Bose-Einstein condensation in a minimal inhomogeneous system

TL;DR

This paper investigates how disorder and interactions affect Bose-Einstein condensation in a minimal two-site system, revealing limitations of common approximations and emphasizing the importance of quantum operator properties.

Contribution

It demonstrates the failure of the Bogoliubov approximation in disordered systems and highlights the necessity of considering the noncommutative nature of the condensate operator for accurate modeling.

Findings

Bogoliubov approximation incorrectly predicts condensate depletion increase due to disorder.

Exact numerical results show the importance of noncommutative operators in disordered systems.

Disorder effects are significant even in minimal two-site models.

Abstract

We study the effects of repulsive interaction and disorder on Bosons in a two-site Bose-Hubbard system, which provides a simple model of the dirty boson problem. By comparison with exact numerical results, we demonstrate how a straightforward application of the Bogoliubov approximation fails even to deliver a qualitatively correct picture: It wrongly predicts an increase of the condensate depletion due to disorder. We show that, in the presence of disorder, the noncommutative character of the condensate operator has to be retained for a correct description of the system.