Lattice bosons in a quasi-disordered environment

TL;DR

This study explores how deterministic disorder affects non-interacting bosons in a one-dimensional optical lattice with a harmonic trap, revealing impacts on localization, Bose-Einstein condensation, and thermal properties.

Contribution

It provides new insights into the localization and condensation behavior of bosons under Aubry-André disorder in finite and open chains with harmonic confinement.

Findings

Disorder reduces the BEC temperature and condensate fraction.

Localization sensitivity varies with chain boundary conditions.

Condensate fraction sharply drops at the localization transition.

Abstract

In this paper, we study non-interacting bosons in a disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic disorder produced by an Aubry-Andr\'{e} potential. Using exact diagonalization, we investigate both the zero temperature and the finite temperature properties. We investigate the localization properties by using an entanglement measure. We find that the extreme sensitivity of the localization properties to the number of lattice sites in finite size closed chains disappear in open chains. This feature continues to be present in the presence of a harmonic confining potential. The disorder is found to strongly reduce the Bose-Einstein condensation temperature and the condensate fraction in open chains. The low temperature thermal depletion rate of the condensate fraction increases considerably with increasing disorder strength. We also find that the critical disorder strength required for localization increases with increasing strength of the harmonic potential. Further, we find that the low temperature condensate fraction undergoes a sharp drop to 0.5 in the localization transition region. The temperature dependence of the specific heat is found to be only marginally affected by the disorder.