  Topology and disorder have deep connections and a rich combined influence on
quantum transport. In order to probe these connections, we synthesized
one-dimensional chiral symmetric wires with controllable disorder via
spectroscopic Hamiltonian engineering, based on the laser-driven coupling of
discrete momentum states of ultracold atoms. We characterize the system's
topology through measurement of the mean chiral displacement of the bulk
density extracted from quench dynamics. We find evidence for the topological
Anderson insulator phase, in which the band structure of an otherwise trivial
wire is driven topological by the presence of added disorder. In addition, we
observed the robustness of topological wires to weak disorder and measured the
transition to a trivial phase in the presence of strong disorder. Atomic
interactions in this quantum simulation platform will enable future
realizations of strongly interacting topological fluids.
