Bose Hubbard model

Introduction

The Bose-Hubbard Model (BHM) was first studied in detail in 1989 by Fisher et al. (need to cite phys rev b article by fisher et al.) They studied a three dimensional Bose gas in several different types of systems, including the most simple case at zero temperature. --> This is just an idea, I havent finished it yet, and dont know if it is necessary so let me know what you guys think about it.

Phase Diagram for Zero Temperature BHM from Fisher et al paper.

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Experimental Evidence of BHM

First Experiment (Nature Paper)

The first experimental evidence in support of the BHM was observed in 2002. Greiner and collaborators (Nature paper, need to cite) created a $^{87}Rb$ Bose-Einstein condensate that was spherically symmetric. To form the three dimensional lattice potential three optical standing waves were set up perpendicular to eachother with the crossing point of the three beams positioned at the center of the condensate.