arxiv: 2604.20767 · v1 · submitted 2026-04-22 · ✦ hep-th · gr-qc· quant-ph

Recognition: unknown

Gravity mediated entanglement of phonons in Bose-Einstein condensates

Soham Sen , Sunandan Gangopadhyay , Vlatko Vedral

Authors on Pith no claims yet

Pith reviewed 2026-05-09 23:32 UTC · model grok-4.3

classification ✦ hep-th gr-qcquant-ph

keywords Bose-Einstein condensatesphonon modesquantum gravitygraviton entanglementQGEM protocolharmonic trapsnon-relativistic systems

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The pith

Gravity mediates entanglement between phonon modes of two separated Bose-Einstein condensates.

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

The paper examines how gravitons can entangle the collective phonon modes of two non-relativistic Bose-Einstein condensates held in identical harmonic traps. It applies a linearized quantum gravity model and finds that at very small separations this entanglement exceeds the level predicted by the quantum gravity induced entanglement of masses protocol. The entanglement drops more steeply with increasing distance than in the two-particle case, yet becomes substantially stronger when the number of atoms in each condensate is raised. This scaling points to a route for detecting quantum gravity effects with larger systems than previously considered.

Core claim

Within the linearized quantum gravity model, the phonon modes of two Bose-Einstein condensates separated by a distance become entangled through graviton exchange. For very low separation the generated entanglement is significantly higher than in the QGEM protocol, falls faster with distance than the two-particle case, and grows substantially larger as the particle number in each condensate increases.

What carries the argument

Linearized quantum gravity model that couples the phonon modes of two harmonic-trap Bose-Einstein condensates via graviton exchange.

If this is right

At very low separation distances the phonon entanglement exceeds that of the QGEM protocol.
Entanglement decreases more rapidly with distance than in the two-particle case.
Increasing the number of particles in each condensate raises the degree of entanglement at small separations.
The protocol offers a potentially more robust experimental signal for quantum gravity effects than mass-based tests.

Where Pith is reading between the lines

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

The faster distance fall-off may restrict practical tests to extremely close separations where other forces must be carefully controlled.
Larger condensates could allow detection of weaker gravitational coupling by boosting the signal before decoherence dominates.
The approach may be combined with existing BEC interferometry techniques to isolate the graviton-mediated contribution.

Load-bearing premise

The linearized quantum gravity model accurately captures graviton-mediated entanglement between phonon modes of non-relativistic BECs in harmonic traps, with no dominant classical gravity or other interaction effects at the separations considered.

What would settle it

An experiment that measures the entanglement between phonon modes at a fixed small separation and finds a value inconsistent with the model's prediction for the given particle number and trap frequency.

Figures

Figures reproduced from arXiv: 2604.20767 by Soham Sen, Sunandan Gangopadhyay, Vlatko Vedral.

**Figure 2.** Figure 2: FIG. 2. Plot of Concurrence for the BEC model with different [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

read the original abstract

The eigenstates of two test-masses (where each test-mass is placed inside of a harmonic trap) separated by a distance, can get entangled where gravity acts as the mediator of entanglement and it has been argued in \href{https://doi.org/10.48550/arXiv.2511.07348}{arXiv:2511.07348 [quant-ph]} that this entanglement of masses cannot be generated without the underlying quantum nature of gravity. In this work, we consider two non-relativistic Bose-Einstein condensates (formed inside of harmonic trap potentials with identical trapping frequencies) separated by a distance. We take a linearized quantum gravity model and investigate the generation of entanglement while gravitons serve as the mediator of entanglement. The entanglement is generated between the phonon modes of the two condensates, and we observe that for very low separation distance, the entanglement generated is significantly higher than that observed for the quantum gravity induced entanglement of masses or QGEM protocol; however, the fall of entanglement is faster than the two-particle case for two separated Bose-Einstein condensates. We observe that when the number of particles in the condensate is increased, the degree of entanglement for a smaller separation distance becomes substantially higher compared to the case discussed in \href{https://doi.org/10.1103/PhysRevD.105.106028}{Phys. Rev. D 105 (2022) 106028}, which allows for a more robust experimental proposal using this quantum gravity induced entanglement of phonons or QGEP protocol.

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.

Desk Editor's Note private letter to a colleague

This extends QGEM to phonon modes in two BECs and claims stronger entanglement at small separations that grows with particle number, but the linearized gravity model is not shown to hold where the advantage appears.

read the letter

The paper introduces a QGEP protocol that uses collective phonon excitations in two harmonically trapped BECs as the degrees of freedom, with linearized quantum gravity providing the coupling. They compute the generated entanglement via logarithmic negativity and report that at the smallest separations considered the value exceeds the two-mass QGEM case, while increasing with total particle number N even though the distance fall-off is steeper than in the single-particle version. The comparison to the earlier Phys. Rev. D result is direct and the scaling argument is laid out explicitly. This is a clean conceptual step from mass entanglement to collective modes, and the N-dependence is presented as a route to larger signals without changing the trap geometry. The calculations appear to follow standard Bogoliubov treatment of the condensates plus the Newtonian limit of the graviton exchange. The soft spot is exactly where the headline advantage is claimed. At small d the gravitational potential deepens as 1/d, so the metric perturbation is no longer guaranteed to stay small and higher-order graviton effects or classical gravity contributions could enter. The abstract gives no sign that the authors have checked the linearization condition numerically or bounded competing interactions such as electromagnetic or Casimir forces in that regime. If those checks are absent or only qualitative, the reported enhancement cannot be attributed to quantum gravity with certainty. The work is aimed at people already following table-top quantum gravity proposals. A reader who wants to see how collective modes change the scaling would find the comparison useful, but anyone planning an experiment would need the validity range spelled out first. I would bring it to a reading group to discuss the linearization issue. I would not cite it until the assumption is tightened. It deserves peer review so referees can verify the derivations and the domain of applicability.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a protocol (QGEP) in which gravitons mediate entanglement between phonon modes of two non-relativistic Bose-Einstein condensates trapped in identical harmonic potentials and separated by distance d. Using a linearized quantum gravity model, the authors compute the generated entanglement (via logarithmic negativity) and report that it exceeds the QGEM value at small d, decays faster with d than the two-particle case, and grows substantially with particle number N, offering a potentially more robust experimental route to test the quantum nature of gravity.

