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Topological insulators are fascinating states of matter exhibiting protectededge states and robust quantized features in their bulk. Here, we propose andvalidate experimentally a method to detect topological properties in the bulkof one-dimensional chiral systems. We first introduce the mean chiraldisplacement, and we show that it rapidly approaches a multiple of the Zakphase in the long time limit. Then we measure the Zak phase in a photonicquantum walk, by direct observation of the mean chiral displacement in itsbulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe,and combine the two windings to characterize the full phase diagram of thisFloquet system. Finally, we prove the robustness of the measure by introducingdynamical disorder in the system. This detection method is extremely general,as it can be applied to all one-dimensional platforms simulating static orFloquet chiral systems.

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons