Localization and delocalization of ultracold bosonic atoms in finite optical lattices

TL;DR

This paper investigates how ultracold bosonic atoms behave in small optical lattices, revealing phenomena similar to larger systems and showing effects of lattice imperfections and symmetry breaking.

Contribution

It provides a detailed analysis of localization, delocalization, and phase transition phenomena in finite optical lattices using exact diagonalization, including higher orbital effects.

Findings

Weak size dependence of momentum distribution and energy gap

Presence of localized and delocalized particles in deep lattices at noncommensurate filling

Lattice symmetry breaking induces Bose-glass-like behavior

Abstract

We study bosonic atoms in small optical lattices by exact diagonalization and observe a striking similarity to the superfluid to Mott insulator transition in macroscopic systems. The momentum distribution, the formation of an energy gap, and the pair correlation function show only a weak size dependence. For noncommensurate filling we reveal in deep lattices a mixture of localized and delocalized particles, which is sensitive to lattice imperfections. Breaking the lattice symmetry causes a Bose-glass-like behavior. We discuss the nature of excited states and orbital effects by using an exact diagonalization technique that includes higher bands.