Lellouch-Lüscher relation for ultracold few-atom systems under confinement

2025/11/14 by Li, Jing-Lun, Julienne, Paul S., Denschlag, Johannes Hecker +1
#Atomic Physics (physics.atom-ph) #FOS: Physical sciences #Quantum Gases (cond-mat.quant-gas)

paper · doi:10.48550/arxiv.2511.11906

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 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.

Citations

• Spin structure of diatomic van der Waals molecules of alkali atoms
• Spin hierarchy in van der Waals molecule formation via ultracold three-body recombination
• Lüscher equation with long-range forces
• Erasure-cooling, control, and hyper-entanglement of motion in optical tweezers
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• A Short Note on The Volume of Hypersphere

Related

• d-dimensional Lüscher's formula and the near-threshold three-body states in a finite volume
• Few-body physics
• Universal relations for dilute systems with two-body decays in reduced dimensions
• Bosonic drops with two- and three-body interactions close to the unitary limit
• On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD