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

Gauge fields are central in our modern understanding of physics at all scales. At the highest
energy scales known, the microscopic universe is governed by particles interacting with …

We experimentally implement the Harper Hamiltonian for neutral particles in optical lattices
using laser-assisted tunneling and a potential energy gradient provided by gravity or …

Extensions of Berry's phase and the quantum Hall effect have led to the discovery of new
states of matter with topological properties. Traditionally, this has been achieved using …

We propose a scheme which realizes spin-orbit coupling and the quantum spin Hall effect
for neutral atoms in optical lattices without relying on near resonant laser light to couple …

Fractal Hofstadter bands have become widely accessible with the advent of moiré
superlattices, opening the door to studies of the effect of interactions in these systems. In this …

We study mean-field states resulting from the pairing of electrons in time-reversal broken
fractal Hofstadter bands, which arise in two-dimensional lattices where the unit cell traps …

Realizing strongly correlated topological phases of ultracold gases is a central goal for
ongoing experiments. While fractional quantum Hall states could soon be implemented in …

On top of the mean-field analysis of a Bose-Einstein condensate, one typically applies the
Bogoliubov theory to analyze quantum fluctuations of the excited modes. Therefore, one has …

Recent experiments in ultracold atoms and photonic analogs have reported the
implementation of artificial gauge fields in lattice systems, facilitating the realization of …