Theory of Bose-Einstein condensation in trapped gases

TL;DR

This paper reviews the theoretical understanding of Bose-Einstein condensation in trapped dilute gases, emphasizing mean-field theory's role in explaining static and dynamic properties, superfluid effects, and coherence phenomena, with comparisons to experiments.

Contribution

It provides a comprehensive theoretical framework for Bose-Einstein condensation in trapped gases, highlighting the accuracy and limitations of mean-field theory.

Findings

Mean-field theory accurately predicts density profiles and ground state energies.

Interactions significantly influence static and dynamic properties despite gas diluteness.

Experimental results align well with theoretical predictions.

Abstract

The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions between particles. Various properties of these systems are discussed, including the density profiles and the energy of the ground state configurations, the collective oscillations and the dynamics of the expansion, the condensate fraction and the thermodynamic functions. The thermodynamic limit exhibits a scaling behavior in the relevant length and energy scales. Despite the dilute nature of the gases, interactions profoundly modify the static as well as the dynamic properties of the system; the predictions of mean-field theory are in excellent agreement with available experimental results. Effects of superfluidity including the existence of quantized vortices and the reduction of the moment of inertia are discussed, as well as the consequences of coherence such as the Josephson effect and interference phenomena. The review also assesses the accuracy and limitations of the mean-field approach.