A Spin-Based Pathway to Testing the Quantum Nature of Gravity

Aaron Markowitz; Adrian Kent; Andrew A. Geraci; Anupam Mazumdar; A. T. M. Anishur Rahman; Chiara Marletto; Cyril Laplane; Dami\'an Pital\'ua-Garc\'ia; David C. Moore; David Groswasser

REVIEW 3 major objections 3 minor 2 cited by

A Spin-Based Pathway to Testing the Quantum Nature of Gravity

T0 review · 3 major / 3 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read This paper claims that gravitationally induced entanglement between two spin-split nanodiamonds can provide a tabletop test of whether gravity is quantum, and lays out the experimental roadmap and challenges to reach it.

desk verdict A candid consortium white paper: no new physics, but a genuinely useful and honest roadmap whose central bottleneck—suppressing EM dipole interactions by six orders of magnitude—is clearly acknowledged and unresolved. read the letter →

arxiv 2509.01586 v1 pith:TT24T37R submitted 2025-09-01 quant-ph gr-qcphysics.ins-det

Sougato Bose , Anupam Mazumdar , Roger Penrose , Ivette Fuentes , Marko Toroš , Ron Folman , Gerard J. Milburn , Myungshik Kim

show 47 more authors

Adrian Kent A. T. M. Anishur Rahman Cyril Laplane Aaron Markowitz Debarshi Das Ethan Campos-Méndez Eva Kilian David Groswasser Menachem Givon Or Dobkowski Peter Skakunenko Maria Muretova Yonathan Japha Naor Levi Omer Feldman Damián Pitalúa-García Jonathan M.H. Gosling Ka-Di Zhu Marco Genovese Kia Romero-Hojjati Ryan J. Marshman Markus Rademacher Martine Schut Melanie Bautista-Cruz Qian Xiang Stuart M. Graham James E. March William J. Fairbairn Karishma S. Gokani Joseph Aziz Richard Howl Run Zhou Ryan Rizaldy Thiago Guerreiro Tian Zhou Jason Twamley Chiara Marletto Vlatko Vedral Jonathan Oppenheim Mauro Paternostro Hendrik Ulbricht Peter F. Barker Thomas P. Purdy M. V. Gurudev Dutt Andrew A. Geraci David C. Moore Gavin W. Morley

This is my paper · ORCID

classification quant-phgr-qcphysics.ins-det

keywords QGEMgravitationalentanglementquantumgravityStern-Gerlachinterferometrynitrogen-vacancycentresnanodiamondmacroscopicsuperpositionmatter-wave

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that a tabletop experiment can settle whether gravity itself is quantum: place two micron-sized diamonds in spatial superpositions, let them interact only through gravity, and check whether they become entangled. Because classical mediators, local classical channels, and stochastic semiclassical gravity cannot produce entanglement between two initially independent systems, observing gravitationally generated entanglement would be direct evidence that the gravitational field acts as a quantum channel. The proposed route uses an embedded nitrogen-vacancy spin in each diamond and Stern-Gerlach forces to create the superpositions; the spins are then read out as an entanglement witness. The authors review the technical path, centered on one hard requirement: electromagnetic forces, especially electric dipole interactions, must be suppressed by a factor well over a million relative to gravity. The paper does not claim the experiment is complete, but it claims the components and physics are understood well enough to justify a coordinated building program with defined milestones.

