Optical Quasicrystal for Ultracold Atoms

Quasicrystals represent a rich middle ground between periodic and disordered materials. They possess perfect long-range order, yet they are not periodic. Hence many foundational concepts such as Bloch's theorem do not apply. Therefore, they exhibit exotic properties such as Anderson localisation, fractal energy spectra, or mobility edges. We have realized a two-dimensional optical quasicrystal for ultracold atoms, where the amount of (quasi-)disorder as well as interaction strength can be precisely controlled. We used this experimental platform to observe localisation phenomena, study its underlying fractality and connection to four-dimensional periodic lattices, as well as the resulting many-body phase diagram. In addition, we developed a Hubbard model able to describe this quasiperiodic lattice, without resorting to Bloch's theorem . Finally, we show how re-expressing the quasiperiodic Hubbard model in configuration space – where sites are arranged in terms of shape and local environment – provides valuable insight in the description of the infinite-size limit quasicrystal.