Topological Pumping in Optical Quasicrystals

Cold atoms have become a rich platform for realising topological phases of matter, characterised by finite Chern numbers. In particular, quasiperiodic lattices can exhibit up to infinite Chern numbers, inherited from higher-dimensional parent Hamiltonians. Here, we design an experimentally realizable pumping protocol for optical quasicrystals that leads to bulk currents of topological nature, and harness it to measure the hierarchy of increasing Chern numbers. Expanding the configuration space representation developed in [1], we offer a simple explanation of the fractal energy spectrum based on resonances between increasingly distant sites as well as a general way of understanding the adiabatic pumping of optical quasicrystals. The pumping protocol is illustrated in the case of the one-dimensional Aubry-André model, but is general and applicable for different quasiperiodic lattices, and higher dimensions.

[1] E. Gottlob, U. Schneider, "Hubbard Models for Quasicrystalline Potentials" arXiv:2210.05691