Many-body localization and the localization transition in quasiperiodic potentials*

Quasiperiodic potentials, in particular Aubry-Andre-type models, have routinely been employed by us and others as substitutes for real random disorder in the study of many-body localization with ultracold atoms. Far away from the transition, the resulting localized phases are indeed expected to be essentially identical. However, quasiperiodic potentials are not random but long-range ordered. Hence their physics must ultimately be very different. For instance, they do not contain any rare region and, as a result, the nature of the localization transition could be entirely different.

I will briefly review our experimental realization of many-body localization of interacting fermions in the presence of quasiperiodic disorder in 1D and 2D, with a particular focus on slow relaxation close to the localization transition. Furthermore, I will discuss a recent extension to 2D quasicrystals with high rotational symmetries. Matter-wave diffraction experiments in our eightfold symmetric optical quasicrystal directly reveal the presence of a fractal structure in momentum space. I will close with first measurements of the localization transition in these potentials.