Table of Contents
ISRN Condensed Matter Physics
Volume 2013, Article ID 393616, 39 pages
http://dx.doi.org/10.1155/2013/393616
Review Article

Out-of-Equilibrium Dynamics of the Bose-Hubbard Model

Department of Physics, Simon Fraser University, 8888 University Drive, Burnaby, BC, Canada V5A 1S6

Received 14 November 2012; Accepted 6 December 2012

Academic Editors: K. Kasamatsu and A. A. Kordyuk

Copyright © 2013 Malcolm P. Kennett. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and experimental efforts to understand out-of-equilibrium dynamics in this model, focusing on quantum quenches, both instantaneous and of finite duration. I discuss slow dynamics that have been observed theoretically and experimentally for some quenches from the superfluid phase to the Mott insulating phase and the picture of two timescales, one for fast local equilibration and another for slow global equilibration, that appears to characterize this situation. I also discuss the theoretical and experimental observation of the Lieb-Robinson bounds for a variety of quenches and the Kibble-Zurek mechanism in quenches from the Mott insulator to superfluid. I conclude with a discussion of open questions and future directions.