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

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...

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Bibliographic Details
Published in:arXiv.org 2015-08
Main Authors: Mehta, Nirav P, Morehead, Connor D
Format: Article
Language:English
Subjects:
Couplings
Dimers
Fermions
Impurities
Parameter identification
Particle interactions
Scattering
Trimers
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1508.00156