Non-Abelian effects in dissipative photonic topological lattices

In this work, the authors show that photonic topological lattices with dissipative couplings could exhibit non-Abelian dynamics and geometric phases that are in sharp contrast to those arising in typical energy-conserving systems. 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 non-Hermitian bulk-boundary correspondence. Here, we show that Bloch eigenstates associated with lattices with dissipatively coupled elements exhibit geometric properties that cannot be described via scalar Berry phases, in sharp contrast to conservative Hamiltonians with non-degenerate energy levels. This unusual behavior can be attributed to the significant population exchanges among the corresponding dissipation bands of such lattices. Using a one-dimensional example, we show both theoretically and experimentally that such population exchanges can manifest themselves via matrix-valued operators in the corresponding Bloch dynamics. In two-dimensional lattices, such matrix-valued operators can form non-commuting pairs and lead to non-Abelian dynamics, as confirmed by our numerical simulations. Our results point to new ways in which the combined effect of topology and engineered dissipation can lead to non-Abelian topological phenomena.

Automated summary

The researchers demonstrate that photonic topological lattices with dissipative couplings can exhibit non-Abelian dynamics and geometric phases, contrasting with energy-conserving systems. Topology plays a central role in various fields, and its study has extended to open systems, leading to fascinating effects such as topological lasing and exceptional surfaces. They show that the geometric properties of Bloch eigenstates in dissipatively coupled lattices cannot be described by scalar Berry phases, unlike conservative Hamiltonians. This behavior is attributed to significant population exchanges among dissipation bands. The researchers provide theoretical and experimental evidence that such exchanges manifest as matrix-valued operators in Bloch dynamics, resulting in non-commuting pairs and non-Abelian dynamics in two-dimensional lattices.