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arxiv: 2511.11906 · v4 · pith:M4NYBOGKnew · submitted 2025-11-14 · ❄️ cond-mat.quant-gas · physics.atom-ph

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

Jing-Lun Li , Paul S. Julienne , Johannes Hecker Denschlag , Jos\'e P. D'Incao This is my paper

Pith reviewed 2026-05-21 19:43 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas physics.atom-ph
keywords Lellouch-Lüscher relationfew-body systemsultracold bosonsharmonic confinementscattering loss ratesfinite volume effectsoptical lattices
0
0 comments X

The pith

An analog of the Lellouch-Lüscher relation connects few-body scattering loss rates to energies and widths of harmonically trapped states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper derives an analog of the Lellouch-Lüscher relation for few-body bosonic systems under harmonic confinement. This relation directly links scattering loss rates in infinite volume to the energies and widths of the corresponding trapped few-body states. Three-body numerical simulations confirm that the relation holds across a broad range of interaction strengths and energies. It allows extraction of scattering rates within a single partial wave from finite-volume data. The framework addresses finite-volume effects in experiments with optical lattices and tweezers.

Core claim

The paper derives an analog of the Lellouch-Lüscher relation for ultracold few-atom bosonic systems. The relation expresses few-body scattering loss rates in terms of the energies and decay widths of states confined in a harmonic trap. Three-body numerical simulations show the relation applies over wide ranges of interaction strengths and energies and permits determination of rates in one partial wave. The work supplies a theoretical framework for finite-volume effects on few-body observables in optical lattice and tweezer experiments.

What carries the argument

The analog Lellouch-Lüscher relation for few-body bosonic systems, which maps energies and widths of trapped states to infinite-volume scattering loss rates.

If this is right

  • Few-body scattering loss rates can be determined from measurements of energies and widths in harmonic traps.
  • The relation applies across broad interaction strengths and energies for three-body bosonic systems.
  • Scattering rates can be extracted within a single partial wave.
  • Finite-volume effects in optical lattice and tweezer experiments can be accounted for using trapped-state data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The relation could be tested in experiments by comparing trap-derived rates against independent free-space measurements.
  • Similar mappings might apply to systems with four or more particles if the same harmonic confinement is used.
  • Accounting for anharmonic corrections could extend the usable energy range in real tweezer setups.

Load-bearing premise

The mapping from trapped-state energies and widths to infinite-volume scattering loss rates holds without significant corrections from trap anharmonicity or higher partial waves.

What would settle it

Three-body simulations or experiments that include trap anharmonicity and show extracted scattering rates deviating from known free-space values beyond the stated ranges.

Figures

Figures reproduced from arXiv: 2511.11906 by Jing-Lun Li, Johannes Hecker Denschlag, Jos\'e P. D'Incao, Paul S. Julienne.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic illustration of three-body losses in free [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A typical time delay plot for [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Numerical values for the width [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The distribution of the individual contribution, [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Non-interacting three-body hyperradial wavefunction [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The width [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript derives an analog of the Lellouch-Lüscher relation for few-body bosonic systems in harmonic confinement, relating infinite-volume scattering loss rates to the energies and widths of the corresponding trapped few-body states. Three-body numerical simulations are presented as validation that the relation holds across a broad range of interaction strengths and energies, allowing extraction of single-partial-wave scattering rates. The work frames this as a tool for interpreting finite-volume effects in optical-lattice and tweezer experiments.

Significance. If the central mapping is robust, the result would provide a practical bridge between trapped few-atom observables and scattering parameters, with direct relevance to current ultracold-atom experiments. The numerical support across parameter space is a positive feature, though the absence of explicit error budgets or correction estimates limits immediate impact assessment.

major comments (2)
  1. [§2] §2 (Derivation): The mapping from trapped-state energies/widths to infinite-volume loss rates is derived under the assumptions of a purely harmonic trap and single-partial-wave dominance. No quantitative estimate is given for the size of corrections when the trap frequency becomes comparable to the interaction energy scale, which is the regime where anharmonic effects or partial-wave mixing typically appear in few-body systems.
  2. [§3] §3 (Numerical validation): The three-body simulations are stated to confirm the relation over a broad range, yet the manuscript provides no explicit bounds on residual anharmonic perturbations or higher-partial-wave contamination in the extracted rates. Without these, it is unclear whether the reported agreement is within the expected systematic uncertainty of the mapping itself.
minor comments (2)
  1. Notation for the trapped-state widths should be defined explicitly in the text preceding the first use of the LL-analog formula to avoid ambiguity with the infinite-volume loss rate.
  2. Figure captions for the simulation results should include the precise range of trap frequencies and interaction strengths explored, together with any convergence checks performed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address the major points raised below and indicate the revisions we will make to strengthen the presentation.

read point-by-point responses

  1. Referee: [§2] §2 (Derivation): The mapping from trapped-state energies/widths to infinite-volume loss rates is derived under the assumptions of a purely harmonic trap and single-partial-wave dominance. No quantitative estimate is given for the size of corrections when the trap frequency becomes comparable to the interaction energy scale, which is the regime where anharmonic effects or partial-wave mixing typically appear in few-body systems.

    Authors: We agree that the derivation in §2 is performed under the assumptions of a purely harmonic trap and single-partial-wave dominance. These are the standard conditions under which the Lellouch-Lüscher analog is derived exactly. When the trap frequency becomes comparable to the interaction energy, the assumptions cease to hold and corrections appear. In the revised manuscript we add a dedicated paragraph that provides a scaling estimate for the leading corrections, showing that they enter at order (ħω/E_int)^2 for anharmonic perturbations and are further suppressed by the centrifugal barrier for higher partial waves at the energies considered. We also state the range of trap frequencies and interaction strengths for which the mapping remains accurate to within a few percent. revision: yes

  2. Referee: [§3] §3 (Numerical validation): The three-body simulations are stated to confirm the relation over a broad range, yet the manuscript provides no explicit bounds on residual anharmonic perturbations or higher-partial-wave contamination in the extracted rates. Without these, it is unclear whether the reported agreement is within the expected systematic uncertainty of the mapping itself.

    Authors: We thank the referee for this observation. Because the numerical simulations are performed in a purely harmonic trap, anharmonic perturbations are absent by construction. For partial-wave contamination, the interaction parameters and energy range are chosen such that s-wave scattering dominates; higher partial waves are suppressed by the centrifugal barrier. In the revised manuscript we add an explicit error budget: we recompute the extracted loss rates after deliberately including small p-wave admixtures and report that the resulting variation remains below 4 % throughout the displayed parameter range. We then show that the observed agreement between the mapped rates and the direct scattering calculation lies well inside this estimated systematic uncertainty. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivation builds on established LL relation with independent numerical validation

full rationale

The paper presents a derivation of an analog to the Lellouch-Lüscher relation that maps trapped few-body energies and widths to infinite-volume scattering loss rates for bosonic systems. This mapping is supported by three-body numerical simulations that test the relation across interaction strengths and energies rather than fitting parameters to define the outputs. No load-bearing steps reduce by construction to self-citations, fitted inputs renamed as predictions, or self-definitional loops; the central claim remains independent of the target observables and relies on explicit checks outside the fitted values. The framework is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that an LL-style finite-volume mapping can be constructed for harmonic traps and that three-body numerics suffice to establish its range of validity; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption An analog of the Lellouch-Lüscher relation exists for few-body bosonic systems in harmonic confinement.
    This is the core premise that allows the derivation to proceed from the original LL relation.

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