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arXiv · 1808.03930

Measuring a Dynamical Topological Order Parameter in Quantum Walks

Xiao-Ye Xu·Qin-Qin Wang·Markus Heyl·Jan Carl Budich·Wei-Wei Pan·Zhe Chen·Munsif Jan·Kai Sun·Jin-Shi Xu·Yong-Jian Han·Chuan-Feng Li·Guang-Can Guo
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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.

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Xiao-Ye Xu, Qin-Qin Wang, Markus Heyl, Jan Carl Budich, Wei-Wei Pan, Zhe Chen, Munsif Jan, Kai Sun, Jin-Shi Xu, Yong-Jian Han, Chuan-Feng Li, Guang-Can Guo. 2018-08-12. Measuring a Dynamical Topological Order Parameter in Quantum Walks. https://doi.org/10.1038/s41377-019-0237-8

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