Abstract
Topological transport is determined by global properties of physical media where it occurs and is characterized by quantized amounts of adiabatically transported quantities. Discovered for periodic potential, it was also explored in disordered and discrete quasiperiodic systems. Here, we report on experimental observation of pumping of a light beam in a genuinely continuous incommensurate photorefractive quasicrystal emulated by its periodic approximants. We observe a universal character of the transport which is determined by the ratio between periods of the constitutive sublattices, by the sliding angle between them, and by Chern numbers of the excited bands (in the time-coordinate space) of the approximant, for which pumping is adiabatic. This reveals that the properties of quasiperiodic systems determining the topological transport are tightly related to those of their periodic approximants and can be observed and studied in a large variety of physical systems. Our results suggest that the links between quasiperiodic systems and their periodic approximants go beyond the pure mathematical relations: They manifest themselves in physical phenomena which can be explored experimentally.