Non-Abelian Aharonov-Bohm caging in photonic lattices
Sheng Li, Zheng‐Yuan Xue, Ming Gong, Yong Hu
Abstract
Aharonov-Bohm (AB) caging is the localization effect in translational-invariant lattices due to destructive interference induced by penetrated magnetic fields. Although 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 one-dimensional multicomponent rhombic lattice with a 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 on 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.