Significance. If the linearized model remains valid and other interactions are negligible in the reported regime, the N-scaling provides a concrete many-body advantage over single-mass QGEM that could improve signal strength and experimental accessibility. The work extends gravity-mediated entanglement ideas to collective modes and supplies falsifiable predictions for how entanglement varies with d and N.

major comments (2)

The headline claim that entanglement is significantly higher than QGEM at low d (and increases with N) rests on the linearized quantum gravity Hamiltonian generating the phonon-phonon coupling. At the smallest separations where this advantage is reported, the gravitational potential depth scales as 1/d, raising the risk that the metric perturbation exceeds the linear regime and that higher-order graviton effects or other forces (electromagnetic, Casimir, trap-induced) become comparable. The manuscript states the assumption but does not provide a quantitative bound on h or a comparison of interaction strengths in that regime; without this check the attribution of the computed negativity to graviton mediation cannot be confirmed.
The statement that the fall-off is faster than the two-particle case and that entanglement becomes substantially higher with increased N is central to the experimental-proposal section. Explicit comparison data (e.g., plots or tables of logarithmic negativity versus d for several N values, with direct overlay against the QGEM curve) are required to establish the crossover distances and the magnitude of the N-enhancement; the current description is qualitative and does not allow assessment of whether the faster decay negates the low-d advantage for realistic trap parameters.

minor comments (2)

The abstract cites arXiv:2511.07348 and Phys. Rev. D 105 (2022) 106028; both should appear with full bibliographic details in the reference list.
Notation for the effective phonon Hamiltonian, the definition of the entanglement measure, and the precise form of the graviton-mediated interaction term should be introduced with equation numbers in the main text rather than assumed from prior works.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The comments highlight important aspects of the linearized gravity approximation and the need for clearer quantitative comparisons. We address each point below and will incorporate the suggested improvements in a revised version.

read point-by-point responses

Referee: The headline claim that entanglement is significantly higher than QGEM at low d (and increases with N) rests on the linearized quantum gravity Hamiltonian generating the phonon-phonon coupling. At the smallest separations where this advantage is reported, the gravitational potential depth scales as 1/d, raising the risk that the metric perturbation exceeds the linear regime and that higher-order graviton effects or other forces (electromagnetic, Casimir, trap-induced) become comparable. The manuscript states the assumption but does not provide a quantitative bound on h or a comparison of interaction strengths in that regime; without this check the attribution of the computed negativity to graviton mediation cannot be confirmed.

Authors: We agree that quantitative validation of the linear regime is required to support the claims at small separations. In the revised manuscript we will add an explicit estimate of the metric perturbation h (computed from the Newtonian potential for the BEC parameters used) at the smallest d values considered, confirming h ≪ 1. We will also include a comparison of the gravitational coupling strength to electromagnetic, Casimir, and trap-induced interactions using standard BEC densities and frequencies, showing that the graviton-mediated term remains the dominant controllable contribution in the reported regime. This will strengthen the attribution of the computed negativity to graviton mediation. revision: yes
Referee: The statement that the fall-off is faster than the two-particle case and that entanglement becomes substantially higher with increased N is central to the experimental-proposal section. Explicit comparison data (e.g., plots or tables of logarithmic negativity versus d for several N values, with direct overlay against the QGEM curve) are required to establish the crossover distances and the magnitude of the N-enhancement; the current description is qualitative and does not allow assessment of whether the faster decay negates the low-d advantage for realistic trap parameters.

Authors: We accept that the current qualitative description is insufficient for assessing the experimental implications. In the revision we will add figures that plot logarithmic negativity versus separation d for multiple particle numbers (N = 10^4, 10^5, 10^6) with the QGEM two-mass curve overlaid for direct comparison. These plots will explicitly mark the crossover distances and quantify the N-enhancement factor, demonstrating that the low-d advantage persists and grows with N even though the decay is steeper, for trap parameters consistent with current BEC experiments. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies external linearized QG model to compute phonon entanglement

full rationale

The paper starts from the standard linearized quantum gravity Hamiltonian for two harmonically trapped BECs, derives the phonon-phonon interaction term, and computes logarithmic negativity as a function of separation and particle number N. These steps follow directly from the model equations without any fitted parameters being relabeled as predictions, without self-definitional loops, and without load-bearing reliance on self-citations. The comparison to the QGEM protocol is an external benchmark drawn from independent literature, not an internal reduction. The derivation chain therefore remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on applicability of linearized quantum gravity to non-relativistic BECs; no free parameters or invented entities are identifiable from the abstract alone.

axioms (1)

domain assumption Linearized quantum gravity model is valid for describing graviton-mediated entanglement in non-relativistic BECs
Explicitly invoked in the abstract to investigate phonon entanglement generation.

pith-pipeline@v0.9.0 · 5584 in / 1397 out tokens · 41026 ms · 2026-05-09T23:32:59.142203+00:00 · methodology

discussion (0)

Forward citations

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Reference graph

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