Transport in a kicked Aubry-André Harper model

We report the realization of the kicked Aubry-André Harper model using ultracold strontium in a pulsed 1D bichromatic optical lattice. Rich transport dynamics are predicted over a phase diagram of varying disorder and kick periodicity, but the breakdown of the tight-binding approximation for large kick periods and disorder strengths limits investigation. By engineering apodized kicking waveforms, we are able to circumvent the breakdown of the tight-binding approximation and suppress heating. Use of such waveforms extends the range of this quantum simulator by 5 orders of magnitude in parameter space and enables access to regions of anomalous transport. In the revealed regime we both theoretically and experimentally observe signatures of wavefunction multifractality across an extended region away from the critical point.