What carries the argument

The carrying mechanism is the gravitational phase shift: when each diamond is in a superposition of two positions, the Newtonian interaction energy between the pair takes different values for the four possible separation configurations, imprinting a configuration-dependent phase onto the joint state and entangling the two diamonds' paths. The spin of the nitrogen-vacancy centre is the handle that prepares and reads out this state: an inhomogeneous magnetic field creates the spatial split, microwave spin flips recombine the paths, and a final spin measurement realizes a Bell-type entanglement witness. The paper's quantitative target is the ratio U_dipole/U_gravity ≈ 3 × 10^6 from Eq. (1), wit

What would settle it

Characterize the permanent electric dipole moment of a QGEM-grade 1-micron diamond after neutralization, annealing, hydrogen passivation, rotational averaging, and any proposed shielding; plug the measured value into the paper's Eq. (1) at the intended mass, superposition size, and separation. If the residual dipole-dipole energy is not at least a factor of 10^6 below the gravitational energy, the gravity-dominated regime the protocol requires does not exist. The direct experimental falsifier is the full two-interferometer run: no entanglement witness after the Stern-Gerlach sequence, with ele

Watch

Extended reading notes

Core claim

The central claim is that the QGEM protocol—two diamonds, each placed in a spatial superposition by a spin-based Stern-Gerlach sequence and then allowed to interact only through their mutual Newtonian gravity—can produce a measurable entanglement witness that distinguishes quantum gravity from classical or semiclassical alternatives. The paper's logic is that two unentangled quantum systems cannot become entangled through local operations and classical communication alone, so a classical gravitational mediator cannot entangle the diamonds. A positive witness would therefore be the first empirical demonstration that gravity, and hence spacetime, has quantum degrees of freedom, even in the low

Load-bearing premise

The entire protocol rests on being able to suppress the electromagnetic interaction between the two diamonds—chiefly electric dipole forces—by more than a factor of about a million below their mutual gravity, a level no current experiment has demonstrated.

Editorial extensions

If this is right

If gravity is quantum, a positive entanglement witness in this geometry provides the first laboratory evidence that spacetime itself has quantum degrees of freedom, at energies where general relativity reduces to the Newtonian potential.
A positive result would rule out any theory in which gravity is a classical mediator and quantum systems interact only through local or screened classical channels, including stochastic semiclassical models.
A null result, with all electromagnetic and environmental backgrounds accounted for, would support classical or collapse-modified gravity and constrain the common prediction of many quantum-gravity approaches.
The pathfinder experiments—small Stern-Gerlach superpositions of nanodiamonds—already test macroscopic-superposition bounds from collapse models, independently of the full QGEM goal.
The same apparatus, before gravity-level sensitivity is reached, enables force sensing at femto- to zeptonewton scales, useful for Casimir studies and searches for fifth forces and dark matter.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural control experiment would be to run the identical two-interferometer protocol at separations or masses where gravitational coupling is negligible, so only electromagnetic interactions remain; observing an entanglement witness there would calibrate the apparatus and show the witness is not an artifact.
The central assumption can be tested before the full QGEM experiment: measure the electric dipole moments of the actual high-purity 1-micron diamonds after neutralization, annealing, and surface passivation; if these moments cannot be reduced enough, no other part of the protocol matters.
The paper leaves implicit that the same geometry can be recycled as a low-energy probe of gravitational decoherence: measuring the entanglement witness as a function of separation d would map the rate at which gravity-induced noise, if any, destroys the superposition.
If successful, the protocol would establish the low-energy quantum-coherence property of gravity but would not determine how geometry is quantized at the Planck scale, leaving that question for other experiments and theory.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: this is a white paper, not a research preprint. There is no new protocol, measurement, or derivation; the QGEM idea is Refs [1-4] and the Stern-Gerlach path is Refs [49,115]. What this paper actually does is consolidate a large community's plan, and it does that well. The write-up is clear about what has been demonstrated, what is speculative, and what the milestones are. Give credit: it explicitly lists challenges C1-C5, and it doesn't oversell. The discussion of electric dipole backgrounds in Sec 5.1 is the most useful part—Eq. 1 gives a concrete ratio, and the paper states plainly that suppression by >1e6 is required and not yet demonstrated. It even flags that a conducting shield may fail because of image-dipole forces and patch potentials; that level of honesty is rare.

