Bose-Hubbard Hamiltonian: Quantum Chaos approach

TL;DR

This paper explores the application of Quantum Chaos theory to the Bose-Hubbard model, linking quantum and classical dynamics, and analyzing phenomena like Bloch oscillations in ultracold atoms.

Contribution

It introduces a semiclassical approach to the Bose-Hubbard model and connects quantum chaos concepts with experimental observations in cold atom systems.

Findings

Classical counterpart of the Bose-Hubbard model is formulated.

Semiclassical equations of motion are derived and analyzed.

The approach explains experimental results on Bloch oscillations.

Abstract

We discuss applications of the theory of Quantum Chaos to one of the paradigm models of many-body quantum physics -- the Bose-Hubbard model, which describes, in particular, interacting ultracold Bose atoms in an optical lattice. After preliminary, pure quantum analysis of the system we introduce the classical counterpart of the Bose-Hubbard model and the governing semiclassical equations of motion. We analyze these equations for the problem of Bloch oscillations of cold atoms where a number of experimental results are available. The review is written for non-experts and can be viewed as an introduction to the field.