Quasicrystals are long-range ordered and non-periodic at the same time. This interplay leads to a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and non-trivial structure on all lengthscales. In my talk I will report on the first experimental realization of a two-dimensional optical quasicrystal for ultracold atoms. Using matter- wave diffraction we observe the striking self-similarity of the quasicrystal, a fractal in momentum space. The diffraction dynamics are shown to represent a continuous-time quantum walk on a four-dimensional tight-binding lattice. These measurements open up entirely new possibilities for quantum simulation in higher dimensions. Additionally, our system will enable the observation of phenomena, such as non-power-law scaling near criticality, that have so far been unattainable with quasicrystalline systems in the context of condensed matter and photonics.
Host: Nir Navon