Soft spots: the whole program hinges on that dipole suppression, and there is no experimental demonstration that it can be done. The paper offers five mitigation ideas, but none is quantified beyond scaling arguments. Also, the requirements—~1s coherence, ~100um superpositions, two adjacent interferometers—are far beyond what has been shown. None of this is hidden, and the paper frames it as a roadmap, so it's not a flaw in the presentation. But it means the central claim of 'viable pathway' is unproven. That's the nature of a white paper.

The citation pattern is heavy on self-citation, but the prior results are real and independently published; I don't see a circularity problem. No invented entities, no fitting.

Who is this for? Anyone working on levitated optomechanics, macroscopic superpositions, or quantum gravity phenomenology will get a useful overview of where the field stands. It's a good reading-group paper for a graduate seminar on this topic.

My recommendation: send it to peer review as a white paper/roadmap. It's not a research paper and shouldn't be judged as one, but it deserves a serious referee to check the feasibility estimates and the completeness of the risk discussion. I'd accept it with revisions that tighten the milestones and add quantitative targets for the five mitigations.

Referee Report

3 major / 3 minor

Summary. This white paper presents the QGEM (Quantum-Gravity-Induced Entanglement of Masses) protocol as a spin-based pathway to testing whether gravity is quantum. The proposed experiment uses two micron-sized diamonds, each containing a single NV center, prepared in spatial superposition via Stern-Gerlach interferometry. The gravitational interaction between the two superposed masses is expected to generate entanglement that can be witnessed through spin measurements. The paper reviews the scientific context, lists five technical challenges (C1-C5), discusses mitigation strategies for electromagnetic backgrounds—particularly electric dipole-dipole interactions (Eq. 1)—and outlines a timeline for pathfinder experiments. The central claim is that observing such entanglement would provide a key fundamental test of the quantum nature of gravity, assuming gravity is not an action at a distance.

Significance. If the experimental pathway proves viable, this would constitute a landmark low-energy test of quantum gravity, with implications for fundamental physics. The paper is a roadmap/white paper that consolidates proposals from the authors' community and connects them to concrete experimental milestones. Strengths include the explicit enumeration of open challenges (C1-C5), quantitative estimates such as Eq. (1), and the clear falsifiability of the central prediction: gravity must generate entanglement if it is quantum. The authors also candidly list limitations, including the unsolved EM suppression problem. However, the paper provides no new experimental demonstration and its feasibility claims rest on previously published work.

major comments (3)

[§5.1, Eq. (1)] The central feasibility claim depends on suppressing the dipole-dipole interaction by a factor ≫ 10^6 relative to gravity. The paper itself states this is required, but none of the five proposed mitigations (distance, averaging, annealing, shielding, materials) is quantified for the nominal parameters. The shielding option is explicitly acknowledged to introduce image-dipole forces of similar order and patch-potential decoherence. Since the gravitational phase is small and requires ~1 s coherence, the lack of a quantitative analysis means the pathway's viability is not yet established. This is an open challenge (C4), but it is load-bearing for the central claim rather than a peripheral technical detail.
[§3, C3 and §5.3] The requirement of coherence times ~1 s for both spin and matter wave is stated, with the longest nanodiamond spin coherence cited as 780 µs at room temperature (Ref. [41]). The paper extrapolates to >1 s via cryogenic cooling and high-purity fabrication, citing Ref. [141] for NV coherence in bulk diamond. However, the transfer of these coherence properties to a levitated microdiamond with 10,000 surface dangling-bond spins is not demonstrated; the proposed prepolarization in a 10 T field (Ref. [107]) is not quantitatively integrated into the error budget. This is a major gap between current demonstrations and the required conditions.
[§5.1, shielding paragraph] The manuscript notes that even a perfectly ideal conductive shield creates an image-dipole force 'of a similar order of magnitude to the dipole-dipole interaction' and that motional dynamic decoupling could 'partially overcome' the resulting decoherence. This is a direct admission that the primary suggested mitigation for C4 is not viable on its own. Since the paper's roadmap explicitly lists shielding as one of only five methods, and the other four are equally unquantified, the paper does not yet provide a convincing path to satisfying the ≫10^6 suppression required by Eq. (1).

