Non-Abelian effects in dissipative photonic topological lattices

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.

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
• Topological Photonics
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Topological Acoustics
• An Open-System Quantum Simulator with Trapped Ions
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Nonlinear control of PT-symmetry and non-Hermitian topological states
• Active topological photonics
• Non-Abelian braiding on photonic chips

Cited by in corpus (22)

• Non-Abelian lattice gauge fields in the photonic synthetic frequency dimension
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Realizing exceptional points by Floquet dissipative couplings in thermal atoms
• Topological Dissipative Photonics and Topological Insulator Lasers in Synthetic Time-Frequency Dimensions
• Non-Markovian skin effect
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Large-scale time-multiplexed nanophotonic parametric oscillators
• Interaction-Induced Second-Order Skin Effect
• Coherent-cluster-state generation in networks of degenerate optical parametric oscillators
• Chiral-Extended Photon-Emitter Dressed States in Non-Hermitian Topological Baths
• Frustration Elimination and Excited State Search in Coherent Ising Machines
• Gain-loss-induced non-Abelian Bloch braids
• Exotic quantum light-matter interactions in bilayer square lattices
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• How to realize compact and non-compact localized states in disorder-free hypercube networks
• Topological state permutations in time-modulated non-Hermitian multiqubit systems with suppressed non-adiabatic transitions
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Scattering States in One-Dimensional Non-Hermitian Baths
• Efficient Simulation of Open Quantum Systems on NISQ Trapped-Ion Hardware
• Reshaping coupled bosonic networks: A bipartite-graph framework for optimal quantum excitation transfer