Quantum chaos and entanglement in the Bose-Hubbard model

We analyze the relation between quantum chaos and entanglement on the basis of the Bose-Hubbard model. This quantum many-body system can be realized experimentally by means of ultracold gases in optical lattices, and all its properties can be controlled very accurately. It is therefore a paradigm for quantum simulation and a promising candidate for quantum computation. Firstly, we discuss the quantum chaotic characteristics of this system, and derive a new measure for the detection of quantum chaos. We then provide a comprehensive introduction to entanglement theory, as it is needed for this model of many indistinguishable particles. We propose an experiment for the generation of practically useful entanglement. Finally, we compare quantum chaos and entanglement.