minor comments (3)

[§2, 'superpositon' typo] The text contains a typo: 'superpositon' appears in the sentence describing two spatial quantum superpositions. Proofreading is needed.
[§5.2, 'perpendcular' typo] The text contains a typo: 'perpendcular' should be 'perpendicular'. Minor proofreading issue.
[§5.1, Eq. (1) scaling] Eq. (1) displays scaling with (10 pg/m)^2 and (100 µm/d)^2, but the text states a d^-3 dependence for the dipole-dipole interaction and d^-1 for gravity. The ratio should scale as d^-2, consistent with the displayed formula; however, the text immediately preceding the equation does not explicitly derive the d^-2 dependence, which may confuse readers. Clarify the derivation.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the paper is a roadmap/white paper that reviews externally published QGEM derivations; no prediction reduces to a fit or to the paper's own construction.

full rationale

The paper's central claim is that two micron-sized diamonds in spin-dependent Stern-Gerlach superpositions can become entangled through gravity, and that this would witness quantum gravity. This claim is not derived from parameters fitted in this paper; it is imported from prior peer-reviewed work (e.g., Refs [1, 32, 33, 49, 115]). The one quantitative estimate, Eq. (1), is a background budget: U_dipole/U_gravity ≈ 3e6 for nominal parameters, and the paper explicitly labels the needed suppression as a requirement ('we expect to need to reduce this interaction by a factor ≫ 10^6'), not as a prediction of the protocol. The no-entanglement theorem for classical gravity is cited to Ref [44], an independent peer-reviewed result co-authored by one of the present authors, but it is not a restatement of the paper's definitions or a fitted parameter. The paper is candid about the open challenges (C1-C5) and specifically admits in Section 5.1 that a perfectly conducting shield would produce image-dipole forces comparable to the original dipole-dipole interaction, so shielding alone cannot be assumed to work. This honesty further weighs against circularity. Heavy self-citation occurs, but none of the citations is used as an unverified premise that forces the desired conclusion; the cited works are externally published and independently falsifiable. Therefore no step reduces by construction, and the score is low.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The roadmap rests on a few domain assumptions inherited from prior work (notably the LOCC-based argument that classical mediators cannot entangle, and the use of Newtonian potential at low energy) and several design parameters chosen by hand (dipole moment, superposition distance, separation, duration). No new entities are postulated and no data are fitted.

free parameters (5)

Electric dipole moment p = 10^-4 e cm
Assumed for ~10 pg particles, extrapolated from measurements of 10 um silica particles (Ref [120]); used in Eq. 1 to estimate dipole-dipole vs gravity ratio.
Target superposition distance Delta x = ~100 um
Design parameter chosen in Section 3 (C2) to make gravitational entanglement detectable.
Interferometer separation d = ~400 um
Design parameter from Section 3 (C4); depends on protocol and screening.
Interaction/coherence time tau = ~1 s
Design requirement from Section 3 (C3); matches expected cryogenic spin coherence times.
Surface dangling bond density = 0.01 spins/nm^2 (leading to >10,000 unpaired spins per nanodiamond)
Used to quantify spin-noise source; taken from Ref [105] and applied in Section 3.

assumptions (5)

domain assumption Newtonian gravitational potential is sufficient at low energies; GR corrections negligible
Stated in Section 2: 'even at low energies, when we are prone to the lowest order contribution in the gravitational potential, such as the Newtonian potential'.
domain assumption Classical mediators cannot generate entanglement between two initially unentangled quantum systems without local operations and classical communication
Invoked in Section 2 (Refs [43,44]) to claim that a classical gravity theory would not entangle the masses.
domain assumption Quantum gravity entails a quantum mediator that can generate entanglement
Section 2: 'If gravity can be in a quantum superposition, the two quantum systems will become entangled'.
domain assumption Spin coherence can be maintained through a Stern-Gerlach interferometer sequence with microwave pulses
Assumed in the protocol in Section 5.3, following Refs [39,115].
domain assumption The entanglement witness measured on spins after interferometry reliably reveals gravitational entanglement
Section 2 and C5; relies on the spins being good witnesses, as argued in prior papers.

