Quantum corrections to the ground-state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

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(0)a(3)less than or equal to 2x10(-3) [n(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=2-50 particles in the trap with positive s-wave scattering length a = 100-10 000 a.u. 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.