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

Published

October 28, 2014

Author(s)

X. Y. Yin, D Blume, Philip Johnson, Eite Tiesinga

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.

Citation

New Journal of Physics

Volume

90

Pub Type

Journals

Download Paper

https://doi.org/10.1103/PhysRevA.90.043631

Local Download

Keywords

ultra-cold atoms, effective field theory, three-body interaction

Citation

Yin, X. , Blume, D. , Johnson, P. and Tiesinga, E. (2014), Universal and non-universal effective N-body interactions for ultracold harmonically-trapped few-atom systems, New Journal of Physics, [online], https://doi.org/10.1103/PhysRevA.90.043631, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=916321 (Accessed October 9, 2025)