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Journal of Physics B Atomic Molecular and Optical Physics

Density functional theory of the inhomogeneous Bose-Einstein condensate

Guilherme Nunes

Published Aug 27, 1999• 36 citations
Publisher

Abstract

I present a new bosonic density functional especially conceived for the alkali atom Bose gas, together with the corresponding Kohn-Sham equation. The new formalism provides the simplest theory of the observed inhomogeneous Bose-Einstein condensate, beyond the level of mean-field theory.
DOI
10.1088/0953-4075/32/17/312

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The refinement and the combination of laser cooling and evaporative cooling in dilute systems of alkali atoms lead to the achievement of Bose-Einstein condensation in 1995. Nowadays there is a fruitful interplay between theoretical and experimental results: in this context, the study of uniform Bose gases plays an important role in the comprehension of the static and dynamic properties of a bosonic system. Here we use quantum field theory, within the approach of functional integration, to study an homogeneous system of weakly-interacting bosonic cold atoms. After characterizing their thermodynamical properties, we derive - at a gaussian level - the number density and the superfluid density in three and in two spatial dimensions, expressed as functions of the condensate density and the temperature. Since the equations derived are valid for a generic interaction potential, we implement these formulas for bosons with a zero-range interaction, providing also an extension of these results with the inclusion of a finite-range interaction.
The grand canonical density functional theory for inhomogeneous systems of interacting bosons is developed in the effective action approach. The Legendre transform of the generating functional for Green's functions is used to define the effective action as a functional of both the particle density and the order parameter. Expanding the thermal effective action in powers of the Planck constant we obtain a systematic approximation scheme, which practically implements the Kohn-Sham idea: the problem of interacting bosons is reduced to a single-particle system in a fictitious external potential. The Kohn-Sham potential, the density and the order parameter have to be determined self-consistently in a given order approximation.