Bose condensates in a harmonic trap near the critical temperature - art. no. 063605

The mean-field properties of finite-temperature Bose-Einstein gases confine d in spherically symmetric harmonic traps are surveyed numerically. The sol utions of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equat ions for the condensate and low-lying quasiparticle excitations are calcula ted self-consistently using the discrete variable representation, while the most high-lying states are obtained with a local-density approximation. Co nsistency of the theory for temperatures through the Bose condensation poin t T-c requires that the thermodynamic chemical potential differ from the ei genvalue of the GP equation; the appropriate modifications lead to results that are continuous as a function of the particle interactions. The HFB equ ations are made gapless either by invoking the Popov approximation or by re normalizing the particle interactions. The latter approach effectively redu ces the strength of the effective scattering length a(sc), increases the nu mber of condensate atoms at each temperature, and raises the value of T-c r elative to the Popov approximation. The renormalization effect increases ap proximately with the log of the atom number, and is most pronounced at temp eratures near T-c. Comparisons with the results of quantum Monte Carlo calc ulations and various local-density approximations are presented, and experi mental consequences an discussed.