Eur. Phys. J. D 41, 157-162 (2007)
https://doi.org/10.1140/epjd/e2006-00197-8

Atomic density of a harmonically trapped ideal gas near Bose-Einstein transition temperature

Laboratoire Charles Fabry de l'Institut d'Optique, UMR 8501 du CNRS, 91403 Orsay Cedex, France

Corresponding author: ^a denis.boiron@iota.u-psud.fr

Received: 19 August 2005
Revised: 20 May 2006
Published online: 1 September 2006

Abstract

We have studied the atomic density of a cloud confined in an isotropic harmonic trap at the vicinity of the Bose-Einstein transition temperature. We show that, for a non-interacting gas and near this temperature, the ground-state density has the same order of magnitude as the excited states density at the centre of the trap. This holds in a range of temperatures where the ground-state population is negligible compared to the total atom number. We compare the exact calculations, available in a harmonic trap, to semi-classical approximations. We show that these latter should include the ground-state contribution to be accurate.