Occupation numbers of the harmonically trapped few-boson system

摘要

We consider a harmonically trapped dilute N-boson system described by a low-energy Hamiltonian withnpairwise interactions. We determine the condensate fraction, defined in terms of the largest occupation number,nof the weakly interacting N-boson system (N u0002 2) by employing a perturbative treatment within the frameworknof second quantization. The one-body density matrix and the corresponding occupation numbers are comparednwith those obtained by solving the two-body problem with zero-range interactions exactly. Our expressions arenalso compared with high precision ab initio calculations for Bose gases with N = 2–4 that interact throughnfinite-range two-body model potentials. Nonuniversal corrections are identified to enter at subleading order,nconfirming that different low-energy Hamiltonians, constructed to yield the same energy, may yield differentnoccupation numbers. Lastly, we consider the strongly interacting three-boson system under spherically symmetricnharmonic confinement and determine its occupation numbers as a function of the three-body “Efimov parameter.”