Combinatorics

Physics

Topology (electrical circuits)

Pure mathematics

Mathematics

Hermitian matrix

Science

Topology in the open Controlling the topology of a system provides a route to develop devices that are robust against defects. Whereas earlier developments of topological band theory focused on Hermitian (closed) systems, recent efforts have been toward non-Hermitian (open) systems. K. Wang et al. report on the measurement and control of topologically nontrivial windings of a non-Hermitian energy band. By implementing non-Hermitian lattice Hamiltonians along a frequency synthetic dimension formed by optical frequency modes in a modulated ring-resonator, they directly visualized the nontrivial topological band winding and showed that the winding can be controlled. Such control provides a route for the experimental synthesis, characterization, and control of topologically nontrivial phases in open physical systems. Science , this issue p. 1240

Generating arbitrary topological windings of a non-Hermitian band