Approaching universality in weakly-bound three-body systems

TL;DR

This paper investigates universal behaviors in weakly-bound three-body systems of identical bosons, revealing correlations between atom-dimer scattering length and three-body energy, and proposing a new measure of universality.

Contribution

It introduces a rescaling approach to identify universal trends and provides a quantitative measure of universality in three-body systems with short-range interactions.

Findings

Strong correlation between atom-dimer scattering length and three-body energy

Rescaling reveals universal trends near the unitary limit

Provides a new quantitative measure of universality

Abstract

Atom-dimer scattering below the three-body break-up threshold is studied for a system of three identical bosons. The atom-dimer scattering length and the energy of the most weakly-bound three-body state are shown to be strongly correlated. An appropriate rescaling of the observables reveals the subtlety of the correlation, and serves to identify universal trends in the unitary limit of divergent two-body scattering length. The correlation provides a new quantitative measure of the degree of universality in three-body systems with short-ranged interactions, as well as a consistency check of effective field theories and other theoretical models.