Measuring a Dynamical Topological Order Parameter in Quantum Walks

TL;DR

This paper introduces and experimentally verifies a dynamical topological order parameter in quantum walks, linking geometric phase winding to dynamical regimes and quantum phase transitions.

Contribution

It presents the first characterization of quantum walk dynamics using a dynamical topological order parameter and connects it to dynamical quantum phase transitions.

Findings

Observation of distinct dynamical regimes in quantum walks

Experimental measurement of the dynamical topological order parameter

Connection between DTOP changes and quantum phase transitions

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.