Universal and non-universal effective $N$-body interactions for ultracold harmonically-trapped few-atom systems

Abstract

We derive the ground-state energy for a small number of ultracold atoms in an isotropic harmonic trap using effective quantum field theory (EFT). Atoms are assumed to interact through pairwise energy-independent and energy-dependent delta-function potentials with strengths proportional to the scattering length $a$ and effective range volume $V$, respectively. The calculations are performed systematically up to order $l^{-4}$, where $l$ denotes the harmonic oscillator length. The effective three-body interaction contains a logarithmic divergence in the cutoff energy, giving rise to a non-universal three-body interaction in the EFT. Our EFT results are confirmed by nonperturbative numerical calculations for a Hamiltonian with finite-range two-body Gaussian interactions. For this model Hamiltonian, we explicitly calculate the non-universal effective three-body contribution to the energy.

7 pages, 4 figures

References in corpus (5)

• Two-dimensional dynamics of expansion of a degenerate Bose gas
• 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})
• Occupation numbers of the harmonically trapped few-boson system

Cited by in corpus (1)

• Three-body repulsive forces among identical bosons in one dimension