Droplets of Bosons at a Narrow Resonance

TL;DR

This paper investigates the formation and stability of bosonic clusters and droplets near a narrow Feshbach resonance, revealing how their binding energies scale with particle number and interaction parameters.

Contribution

It introduces a theoretical framework for understanding bosonic self-bound states near a narrow resonance, highlighting the transition from clusters to droplets as particle number increases.

Findings

Clusters with energy per particle scale as N^2 for small N.

Droplets form with constant energy per particle for large N.

Stability depends on detuning from the resonance.

Abstract

We consider bosons interacting through a narrow $s$-wave resonance. Such a resonance is characterized by an infinite scattering length and a large and negative effective range $r_0$. We argue that any number $N\ge3$ of bosons can form a self-bound cluster with the binding energy per particle increasing as $N^2$ for $1\ll N\ll (-r_0/a_\text{bg})^{1/2}$, where $a_\text{bg}$ is the background scattering length (between atoms and molecules). In the opposite limit $N\gg (-r_0/a_\text{bg})^{1/2}$, bosons form droplets with binding energy per particle saturating to a constant value independent of the particle number. The stability of clusters and droplets when the interaction is detuned from the resonance is also studied.