  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.