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Cite this review

Pith. "Pith review of A Spin-Based Pathway to Testing the Quantum Nature of Gravity." pith.science (2026). https://pith.science/paper/TT24T37R

@misc{pith2026250901586,
  author       = {Pith},
  title        = {Pith review of: A Spin-Based Pathway to Testing the Quantum Nature of Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TT24T37R}},
  note         = {Machine review of arXiv:2509.01586}
}

read the original abstract

A key open problem in physics is the correct way to combine gravity (described by general relativity) with everything else (described by quantum mechanics). This problem suggests that general relativity and possibly also quantum mechanics need fundamental corrections. Most physicists expect that gravity should be quantum in character, but gravity is fundamentally different to the other forces because it alone is described by spacetime geometry. Experiments are needed to test whether gravity, and hence space-time, is quantum or classical. We propose an experiment to test the quantum nature of gravity by checking whether gravity can entangle two micron-sized crystals. A pathway to this is to create macroscopic quantum superpositions of each crystal first using embedded spins and Stern-Gerlach forces. These crystals could be nanodiamonds containing nitrogen-vacancy (NV) centres. The spins can subsequently be measured to witness the gravitationally generated entanglement. This is based on extensive theoretical feasibility studies and experimental progress in quantum technology. The eventual experiment will require a medium-sized consortium with excellent suppression of decoherence including vibrations and gravitational noise. In this white paper, we review the progress and plans towards realizing this. While implementing these plans, we will further explore the most macroscopic superpositions that are possible, which will test theories that predict a limit to this.

Figures

Figures reproduced from arXiv: 2509.01586 by the authors.

**Figure 2.** Schematic of the protocol from Ref. [115] for creating a spatial superposition using the Stern-Gerlach effect with a single spin. A key technical challenge to realizing the ambitious experiments described above is to ensure the nanoparticles interact only through their mutual gravitational attraction, and no other forces. This challenge is extreme– the intrinsic strength of gravitational interactions is nearly 40… view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

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Using the Feynman-Vernon influence functional, the paper derives state-dependent deterministic and stochastic forces that a qubit exerts on a classical mechanical oscillator, with magnitudes in the zepto- to atto-Newt...
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Grid discretization in qubit simulations generates a generalized uncertainty principle; matching high-energy momentum to special relativity implies a mass-dependent minimum position uncertainty.

Reference graph

Works this paper leans on

158 extracted references · 65 canonical work pages · cited by 2 Pith papers

[41]

J. E. March, B. D. Wood, C. J. Stephen, L. D. Fervenza, B. G. Breeze, S. Mandal, A. M. Edmonds, D. J. Twitchen, M. L. Markham, O. A. Williams, and G. W. Morley, Phys. Rev. Appl. 20, 044045 (2023)

2023
[141]

C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, Phys. Rev. X 9, 031045 (2019)

2019
[107]

B. D. Wood, S. Bose, and G. W. Morley, Phys. Rev. A 105, 012824 (2022)

work page 2022
[1]

S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroˇ s, M. Paternostro, A. Geraci, P. Barker, M. S. Kim, and G. Milburn, Phys. Rev. Lett. 119, 240401 (2017)

2017
[2]

https://www.youtube.com/watch?v=0Fv-0k13s_k (2016), accessed 31st March 2025

2016
[3]

Marletto and V

C. Marletto and V. Vedral, Phys. Rev. Lett. 119, 240402 (2017)

2017
[4]

