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 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

Phase Diagrams for Three-Body and Four-Body Systems in One Dimension

The phase diagrams for three-body and four-body systems with δ-function interactions are presented. The three-body and four body systems considered are the heavy-heavy-light (HHL) and heavy-heavy-heavy-light (HHHL) systems, respectively. The heavy particles are assumed to be identical. Both systems are treated within the Born-Oppenheimer approximation. The results from [16] are extended to arbitrary values of the heavy-heavy (HH) coupling. The phase diagram presented in [8] is reproduced, and the corresponding HHHL phase-diagram is presented. It was found that in both the three and four body systems the scattering lengths (atom-dimer for HHL and atom-trimer for HHHL) and spectra vary smoothly as the heavy-heavy interaction strength λ is varied from 0 to ∞