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arXiv:cond-mat/0408599 · Laser Physics Letters

Principal problems in Bose-Einstein condensation of dilute gases

Vyacheslav I. Yukalov

Published Aug 3, 2004• 145 citations
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Abstract

A survey is given of the present state of the art in studying Bose-Einstein condensation of dilute atomic gases. The bulk of attention is focused on the principal theoretical problems, though the related experiments are also mentioned. Both uniform and nonuniform trapped gases are considered. Existing theoretical contradictions are critically analysed. A correct understanding of the principal theoretical problems is necessary for gaining a more penetrating insight into experiments with trapped atoms and for their proper interpretation.

DOI
10.1002/lapl.200410097

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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.
Abstract This volume introduces the basic concepts of Bose–Einstein condensation and superfluidity. It makes special reference to the physics of ultracold atomic gases; an area in which enormous experimental and theoretical progress has been achieved in the last twenty years. Various theoretical approaches to describing the physics of interacting bosons and of interacting Fermi gases, giving rise to bosonic pairs and hence to condensation, are discussed in detail, both in uniform and harmonically trapped configurations. Special focus is given to the comparison between theory and experiment, concerning various equilibrium, dynamic, thermodynamic, and superfluid properties of these novel systems. The volume also includes discussions of ultracold gases in dimensions, quantum mixtures, and long-range dipolar interactions.