Measuring a dynamical topological order parameter in quantum walks

Quantum processes such as quantum walks are not described by equilibrium ensembles, and identifying governing principles of their unitary dynamics is challenging. Here the authors show and experimentally observe that split-step quantum walks admit a dynamical topological order parameter (DTOP): an integer-quantized winding of the geometric (Pancharatnam) phase acquired by the wavefunction. Distinct dynamical regimes are observed and attributed to qualitatively different temporal behaviors of the DTOP. Mapping to an equivalent many-body problem reveals a connection between nonanalytic DTOP changes in quantum walks and dynamical quantum phase transitions (DQPTs).