Mott-insulator shells in the three-dimensional Bose-Hubbard model with harmonic confinement

Abstract

Ultracold atom experiments offer unprecedented potential for the quantitative comparison of quantum many-body effects with theory. This comparison is hindered by the lack of numerical methods capable of dealing with these large inhomogeneous three-dimensional systems. In this paper we demonstrate the applicability of a highly efficient numerical method based on the Gutzwiller approximation for calculating the ground state of the Bose-Hubbard model in the regimes of the recent cold atom experiments. The numerical method is applied to the experimental regime employed by Campbell et al. [Science 314, 281 (2006)], where Mott-insulator shells were directly imaged via atomic clock shifts. We calculate several quantities that are closely related to the current experimental measurement methods: average number distributions, momentum distributions, two-photon spectra, and three-body recombination loss rates. Our results shed light on a number of features of the experimental observations and clarify both the crossover behavior around the superfluid--Mott-insulator transition point and the experimentally observed three-body decay rate of the Mott-insulator shells.