Non-Abelian Aharonov-Bohm Caging in Photonic Lattices

Abstract

Aharonov-Bohm (AB) caging is the localization effect in translational-invariant lattices due to destructive interference induced by penetrated magnetic fields. While current research focuses mainly on the case of Abelian AB caging, here we go beyond and develop the non-Abelian AB caging concept by considering the particle localization in a 1D multi-component rhombic lattice with non-Abelian background gauge field. In contrast to its Abelian counterpart, the non-Abelian AB cage depends on both the form of the nilpotent interference matrix and the initial state of the lattice. This phenomena is the consequence of the non-Abelian nature of the gauge potential and thus has no Abelian analog. We further propose a circuit quantum electrodynamics realization of the proposed physics, in which the required non-Abelian gauge field can be synthesized by the parametric conversion method, and the non-Abelian AB caging can be unambiguously demonstrated through the pumping and the steady-state measurements of only a few sites on the lattice. Requiring only currently available technique, our proposal can be readily tested in experiment and may pave a new route towards the investigation of exotic photonic quantum fluids.

10 pages, 4 figures, revised with discussion added

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• Non-Abelian inverse Anderson transitions
• Many-body Aharonov-Bohm caging in a lattice of rings
• Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields
• Topological photonics on superconducting quantum circuits with parametric couplings
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• Impurity flat band states in the diamond chain
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings
• Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion