Observation of average topological phase in disordered Rydberg atom array

Topological phases have been extensively studied over the past two decades, primarily in quantum pure states, where they are protected by exact symmetries. Recently, numerous studies have theoretically demonstrated the existence of average symmetry-protected topological (SPT) phases in mixed quantum states, which naturally arise in real systems due to decoherence or disorder. Despite extensive experimental observations of exact SPT phases in various systems, ranging from solid-state materials to synthetic matters, average SPT phases are yet to be observed until this work. Here we report direct observations of disorder-induced many-body interacting average SPT phase in an atom array at half-filling, whereby random offsets to tweezer locations forming a lattice implement structural disorder, resulting in fluctuating long-range dipolar interactions between tweezer confined single atoms. The induced topological phase is vindicated by the spatially resolved atom-atom correlation functions for different forms of dimer compositions. The ground state degeneracy in disordered configurations is detected and compared to the regular lattice without disorder. By probing the quench dynamics of a highly excited state, we observe markedly slower decay of edge spin magnetization in comparison to the bulk spin, consistent with the presence of topologically protected edge modes in disordered lattices.