Lellouch-L\"uscher relation for ultracold few-atom systems under confinement

TL;DR

This paper derives a relation connecting few-body scattering loss rates to trapped state energies, validated by simulations, aiding precise measurement of multi-body scattering in ultracold atom experiments.

Contribution

It introduces an analog of the Lellouch-L"uscher relation for ultracold few-atom systems, applicable across various interaction strengths and energies.

Findings

The LL relation applies broadly in ultracold few-body systems.

Simulations confirm the relation's validity for different energies and interactions.

Enables determination of scattering rates from trapped state measurements.

Abstract

We derive an analog of the Lellouch-L\"uscher (LL) relation for few-body bosonic systems, linking few-body scattering loss rates to the energies and widths of the corresponding harmonically trapped few-body states. Three-body numerical simulations show that the LL relation applies across a broad range of interaction strengths and energies and allows the determination of scattering rates within a single partial wave. Our work establishes a robust theoretical framework for understanding the role of the finite volume effect in few-body observables in optical lattice and tweezer experiments, enabling precise determination of multi-body scattering rates.