Experimental evidence for the breakdown of a Hartree-Fock approach in a   weakly interacting Bose gas
  We study the formation of a quasi-condensate in a nearly one dimensional, weakly interacting trapped atomic Bose gas. We show that a Hartree Fock (mean-field) approach fails to explain the presence of the quasi-condensate in the center of the cloud: the quasi-condensate appears through an interaction-driven cross-over and not a saturation of the excited states. Numerical calculations based on Bogoliubov theory give an estimate of the cross-over density in agreement with experimental results. 
Jean-Baptiste Trebbia (LCFIO), J\'er\^ome Est\`eve (LCFIO), Christoph   I. Westbrook (LCFIO), Isabelle Bouchoule (LCFIO)