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

Rodolphe Hoppeler (1) , Jose Viana Gomes (1) , Denis Boiron (1)

1 LCFIO - Laboratoire Charles Fabry de l'Institut d'Optique

We investigate the atomic density of a cloud confined in an isotropic harmonic trap at the vicinity of Bose-Einstein transition temperature. We show that, for an ideal gas and near this temperature, the ground-state density cannot be neglected, even at the thermodynamic limit. In particular, at the transition temperature, the value of $\rho(0)\lambda^3$ with $\rho(0)$ the total peak density and $\lambda$ the thermal de Broglie wavelength, is more than two times the famous $\zeta(3/2)\approx 2.612$. We compare the exact calculations, available in an harmonic trap, to semi-classical approximations.

Mots clés: cold atoms; Bose-Einstein condensation; ideal gas

Domaines: Physique Quantique [quant-ph]

Rodolphe Hoppeler, Jose Viana Gomes, Denis Boiron. Atomic density of an harmonically trapped ideal gas near Bose-Einstein transition temperature. 2005. ⟨hal-00008200v1⟩