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

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Cited by in corpus (11)

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• On a scale-invariant Fermi gas in a time-dependent harmonic potential
• Trapped unitary two-component Fermi gases with up to ten particles
• Harmonically trapped two-atom systems: Interplay of short-range s-wave interaction and spin-orbit coupling
• Harmonically trapped Fermi gas: Temperature dependence of the Tan contact
• Weakly nonadditive Polychronakos statistics
• Temperature-dependence of small harmonically trapped atom systems with Bose, Fermi and Boltzmann statistics
• Universal and non-universal effective $N$-body interactions for ultracold harmonically-trapped few-atom systems
• Two-body quench dynamics of harmonically trapped interacting particles
• Energy spectra of two interacting fermions with spin-orbit coupling in a harmonic trap
• Fermionic properties of two interacting bosons in a two-dimensional harmonic trap