Quantum emulation of quasiperiodic systems*

Tunable quasiperiodic optical traps can enable quantum emulation of electronic phenomena in quasicrystals.~ A 1D bichromatic lattice or a Gaussian beam intersecting a 2D square lattice in a direct analogy of the "cut-and-project" construction can be used to create tunable 1D quasiperiodic potentials for cold neutral atoms.~ We report on progress towards the observation of singular continuous diffraction patterns, fractal energy spectra, and Bloch oscillations in these synthetic quasicrystals. We will also discuss the existence of edge states which can be topologically pumped across the lattice by varying a phasonic parameter.