 2017/05/05
We present a review on the progress in the understanding and characterization of holonomy and topology of a discrete-time quantum walk architecture, consisting of a unitary step given by a sequence of two non-commuting rotations in parameter space \citePuentesarxiv. Unlike other similar systems recently studied in detail in the literature, this system does not present continous 1D topological boundaries, it only presents a discrete number of Dirac points where the quasi- energy gap closes. At these discrete points the topological winding number is not defined. Therefore, such discrete points represent topological boundaries of dimension zero, and they endow the system with a non-trivial topology. We illustrate the non-trivial character of the system by calculating the Zak phase. We also propose a suitable experimental scheme to implement these ideas, and we present preliminary experimental data.