Physics

Diffraction grating

Isotropy

Mathematics

Fractal

Dynamical theory of diffraction

Mathematical analysis

Diffraction

Acoustics

Quasicrystal

Condensed matter physics

Lattice (music)

Quantum mechanics

Electron diffraction

Quantum

Acousto-optics

Physical Review Letters

Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and the presence of non-trivial structure on all scales. Here we report on the first experimental demonstration of an eightfold rotationally symmetric optical lattice, realising a two-dimensional quasicrystalline potential for ultracold atoms. Using matter-wave diffraction we observe the self-similarity of this quasicrystalline structure, in close analogy to the very first discovery of quasicrystals using electron diffraction. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. These measurements pave the way for quantum simulations in fractal structures and higher dimensions.

Matter-Wave Diffraction from a Quasicrystalline Optical Lattice