Few-Boson Processes in the Presence of an Attractive Impurity under One-Dimensional Confinement

TL;DR

This paper investigates the behavior of a few-boson system with an impurity in one dimension, analyzing how mass imbalance and interaction ratios affect binding energies and scattering, with implications for experiments involving trapped fermions.

Contribution

It provides a detailed analysis of few-boson systems with an impurity, identifying conditions for scattering length divergences and inelastic processes based on mass and interaction ratios.

Findings

Calculated universal binding energies and scattering lengths as functions of mass and interaction ratios.

Identified parameter regions where scattering lengths vanish or diverge.

Relevance to experiments with trapped fermions and impurities in the Tonks-Girardeau limit.

Abstract

We consider a few-boson system confined to one dimension with a single distinguishable particle of lesser mass. All particle interactions are modeled with $\delta$-functions, but due to the mass imbalance the problem is nonintegrable. Universal few-body binding energies, atom-dimer and atom-trimer scattering lengths are all calculated in terms of two parameters, namely the mass ratio: $m_{\text{L}}/m_{\text{H}}$, and ratio $g_{\text{HH}}/g_{\text{HL}}$ of the $\delta$-function couplings. We specifically identify the values of these ratios for which the atom-dimer or atom-trimer scattering lengths vanish or diverge. We identify regions in this parameter space in which various few-body inelastic process become energetically allowed. In the Tonks-Girardeau limit ($g_{\text{HH}}\rightarrow \infty$), our results are relevant to experiments involving trapped fermions with an impurity atom.