Born-Oppenheimer study of two-component few-particle systems under one-dimensional confinement

TL;DR

This paper uses the Born-Oppenheimer approximation to analyze the energy spectrum and scattering lengths of few-atom systems confined in one dimension, considering various mass ratios and quantum statistics.

Contribution

It introduces a systematic study of three- and four-body ultracold atom systems under one-dimensional confinement using the Born-Oppenheimer approach, including different particle statistics.

Findings

Energy spectra and scattering lengths depend on mass ratios.

Both fermionic and bosonic heavy atoms are analyzed.

Zero-range interactions are modeled for different atom pairs.

Abstract

The energy spectrum, atom-dimer scattering length, and atom-trimer scattering length for systems of three and four ultracold atoms with $\delta$-function interactions in one dimension are presented as a function of the relative mass ratio of the interacting atoms. The Born-Oppenheimer approach is used to treat three-body ("HHL") systems of one light and two heavy atoms, as well as four-body ("HHHL") systems of one light and three heavy atoms. Zero-range interactions of arbitrary strength are assumed between different atoms, but the heavy atoms are assumed to be noninteracting among themselves. Both fermionic and bosonic heavy atoms are considered.