Interacting bosons in a nearly-resonant potential well

TL;DR

This paper explores how a nearly-resonant trapping potential significantly enhances the binding of weakly-interacting bosons, revealing divergent behaviors near the single-particle bound-state threshold and collective bound states for attractive interactions.

Contribution

It demonstrates the dramatic effects of near-threshold potentials on boson binding, including divergence phenomena and collective state formation, which are novel insights in quantum trapping.

Findings

Bound bosons diverge near the single-particle threshold for super-threshold traps.

A collective bound state forms for large boson numbers with attractive interactions.

Weak interactions can lead to bound states due to near-resonant trapping potentials.

Abstract

We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for repulsive particles and a super-threshold trapping potential the equilibrium number of bound bosons and the size of the ground state diverge upon approaching the single-particle threshold from above. For attractive interactions and a sub-threshold trap a collective bound state always forms for a sufficiently large number of bosons despite the inability of interparticle attraction alone to form a two-body bound state.