Quantum simulation of a 2D quasicrystal with cold atoms

We describe a way to obtain a two-dimensional quasiperiodic tiling with eight-fold symmetry using cold atoms. A series of such optical tilings, related by scale transformations, is obtained for a series of specific values of the chemical potential of the atoms. A theoretical model for the optical system is described and compared with that of the well-known cut-and-project method for the Ammann-Beenker tiling. This type of cold atom structure should allow the simulation of several important lattice models for interacting quantum particles and spins in quasicrystals.