Universal bound states of one-dimensional bosons with two- and three-body attractions

TL;DR

This paper predicts universal three-body bound states in one-dimensional bosonic systems with weak two- and three-body attractions, revealing their energies depend on scattering lengths and highlighting conditions for excited state formation.

Contribution

It introduces the existence and universal properties of three-body bound states in 1D bosons with combined two- and three-body attractions, a novel theoretical insight.

Findings

Two three-body bound states exist with energies as universal functions of scattering lengths.

An infinitesimal three-body attraction induces an excited bound state only for three, 39, or more bosons.

Results are relevant for ultracold atom experiments in quasi-one-dimensional setups.

Abstract

When quantum particles are confined into lower dimensions, an effective three-body interaction inevitably arises and may cause significant consequences. Here we study bosons in one dimension with weak two-body and three-body interactions, predict the existence of two three-body bound states when both interactions are attractive, and determine their binding energies as universal functions of the two-body and three-body scattering lengths. We also show that an infinitesimal three-body attraction induces an excited bound state only for 3, 39, or more bosons. Our findings herein have direct relevance to a broad range of quasi-one-dimensional systems realized with ultracold atoms.