S. Bose, I. Fuentes, A. A. Geraci, S. M. Khan, S. Qvarfort, M. Rademacher, M. Rashid, M. Toroˇ s, H. Ulbricht, and C. C. Wanjura, Reviews of Modern Physics 97, 015003 (2025)

2025
[5]

Hanif, D

F. Hanif, D. Das, J. Halliwell, D. Home, A. Mazumdar, H. Ulbricht, and S. Bose, Physical Review Letters 133, 180201 (2024)

2024

Show all 158 references

[6]

Krisnanda, G

T. Krisnanda, G. Y. Tham, M. Paternostro, and T. Paterek, npj Quantum Information 6, 12 (2020)

2020
[7]

R. Howl, V. Vedral, D. Naik, M. Christodoulou, C. Rovelli, and A. Iyer, PRX Quantum 2, 010325 (2021)

2021
[8]

S. A. Haine, New Journal of Physics 23, 033020 (2021)

2021
[9]

Oppenheim, C

J. Oppenheim, C. Sparaciari, B. ˇSoda, and Z. Weller-Davies, Nature Communications 14, 7910 (2023)

2023
[10]

L. Lami, J. S. Pedernales, and M. B. Plenio, Physical Review X 14, 021022 (2024)

2024
[11]

Kryhin and V

S. Kryhin and V. Sudhir, Physical Review Letters 134, 061501 (2025)

2025
[12]

Carney, P

D. Carney, P. C. Stamp, and J. M. Taylor, Classical and Quantum Gravity 36, 034001 (2019)

2019
[13]

Belenchia, R

A. Belenchia, R. M. Wald, F. Giacomini, E. Castro-Ruiz, ˇC. Brukner, and M. Aspelmeyer, Phys. Rev. D 98, 126009 (2018)

2018
[14]

Guerreiro, Classical and Quantum Gravity 37, 155001 (2020)

T. Guerreiro, Classical and Quantum Gravity 37, 155001 (2020)

2020
[15]

Parikh, F

M. Parikh, F. Wilczek, and G. Zahariade, Physical Review D 104, 046021 (2021)

2021
[16]

Tobar, S

G. Tobar, S. K. Manikandan, T. Beitel, and I. Pikovski, Nature Communications 15, 7229 (2024). 10

2024
[17]

S. M. Vermeulen, T. Cullen, D. Grass, I. A. O. MacMillan, A. J. Ramirez, J. Wack, B. Korzh, V. S. H. Lee, K. M. Zurek, C. Stoughton, and L. McCuller, Physical Review X 15, 011034 (2025)

2025
[18]

S. M. Vermeulen, L. Aiello, A. Ejlli, W. L. Griffiths, A. L. James, K. L. Dooley, and H. Grote, Classical and Quantum Gravity 38, 085008 (2021)

2021
[19]

G. D. Pietra, F. Piacentini, E. Bernardi, E. Moreva, C. Napoli, I. P. Degiovanni, M. Genovese, V. Vedral, and C. Marletto, (2024), arXiv:2410.19601

2024 arXiv
[20]

Vicentini, E

M. Vicentini, E. Bernardi, E. Moreva, F. Piacentini, C. Napoli, I. P. Degiovanni, A. Manzin, and M. Genovese, (2024), arXiv:2405.21029

2024
[21]

Marletto and V

C. Marletto and V. Vedral, Rev. Mod. Phys. 97, 015006 (2025)

2025
[22]

Marletto and V

C. Marletto and V. Vedral, Phys. Rev. D 102, 086012 (2020)

2020
[23]

Marletto and V

C. Marletto and V. Vedral, Phys. Rev. D 98, 046001 (2018)

2018
[24]

D. Miki, Y. Kaku, Y. Liu, Y. Ma, and Y. Chen, (2025), 2503.11882 [quant-ph]

2025
[25]

A. Mari, S. Zippilli, and D. Vitali, (2025), 2504.05998 [quant-ph]

2025
[26]

