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Quasiperiodic lattices have recently been shown to be a non-trivialtopological phase of matter. Charge pumping -- one of the hallmarks oftopological states of matter -- was recently realized for photons in aone-dimensional (1D) off-diagonal Harper model implemented in a photonicwaveguide array. The topologically nontrivial 1D Fibonacci quasicrystal (QC) isexpected to facilitate a similar phenomenon, but its discrete nature and lackof pumping parameter hinder the experimental study of such topological effects.In this work we overcome these obstacles by utilizing a family of topologicallyequivalent QCs which ranges from the Fibonacci QC to the Harper model.Implemented in photonic waveguide arrays, we observe the topological propertiesof this family, and perform a topological pumping of photons across a FibonacciQC.

Topological Pumping over a Photonic Fibonacci Quasicrystal