Exponential localization in one-dimensional quasiperiodic optical lattices

TL;DR

This paper explores how exponential localization arises in one-dimensional quasiperiodic optical lattices, analyzing the transition from extended to localized states and its implications for experiments on Anderson localization in Bose-Einstein condensates.

Contribution

It provides a detailed analysis of localization phenomena in quasiperiodic lattices and connects theoretical models with experimental observations.

Findings

Exponential localization occurs upon changing the lattice's commensurability.

The momentum distribution changes significantly during the transition.

The study relates the Aubry-Andre' model to experimental results on Anderson localization.

Abstract

We investigate the localization properties of a one-dimensional bichromatic optical lattice in the tight binding regime, by discussing how exponentially localized states emerge upon changing the degree of commensurability. We also review the mapping onto the discrete Aubry-Andre' model, and provide evidences on how the momentum distribution gets modified in the crossover from extended to exponentially localized states. This analysis is relevant to the recent experiment on Anderson localization of a noninteracting Bose-Einstein condensate in a quasiperiodic optical lattice [G. Roati et al., Nature 453, 895 (2008)].