Weakly Interacting, Dilute Bose Gases in 2D

TL;DR

This paper reviews theoretical challenges and recent experimental findings related to two-dimensional dilute Bose gases with weak interactions, highlighting differences from three-dimensional systems and the impact of external trapping.

Contribution

It provides a comprehensive survey of theoretical models and discusses the conditions under which Bose-Einstein condensation may occur in 2D dilute Bose gases.

Findings

Experimental indications of condensate formation in 2D systems

Reevaluation of theoretical predictions for inhomogeneous systems

Analysis of the validity of perturbative approaches in 2D

Abstract

This article surveys a number of theoretical problems and open questions in the field of two-dimensional dilute Bose gases with weak repulsive interactions. In contrast to three dimensions, in two dimensions the formation of long-range order is prohibited by the Bogoliubov-Hohenberg theorem, and Bose-Einstein condensation is not expected to be realized. Nevertheless, first experimental indications supporting the formation of the condensate in low dimensional systems have been recently obtained. This unexpected behaviour appears to be due to the non-uniformity, introduced into a system by the external trapping potential. Theoretical predictions, made for homogeneous systems, require therefore careful reexamination. We survey a number of popular theoretical treatments of the dilute weakly interacting Bose gas and discuss their regions of applicability. The possibility of Bose-Einstein condensation in a two-dimensional gas, the validity of perturbative t-matrix approximation and diluteness condition are issues that we discuss in detail.