This is a review of recent developments in Monte Carlo methods in the field of ultracold
gases. For bosonic atoms in an optical lattice we discuss path-integral Monte Carlo …

During the last decade, many exciting phenomena have been experimentally observed and
theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid …

We investigate the nonlinear light-matter interaction of a Bose-Einstein condensate trapped
in an external periodic potential inside an optical cavity which is weakly coupled to vacuum …

Mott insulator plateaus in optical lattices are a versatile platform to study spin physics. Using
sites occupied by two bosons with an internal degree of freedom, we realize a uniaxial …

We numerically simulate strongly correlated ultracold bosons coupled to a high-finesse
cavity field, pumped by a laser beam in the transverse direction. Assuming a weak classical …

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

We study the Bose-Hubbard and Fermi-Hubbard models in the (formal) limit of large
coordination numbers Z≫ 1. Via an expansion into powers of 1/Z, we establish a hierarchy …

Recent experiments have illustrated that long-range two-body interactions can be induced
by laser coupling atoms to highly excited Rydberg states. Stimulated by this achievement …

Recent experiments in ultracold atoms have reported the realization of quantum anomalous
Hall phases in spin-orbit coupled systems. Motivated by such advances, we investigate spin …

Spin-orbit coupling plays an important role in understanding exotic quantum phases. In this
work, we present a scheme to combine spin-orbital-angular-momentum (SOAM) coupling …