Occupation numbers of the harmonically trapped few-boson system

Abstract

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".

16 pages, 7 figures

References in corpus (7)

• The Equation of State of a Low-Temperature Fermi Gas with Tunable Interactions
• Bragg spectroscopy of a strongly interacting 85Rb Bose-Einstein condensate
• n-Boson Energies at Finite Volume and Three-Boson Interactions
• Three-boson problem at low energy and Implications for dilute Bose-Einstein condensates
• The Energy of n Identical Bosons in a Finite Volume at O(L^{-7})
• Single-Particle Momentum Distribution of an Efimov trimer
• Ground State Properties of Cold Bosonic Atoms At Large Scattering Lengths