Bose-Hubbard Models in Confining Potentials: An Inhomogeneous Mean-Field Theory

TL;DR

This paper develops an inhomogeneous mean-field theory for Bose-Hubbard models in harmonic traps, accurately describing MI and SF shells in large 3D optical lattice systems and extending to multi-species and spin-1 bosons.

Contribution

The authors introduce a numerically efficient inhomogeneous mean-field approach that matches QMC results and applies to complex multi-species and spinor boson systems in realistic traps.

Findings

Quantitative agreement with QMC simulations for single-species models

Rich phase diagrams with multiple SF and MI shells for two-species systems

Predictions of alternating shells of polar SF and MI phases in spin-1 bosons

Abstract

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 develop an inhomogeneous mean-field theory. Our results for the BH model with one type of spinless bosons agrees quantitatively with quantum Monte Carlo (QMC) simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculation on experimentally realistic, large 3D systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also generalize 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.