Zero temperature correlations in trapped Bose-Einstein condensates

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We introduce a family of correlated trial wave functions for the N-particle ground state of an interacting Bose gas in a harmonic trap. For large N, the correlations lead to a relative energy decrease of a fraction 3/5N, compared to mean field Gross-Pitaevskii theory. The kinetic energy in the weakly confining direction turns out to be most sensitive to our correlations and, remarkably, is higher by as much as a few per cent for condensates with atom numbers of a few thousand. Thus, the predicted deviations from Gross-Pitaevskii theory originating from ground state correlations might be observed in momentum distribution measurements of small condensates.