Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass

Abstract

The topological orders in amorphous systems that lack crystalline symmetry have gained considerable attention recently. Here we propose the Floquet amorphous topological matter, among which the topological orders are explored in experimentally accessible one-dimensional array of randomly pointed Rydberg atoms with periodic driving. The topological properties are comprehensively characterized, considering both the single-particle and many-body perspectives. It is found that the periodic driving leads to rich topological phases of matter. At the single-particle level, we evaluate the real space winding numbers and polarization, revealing robust amorphous topological phases with 0-type and $\pi$-type edge modes. We show a structural disorder induced topological phase transition associated with localization transition in the nonequilibrium system. Remarkably, in the many-body case it is discovered that the amorphous topological order exists in the chain of hardcore bosons, captured by the topological entanglement entropy and the string order. Moreover, feasible experimental probe protocols are also elaborated.