Observation of π/2 Modes in an Acoustic Floquet System.

Topological phases of matter have remained an active area of research in the last few decades. Periodic driving is a powerful tool for enriching such exotic phases, leading to various phenomena with no static analogs. One such phenomenon is the emergence of the elusive π/2 modes, i.e., a type of topological boundary state pinned at a quarter of the driving frequency. The latter may lead to the formation of Floquet parafermions in the presence of interaction, which is known to support more computational power than Majorana particles. In this Letter, we experimentally verify the signature of π/2 modes in an acoustic waveguide array, which is designed to simulate a square-root periodically driven Su-Schrieffer-Heeger model. This is accomplished by confirming the 4T-periodicity (T being the driving period) profile of an initial-boundary excitation, which we also show theoretically to be the smoking gun evidence of π/2 modes. Our findings are expected to motivate further studies of π/2 modes in quantum systems for potential technological applications.