The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, ${n\left(0\right)a}^3<~2\times {10}^{-3}$ $\left[n\right(0),$ peak density; a, s-wave scattering length], our calculations confirm that the exact ground-state energy for a sum of two-body interactions depends to a good approximation on only the atomic-physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for $N=2\mathrm{}–50$ particles in the trap with positive s-wave scattering length $a=100\mathrm{}–10000\mathrm{a}.\mathrm{u}.\mathrm{}$ Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see, e.g., E. Braaten and A. Nieto, Phys. Rev. B 56, 14 745 (1997)], leads to a greatly improved description of trapped Bose gases.

• Received 7 December 2000

DOI:https://doi.org/10.1103/PhysRevA.63.063601