The dynamics of ultracold bosons in optical lattices is a rich field with many fundamental physics questions and applications. Cold atoms in lattices represent a very versatile tool for the quantum simulation of various other states of matter. Theoretical methods for the treatment of the dynamics in one-dimensional lattices are available, but despite the large interest in the field, to date no reliable theoretical method to describe the dynamics of two- and three-dimensional systems has been formulated.
An application of the multiconfigurational time-dependent Hartree method for bosons (MCTDHB, see http://ultracold.org) to describe the dynamics of the Bose-Hubbard Hamiltonian yields reliable predictions with a controlled error for the dynamics in one-, two-, and three-dimensional systems and therefore fills in this gap. The theory is introduced and example applications of beyond mean-field dynamics are discussed.
