Josephson-junction arrays are ideal model systems to study a variety of phenomena such as
phase transitions, frustration effects, vortex dynamics and chaos. In this review, we focus on …

We review the experimental realization of a single bosonic Josephson junction for ultracold
gases, which was made possible by the generation of a precisely controllable double-well …

We review recent developments in the physics of ultracold atomic and molecular gases in
optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard …

Quantum computers, though not yet available on the market, will revolutionize the future of
information processing. Quantum computers for special purposes like quantum simulators …

Variational quantum circuits have been widely employed in quantum simulation and
quantum machine learning in recent years. However, quantum circuits with random …

We propose the creation of a molecular Bose-Einstein condensate by loading an atomic
condensate into an optical lattice and driving it into a Mott insulator with exactly two atoms …

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 …

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of
correct self-consistent description of arbitrary systems with Bose-Einstein condensate are …

We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in
one dimension using the density matrix renormalization group. For integer filling the Mott …

We study the sweep through the quantum phase transition from the superfluid to the Mott
state for the Bose-Hubbard model with a time-dependent tunneling rate J (t). In the …