Probing chirally-protected non-Abelian holonomy of 1D anyons with ultracold atoms in an optical lattice

Non-Abelian holonomies are of fundamental and practical interest, with applications towards robust holonomic quantum computing. While typical schemes focus on the braiding statistics of non-Abelian anyons in two dimensions, there are also various complementary proposals for non-Abelian holonomic operations in one dimension (1D). Our work focuses on the Wilczek-Zee phase factor, an extension of the geometric Berry's phase towards non-Abelian phases. Also known as the non-Abelian holonomy, it manifests as a unitary transformation or rotation within a degenerate subspace. We realize the Wilczek-Zee phase using the 1D anyon-Hubbard model with ultracold atoms in an optical lattice, the spectrum of which hosts a degenerate zero-energy subspace protected by chiral symmetry. We traverse a loop in phase space by tuning the exchange angle between particles from 0 to 2π, after which the final state should be rotated with respect to the initial state. This poster discusses the experimental techniques and challenges towards realizing such non-Abelian state manipulation.