Non-Abelian topological insulators, arising from a non-Abelian gauge field, not only link to particle physics and the strong and weak forces of nature, but also create coveted topological phenomena with remarkable properties. Although significant efforts have been made to develop artificial non-Abelian gauge fields, few of them applied to momentum space to realize non-Abelian topological insulators. Here, we propose a scheme to create artificial SU(2) gauge fields in phononic crystals. By implementing this scheme to a non-Abelian Hofstadter model, we overcome the challenge of constructing an analog of the non-Abelian magnetic field in momentum space that opens nontrivial band gaps. We experimentally realize and observe such a non-Abelian topological insulating phase in a phononic crystal. Furthermore, we experimentally investigate the spin rotation and flipping phenomena of non-Abelian topological boundary states along a specific plane of the Bloch sphere, which are linked to the signatures of the underlying non-Abelian gauge field. Our Letter not only opens the door to the realization and characterization of non-Abelian topological insulators, but also provides a reconfigurable platform for exploring non-Abelian physics in a classical system.

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• Non-Abelian gauge theories
• Topological effects in acoustic systems
• Phononic crystals
• Topological insulators