Expansion of Bose-Hubbard Mott insulators in optical lattices

TL;DR

This paper investigates how bosonic Mott insulators expand in optical lattices after removing confinement, revealing the formation of condensates with distinct momentum properties and potential applications like atom lasers.

Contribution

It provides a mean-field analysis of Mott insulator expansion in optical lattices, highlighting the emergence of multiple condensates and their momentum distributions, with an analytic explanation in the hard-core limit.

Findings

Two condensates with well-defined momenta form during restricted expansion.

A single condensate develops during unrestricted expansion, with bosons populating many momentum modes.

Analytic understanding based on the dispersion relation explains both phenomena.

Abstract

We study the expansion of bosonic Mott insulators in the presence of an optical lattice after switching off a confining potential. We use the Gutzwiller mean-field approximation and consider two different setups. In the first one, the expansion is restricted to one direction. We show that this leads to the emergence of two condensates with well defined momenta, and argue that such a construct can be used to create atom lasers in optical lattices. In the second setup, we study Mott insulators that are allowed to expand in all directions in the lattice. In this case, a simple condensate is seen to develop within the mean-field approximation. However, its constituent bosons are found to populate many nonzero momentum modes. An analytic understanding of both phenomena in terms of the exact dispersion relation in the hard-core limit is presented.