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Journal of Research of the National Institute of Standards and Technology

Zero-temperature, mean-field theory of atomic Bose-Einstein condensates

Mark Edwards, R. J. Dodd, Charles W. Clark, Keith R. Burnett

Published Jul 1, 1996• 68 citations
Publisher

Abstract

We review the application of zero-temperature, mean-field theory to current experimental atomic Bose-Einstein condensates. We assess the validity of the approximations made by comparing the mean-field results with a variety of experimental data.
DOI
10.6028/jres.101.055

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We outline the general features of the conventional mean field theory for the description of Bose-Einstein condensates at near zero temperatures. This approach, based on a phenomenological model, appears to give excellent agreement with experimental data. We argue, however, that such an approach is not rigorous and cannot contain the full effect of collisional dynamics due to the presence of the mean field. We thus discuss an alternative microscopic approach and explain, within our new formalism, the physical origin of these effects. Furthermore, we discuss the potential formulation of a consistent finite-temperature mean field theory, which we claim necessitates an analysis beyond the conventional treatment. 1.
We outline the general features of the conventional mean–field theory for the description of Bose–Einstein condensates at near zero temperatures. This approach, based on a phenomenological model, appears to give excellent agreement with experimental data. We argue, however, that such an approach is not rigorous and cannot contain the full effect of collisional dynamics due to the presence of the mean–field. We thus discuss an alternative microscopic approach and explain, within our new formalism, the physical origin of these effects. Furthermore, we discuss the potential formulation of a consistent finite–temperature mean–field theory, which we claim necessitates an analysis beyond the conventional treatment.
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There is a wide-spread belief in the literature on Bose-Einstein condensation of interacting atoms that all variants of mean-field theory incorrectly describe the condensation phase transition, exhibiting, instead of the necessary second-order transition, a first-order transition, even for weakly interacting Bose gas. In the present paper, it is shown that a self-consistent mean-field approach is the sole mean-field theory that provides the correct second-order condensation transition for Bose systems with atomic interactions of arbitrary strength, whether weak or strong.