Statistical moments of quantum-walk dynamics reveal topological quantum transitions.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 27102945.
- Also identified by DOI 10.1038/ncomms11439 and PMC identifier 4844751.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
Abstract
Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.