Localization and topology in disordered and quasiperiodic synthetic lattices

Artificial materials based on atoms and photons present unique opportunities to explore aspects of localization and topology. The level of control over such systems has recently been expanded through the introduction of synthetic lattices, wherein tight-binding Hamiltonians can be spectroscopically engineered through the driving of transitions between, e.g., atomic internal states or momentum states. We describe how this spectroscopic approach to Hamiltonian design can be used to create lattice-like systems with tunable disorder and quasiperiodicity, and discuss experimental results on the exploration of parameter-tunable single-particle mobility edges and disorder-induced topology in such systems.