Measuring a dynamical topological order parameter in quantum walks

Quantum processes of inherent dynamical nature, such as quantum walks, defy a description in terms of an equilibrium statistical physics ensemble. Until now, identifying the general principles behind the underlying unitary quantum dynamics has remained a key challenge. Here, we show and experimentally observe that split-step quantum walks 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 wavefunction during a quantum walk. We observe distinct dynamical regimes in our experimentally realized quantum walks, and each regime 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 quantum walks and the occurrence of dynamical quantum phase transitions. Taking stock of a quantum walk A model describing the random walks of quantum particles has been developed by researchers in China and Germany. Classical phenomena such as molecules moving in gases or animals foraging for food can be described by random walks, where every step is chosen through processes like tossing a coin. For quantum particles, randomness arises from the transitions and entanglement of quantum states, but it is difficult to describe the emerging statistical patterns in these quantum walks. Chuan-Feng Li at the University of Science and Technology of China, Hefei, and co-workers used an experimental setup for observing the quantum walks of single photons. They found that the walks could be characterized by a so-called dynamical topological order parameter that describes the behavior of the particle's wavefunction during the walk, thereby linking quantum effects to physical spatial measurements