Occurrence conditions for two-dimensional Borromean systems

TL;DR

This paper investigates the conditions under which three-boson systems in two dimensions can form Borromean states, which are bound without any two-body bound states, highlighting the necessity of specific potential features.

Contribution

It identifies the potential conditions, especially the presence of a barrier outside an attractive pocket, necessary for Borromean states in two-dimensional systems.

Findings

Borromean states require potentials with both attractive and repulsive parts.

Extensive numerical searches found no Borromean states without an outside barrier.

Potential experimental setups for observing these states are proposed.

Abstract

We search for Borromean three-body systems of identical bosons in two dimensional geometry, i.e. we search for bound three-boson system without bound two-body subsystems. Unlike three spatial dimensions, in two-dimensional geometry the two- and three-body thresholds often coincide ruling out Borromean systems. We show that Borromean states can only appear for potentials with substantial attractive and repulsive parts. Borromean states are most easily found when a barrier is present outside an attractive pocket. Extensive numerical search did not reveal Borromean states for potentials without an outside barrier. We outline possible experimental setups to observe Borromean systems in two spatial dimensions.