Toward quantum simulation of ultracold atoms in three-dimensional quasicrystal lattices

Quasicrystals represent a unique class of material that provides long-range order without translational symmetry. Although one and two-dimensional quasicrystal optical lattices have been successfully realized for ultracold atoms, three-dimensional (3D) implementations remain unexplored in this context. We present experimental progress towards the realization of a 3D quasiperiodic icosahedral quasicrystal (IQC) experimental apparatus for quantum gases of ⁸⁷Rb. A 3D IQC provides a simple, well-defined model of pseudodisorder that is expected to exhibit a metal–insulator transition, including mobility edges that can be directly probed via temperature-dependent localization. The ability to engineer aperiodicity in optical lattices opens new possibilities to demonstrate exotic phase transitions and novel localization properties supported by 3D IQCs.