Ultracold bosons with short-range interaction in regular optical lattices

TL;DR

This paper reviews recent theoretical developments in ultracold bosonic atoms in optical lattices, focusing on eigenstates, quantum phase transitions, and the connection between theory and experiments.

Contribution

It provides a comprehensive overview of theoretical methods and results for bosonic systems in various lattice configurations and trapping potentials.

Findings

Analysis of eigenstates in homogeneous lattices

Insights into quantum phase transitions at different temperatures

Discussion of experimental techniques in ultracold atom research

Abstract

During the last decade, many exciting phenomena have been experimentally observed and theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid developments concentrating mainly on the theory. Different types of the bosonic systems in homogeneous lattices of different dimensions as well as in the presence of harmonic traps are considered. An overview of the theoretical methods used for these investigations as well as of the obtained results is given. Available experimental techniques are presented and discussed in connection with theoretical considerations. Eigenstates of the interacting bosons in homogeneous lattices and in the presence of harmonic confinement are analysed. Their knowledge is essential for understanding of quantum phase transitions at zero and finite temperature.