Non-Abelian effects in dissipative photonic topological lattices

TL;DR

This paper demonstrates non-Abelian topological effects in dissipative photonic resonator networks, revealing how engineered dissipation combined with topology can lead to novel non-Abelian phenomena, supported by experimental measurements.

Contribution

It introduces matrix-valued modified Wilson lines to describe dissipative photonic networks and experimentally observes non-Abelian effects in such systems.

Findings

Experimental measurement of geometric phases in dissipative networks

Observation of non-Abelian effects in photonic topological lattices

Identification of new topological phenomena arising from dissipation

Abstract

Topology is central to phenomena that arise in a variety of fields, ranging from quantum field theory to quantum information science to condensed matter physics. Recently, the study of topology has been extended to open systems, leading to a plethora of intriguing effects such as topological lasing, exceptional surfaces, as well as the non-Hermitian bulk-boundary correspondence. Here, we show that resonator networks with dissipative couplings can be governed by matrix-valued modified Wilson lines, leading to non-Abelian effects. This is in contrast to conservative Hamiltonians exhibiting non-degenerate energy levels, where the geometric properties of the Bloch eigenstates are typically characterized by scalar Berry phases. We experimentally measure geometric phases and demonstrate non-Abelian effects in a dissipatively-coupled network of time-multiplexed photonic resonators. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena.