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. 
Nicolas Mac\'e, Anuradha Jagannathan and Michel Duneau
cond-mat.quant-gas cond-mat.str-el