Non-Abelian vibron dynamics in trapped-ion arrays

Trapped-ion arrays offer interesting possibilities for quantum simulation. We show that a proper arrangement of elliptical micro-traps combined with the external driving of the micro-trap frequencies allows, without the need of any precise fine-tuning, for the robust realization of non-Abelian vibron dynamics. We show that this non-Abelian nature may be readily probed experimentally in a simple plaquette arrangement. This study opens interesting perspectives for the study of non-Abelian spin-orbit coupling with motional excitations in two- and three-dimensional ion arrays.