Measuring a Dynamical Topological Order Parameter in Quantum Walks
Abstract
Quantum processes of inherent dynamical nature, such as quantum walks (QWs), defy a description in terms of an equilibrium statistical physics ensemble. Up to now, it has remained a key challenge to identify general principles behind the underlying unitary quantum dynamics. Here, we show and experimentally observe that split-step QWs admit a characterization in terms of a dynamical topological order parameter (DTOP). This integer-quantized DTOP measures, at a given time, the winding of the geometric phase accumulated by the wave-function during the QW. We observe distinct dynamical regimes in our experimentally realized QWs each of which can be attributed to a qualitatively different temporal behavior of the DTOP. Upon identifying an equivalent many-body problem, we reveal an intriguing connection between the nonanalytic changes of the DTOP in QWs and the occurrence of dynamical quantum phase transitions.
Cite
@article{arxiv.1808.03930,
title = {Measuring a Dynamical Topological Order Parameter in Quantum Walks},
author = {Xiao-Ye Xu and Qin-Qin Wang and Markus Heyl and Jan Carl Budich and Wei-Wei Pan and Zhe Chen and Munsif Jan and Kai Sun and Jin-Shi Xu and Yong-Jian Han and Chuan-Feng Li and Guang-Can Guo},
journal= {arXiv preprint arXiv:1808.03930},
year = {2020}
}