UC Berkeley

Ultracold atomic gases trapped at the interference of coherent beams of light constitute an artificial material. This optical lattice material may be used for controlled quantum simulations of condensed matter theories. The bulk of this dissertation concerns the construction and calibration of an optical superlattice that can form the triangular, honeycomb and kagome crystal structures. The properties and geometry of this artificial material may be dynamically changed, allowing for the experiments discussed in this thesis that would be impossible with real materials.

The use of ultracold atoms in optical lattices for quantitative tests is challenging because of the novelty of many of the techniques in the field, and because of the myriad experimental differences between these artificial materials and true materials. This thesis reports the development of a method to characterize optical lattice potentials using matter-wave diffraction. We observe an enhancement of inversion asymmetry in matter-wave diffraction from a honeycomb lattice, which we explain using a time-independent perturbative treatment of the single-particle band structure of the lattice. Our experiment also provides new insight into a commonly used detection technique.

This thesis culminates in the development and experimental realization of a quantitative test of a condensed-matter theory. The test is insensitive to the experimental differences between artificial materials and real materials. We focus on a prediction from a mean-field treatment of the Bose-Hubbard model that concerns the difference in behavior of itinerant particles on lattices that are identical but for their geometry. Using the tunable geometry of our quantum simulator, we measure the properties of ultracold atomic gases trapped in the triangular and kagome lattices under otherwise identical conditions and find that they are consistent with the mean-field scaling prediction.