%0 Journal Article
%T Occupation numbers of the harmonically trapped few-boson system
%A K. M. Daily
%A X. Y. Yin
%A D. Blume
%J Physics
%D 2012
%I arXiv
%R 10.1103/PhysRevA.85.053614
%X We consider a harmonically trapped dilute $N$-boson system described by a low-energy Hamiltonian with pairwise interactions. We determine the condensate fraction, defined in terms of the largest occupation number, of the weakly-interacting $N$-boson system ($N \ge 2$) by employing a perturbative treatment within the framework of second quantization. The one-body density matrix and the corresponding occupation numbers are compared with those obtained by solving the two-body problem with zero-range interactions exactly. Our expressions are also compared with high precision {\em{ab initio}} calculations for Bose gases with $N=2-4$ that interact through finite-range two-body model potentials. Non-universal corrections are identified to enter at subleading order, confirming that different low-energy Hamiltonians, constructed to yield the same energy, may yield different occupation numbers. Lastly, we consider the strongly-interacting three-boson system under spherically symmetric harmonic confinement and determine its occupation numbers as a function of the three-body "Efimov parameter".
%U http://arxiv.org/abs/1203.4586v2