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

Hitoshi Inoue

康之 加藤

Makoto Yamashita, Michael W. Jack

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.

Ramesh V. Pai, Jamshid Moradi Kurdestany, K. Sheshadri +1 more

We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. [Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.

H. Yokoyama, T. Miyagawa, Masao Ogata

Motoyoshi Inoue, Keita Kobayashi, Yusuke Nakamura +1 more

We study the superfluid-Mott insulator (SF-MI) transition in an one-dimensional optical lattice system, and employ the Bose-Hubbard model in two dimension with a combined potential of an optical lattice in one direction and a confining harmonic trap in the other direction, which we refer to as the pseudo one-dimension Bose-Hubbard model. There some excited states with respect to the harmonic trap are considered. The Mott lobes shrink in the $μ$ and $J$ directions of the $μ$-$J$ phase diagram. The shrinkage occurs because the interactions involving the excited states become weaker than that between particles in the ground state. The dispersion of the in-site particle increases because the energy spacing between the eigenstates of the Hamiltonian decreases at finite temperature. The excited states significantly affect the robustness of the MI phase at finite temperate.