Few-body bound state stability of dipolar molecules in two dimensions

TL;DR

This paper rigorously proves the non-existence of bound three- and four-body states of dipolar molecules in two-dimensional multilayer setups with perpendicular dipole orientation, supported by numerical analysis.

Contribution

It provides a rigorous proof that three- and four-body bound states do not form under specific conditions and introduces a general technique applicable to other geometries and molecule counts.

Findings

Three- and four-body states are not bound with perpendicular dipoles.

Numerical calculations support the analytical proof for fermionic and bosonic molecules.

Reduction in intralayer repulsion can enable binding of larger complexes.

Abstract

Bound structures among dipolar molecules in multilayers are a topic of great interest in the light of recent experiments that have demonstrated the feasibility of the setup. While it is known that two molecules in two adjacent layers will always bind, larger complexes have only been scarcely addressed thus far. Here we prove rigorously that three- and four-body states will never be bound when the dipoles are oriented perpendicular to the layers. The technique employed is general and can be used for more molecules/layers and other geometries. Our analytical findings are supported by numerical calculations for both fermionic and bosonic molecules. Furthermore, we calculate the reduction in intralayer repulsion necessary to bind large complexes and estimate the influence of bound complexes in systems with many layers.