C. J. Hogan, Phys. Rev. D 85, 064007 (2012)

2012
[27]

Hogan, O

C. Hogan, O. Kwon, and J. Richardson, Classical and Quantum Gravity 34, 135006 (2017)

2017
[28]

A. S. Chou, R. Gustafson, C. Hogan, B. Kamai, O. Kwon, R. Lanza, L. McCuller, S. S. Meyer, J. Richardson, C. Stoughton, R. Tomlin, S. Waldman, and R. Weiss (Holometer Collaboration), Phys. Rev. Lett. 117, 111102 (2016)

2016
[29]

S. T. Pradyumna, E. Losero, I. Ruo-Berchera, P. Traina, M. Zucco, C. S. Jacobsen, U. L. Ander- sen, I. P. Degiovanni, M. Genovese, and T. Gehring, Commun. Phys. 3 (2020)

2020
[30]

Pikovski, M

I. Pikovski, M. R. Vanner, M. Aspelmeyer, M. S. Kim, and ˇC. Brukner, Nat. Phys. 8, 393 (2012)

2012
[31]

R. Howl, N. Cooper, and L. Hackerm¨ uller, (2023), 2304.00734 [quant-ph]

2023 arXiv
[32]

R. J. Marshman, A. Mazumdar, and S. Bose, Phys. Rev. A 101, 052110 (2020)

2020
[33]

S. Bose, A. Mazumdar, M. Schut, and M. Toroˇ s, Phys. Rev. D 105, 106028 (2022)

2022
[34]

C. M. De Witt, ed., Proceedings: Conference on the Role of Gravitation in Physics, Chapel Hill, North Carolina, Jan 18-23, 1957 (1957)

1957
[35]

Deli´ c, M

U. Deli´ c, M. Reisenbauer, K. Dare, D. Grass, V. Vuleti´ c, N. Kiesel, and M. Aspelmeyer, Science 367, 892 (2020)

2020
[36]

Tebbenjohanns, M

F. Tebbenjohanns, M. Frimmer, V. Jain, D. Windey, and L. Novotny, Physical Review Letters 124, 013603 (2020)

2020
[37]

Westphal, H

T. Westphal, H. Hepach, J. Pfaff, and M. Aspelmeyer, Nature 591, 225 (2021)

2021
[38]

T. M. Fuchs, D. G. Uitenbroek, J. Plugge, N. van Halteren, J.-P. van Soest, A. Vinante, H. Ul- bricht, and T. H. Oosterkamp, Science Advances 10, eadk2949 (2024)

2024
[39]

O. Amit, Y. Margalit, O. Dobkowski, Z. Zhou, Y. Japha, M. Zimmermann, M. A. Efremov, F. A. Narducci, E. M. Rasel, W. P. Schleich, and R. Folman, Phys. Rev. Lett. 123, 083601 (2019)

2019
[40]

Margalit, O

Y. Margalit, O. Dobkowski, Z. Zhou, O. Amit, Y. Japha, S. Moukouri, D. Rohrlich, A. Mazumdar, S. Bose, C. Henkel, and R. Folman, Science Advances 7, eabg2879 (2021). 11

2021
[42]

Christodoulou and C

M. Christodoulou and C. Rovelli, Physics Letters B 792, 64 (2019)

2019
[43]

C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996)

1996
[44]

Oppenheim and Z

J. Oppenheim and Z. Weller-Davies, (2023), 2302.07283 [gr-qc]

2023 arXiv
[45]

Carney, P

D. Carney, P. C. E. Stamp, and J. M. Taylor, Class. Quant. Grav. 36, 034001 (2019)

2019
[46]

D. L. Danielson, G. Satishchandran, and R. M. Wald, Phys. Rev. D 105, 086001 (2022)

2022
[47]

Christodoulou, A

M. Christodoulou, A. Di Biagio, M. Aspelmeyer, ˇC. Brukner, C. Rovelli, and R. Howl, Phys. Rev. Lett. 130, 100202 (2023)

2023
[48]

