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 …

Publisher Summary This chapter explores quantum matter with ultracold atoms in optical
lattices. The chapter focuses on bosonic atoms in optical lattices and on the regime where …

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 …

The mathematical study of the Bose gas goes back to the? rst quarter of the twentieth
century, with the invention of quantum mechanics. The name refers to the Indian physicist …

Ultracold atomic gases in optical lattices have proven to be a controllable, tunable and clean
implementation of strongly interacting quantum many-body systems. An essential prospect …

We study the excitation spectrum of strongly correlated lattice bosons for the Mott-insulating
phase and for the superfluid phase close to localization. Within a Schwinger-boson mean …

We present a strong-coupling expansion of the Bose-Hubbard model which describes both
the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By …

We analyze theoretically the experiment reported in [F. Gerbier, Phys. Rev. Lett. 95, 050404
(2005)]. There, the interference pattern produced by an expanding atomic cloud in the Mott …

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 analyze the quench dynamics of a one-dimensional bosonic Mott insulator and focus on
the time evolution of density correlations. For these we identify a pronounced propagation …