There have been significant recent advances in realizing band structures with geometrical
and topological features in experiments on cold atomic gases. This review summarizes …

We demonstrate the experimental implementation of an optical lattice that allows for the
generation of large homogeneous and tunable artificial magnetic fields with ultracold atoms …

We introduce an all-optical approach to producing high-flux synthetic magnetic fields for
neutral atoms or molecules by designing intrinsically time-periodic optical superlattices. A …

We present a perturbative approach to the study of the Hofstadter model for when the
amount of flux per plaquette is close to a rational fraction. Within this approximation, certain …

We perform a density-matrix renormalization-group study of strongly interacting bosons on a
three-leg ladder in the presence of a homogeneous flux. Focusing on one-third filling, we …

The phase diagram of ultracold bosons in a 2D optical lattice subjected to a uniform
magnetic flux is studied by the inhomogeneous Gutzwiller variational method. With a …

Topological band structures can be designed by subjecting lattice systems to time-periodic
modulations, as was proposed for irradiated graphene, and recently demonstrated in two …

An optical flux lattice is a set of light beams that couple different internal states of an atom,
thereby producing topological energy bands. Here we present a configuration in which the …

Fractional Chern insulators (FCIs) are strongly correlated, topological phases of matter that
may exist on a lattice in the presence of broken time-reversal symmetry. This thesis explores …

The experimental realization of dilute-gas Bose-Einstein condensates (BECS) has
established an extremely versatile and powerful platform for exploring uncharted territories …