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Lellouch-Lüscher Relation for Ultracold Few-Atom Systems under Confinement

Jing-Lun Li1,2,*, Paul S. Julienne3, Johannes Hecker Denschlag1, and José P. D’Incao4,†

  • *Contact author: Jinglun.Li@ist.ac.at
  • †Contact author: Jose.DIncao@umb.edu
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Phys. Rev. Lett. 136, 203401 – Published 19 May, 2026

DOI: https://doi.org/10.1103/pzlp-7k8d

Abstract

We derive an analog of the Lellouch-Lüscher (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 Letter 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 multibody scattering rates.

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Phys. Rev. Lett. 136, 203401– Published 19 May, 2026
  • Received 14 November 2025
  • Accepted 21 April 2026
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