Non-Hermitian non-Abelian topological transition in the S = 1 electron spin system of a nitrogen vacancy centre in diamond.

Non-Abelian topological transitions are well studied in Hermitian systems, exhibiting features like non-Abelian charges and edge states. Introducing non-Hermiticity gives rise to novel topological phenomena, yet non-Hermitian non-Abelian topological transitions remain experimentally unexplored. In this work we observe a non-Hermitian non-Abelian topological transition in a single electron spin system of a nitrogen vacancy centre in diamond, achieved via a dilation method with a nearby nuclear spin. While this transition cannot be detected by traditional topological numbers, we identify the transition through the measured complex eigenvalue braids. We extract the braid invariants from the relative phases between eigenvalues and thereby establish their changes as clear signatures of non-Abelian transitions. Furthermore we experimentally reveal an intriguing consequence of this transition: the creation of a third-order exceptional point through the collision of two second-order exceptional points with opposite charges. Our work unveils the dynamical interplay between exceptional points and provides guidance on the manipulation of spectral topology to achieve functionalities such as robust quantum control.