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

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 ($g_{\text{HH}}\to \infty$), our results are relevant to experiments involving trapped fermions with an impurity atom.

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• Entanglement of an Impurity in a Few-Body One-Dimensional Ideal Bose System
• Three-body bound states of two bosons and one impurity in one dimension
• Ground-State Magnetization in Mixtures of a Few Ultra-Cold Fermions in One-Dimensional Traps