Anomalous localization in a kicked quasicrystal

We report experimental results on the anomalous transport and localization of the kicked Aubry-André-Harper (kAAH) model in an extended parameter space [1]. The experiment consists of loading a Bose-Einstein condensate in a static optical lattice then periodically applying a secondary lattice with a lattice constant incommensurate to the first lattice. The extended parameter space is reached by spectrally tailoring the pulses, which allows us to reduce interband excitation by minimizing unwanted spectral components. This “apodization” technique is a versatile new tool to experimentally implement a single-band lattice model in the presence of periodic driving. In our experiment this technique extends the range of accessible parameter space by 5 orders of magnitude and allows us to explore regions where anomalous transport has been predicted. We experimentally map out the phase diagram via transport measurements, and indeed observe anomalous transport in a wide range of parameter space in the phase diagram. We theoretically show that the observed anomalous transport is a result of the mixed spectra and, in particular, a nonvanishing fraction of critical eigenstates. We also discuss the connection to multifractality, which is theoretically predicted for the kAAH model.

[1] Shimasaki et al., arXiv:2203.09442(2022)