Probing localization in the 2D Aubry-Andre model using ultracold atoms in an optical lattice

The Aubry-Andre model is a quasiperiodic system where a weak, periodic, but incommensurable modulation is applied on the onsite energies of a periodic lattice. It displays novel properties such as a localization transition and topological phenomena and its phase diagram contains the localized Bose glass in addition to the conventional superfluid and Mott insulting phases found in periodic lattices. We implement a 2D Aubry-Andre model by superimposing four retro-reflecting laser beams with different amplitudes under 45 degrees in the horizontal plane. By loading a BEC of bosonic ³⁹K atoms with widely tunable scattering length into this optical lattice, we study the interplay between disorder and interaction on the localization transition of this system. We map out the superfluid to Bose glass/Mott insulator transition phase diagram by measuring the coherence of the atoms through their matter-wave diffraction pattern in time-of-flight imaging. For vanishing interactions, the localization transition is in good agreement with the single-particle prediction. For increasing repulsive interaction we initially observe that superfluidity is preserved for larger disorder strength, similar to our previous experiment on the eight-fold symmetrical quasicrystal. For strong interactions, this trend reverses and the Bose glass transition blends into the Mott transition.