Abstrakt
Optical lattices are experimental devices that use laser light to confine ultracold neutral atoms to periodic spatial structures. A system of bosonic atoms in an optical lattice can be described by the Bose-Hubbard model.
Although there exist powerful analytic and numerical methods to study this model in one dimension, their extensions to multiple dimensions have not been as successful yet. I present an original numerical method based on tree tensor networks to simulate time evolution in multidimensional lattice systems with a focus on the two-dimensional Bose-Hubbard model.
The method is used to investigate phenomena accessible in current experiments. In particular, I have studied phase collapse and revivals, boson expansion, and many-body localization in two-dimensional optical lattices.
The outcome of this work is TEBDOL - a program for modelling one-dimensional and two-dimensional lattice systems.