P. G. C. Rufo, A. Mazumdar, and C. Sab ´ ın, Phys. Rev. A 111, 022444 (2025)

2025
[49]

Scala, M

M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, Phys. Rev. Lett. 111, 180403 (2013)

2013
[50]

Z.-q. Yin, T. Li, X. Zhang, and L. M. Duan, Phys. Rev. A 88, 033614 (2013)

2013
[51]

Kovachy, P

T. Kovachy, P. Asenbaum, C. Overstreet, C. A. Donnelly, S. M. Dickerson, A. Sugarbaker, H. J. M., and M. A. Kasevich, Nature 528, 530 (2015)

2015
[52]

Y. Fein, P. Geyer, P. Zwick, F. Kia lka, S. Pedalino, M. Mayor, S. Gerlich, and M. Arndt, Nature Phys. 15, 1242 (2019)

2019
[53]

Bonvin, L

E. Bonvin, L. Devaud, M. Rossi, A. Militaru, L. Dania, D. S. Bykov, O. Romero-Isart, T. E. Northup, L. Novotny, and M. Frimmer, Phys. Rev. Lett. 132, 253602 (2024)

2024
[54]

Weiss, M

T. Weiss, M. Roda-Llordes, E. Torrontegui, M. Aspelmeyer, and O. Romero-Isart, Phys. Rev. Lett. 127, 023601 (2021)

2021
[55]

Neumeier, M

L. Neumeier, M. A. Ciampini, O. Romero-Isart, M. Aspelmeyer, and N. Kiesel, Proceedings of the National Academy of Sciences 121, e2306953121 (2024)

2024
[56]

Roda-Llordes, A

M. Roda-Llordes, A. Riera-Campeny, D. Candoli, P. T. Grochowski, and O. Romero-Isart, Phys. Rev. Lett. 132, 023601 (2024)

2024
[57]

Bateman, S

J. Bateman, S. Nimmrichter, K. Hornberger, and H. Ulbricht, Nature Comms. 5, 4788 (2014)

2014
[58]

Datta and H

A. Datta and H. Miao, Quantum Science and Technology 6, 045014 (2021)

2021
[59]

Cosco, J

F. Cosco, J. S. Pedernales, and M. B. Plenio, Phys. Rev. A 103, L061501 (2021)

2021
[60]

S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, Optica 4, 356 (2017)

2017
[61]

C. C. Rusconi, M. Perdriat, G. H´ etet, O. Romero-Isart, and B. A. Stickler, Phys. Rev. Lett. 129, 093605 (2022)

2022
[62]

D. C. Moore, A. D. Rider, and G. Gratta, Phys. Rev. Lett. 113, 251801 (2014)

2014
[63]

T. W. van de Kamp, R. J. Marshman, S. Bose, and A. Mazumdar, Phys. Rev. A 102, 062807 (2020). 12

2020
[64]

L. P. Neukirch, E. von Haartman, J. M. Rosenholm, and A. N. Vamivakas, Nat. Photon. 9, 653 (2015)

2015
[65]

T. M. Hoang, J. Ahn, J. Bang, and T. Li, Nature Communications 7, 12250 (2016)

2016
[66]

Kuhlicke, A

A. Kuhlicke, A. W. Schell, J. Zoll, and O. Benson, Applied Physics Letters 105, 073101 (2014), https://pubs.aip.org/aip/apl/article- pdf/doi/10.1063/1.4893575/14316710/073101 1 online.pdf

2014 doi
[67]

Delord, P

T. Delord, P. Huillery, L. Schwab, L. Nicolas, L. Lecordier, and G. H´ etet, Phys. Rev. Lett. 121, 053602 (2018)

2018
[68]

Delord, P

T. Delord, P. Huillery, L. Nicolas, and G. H´ etet, Nature 580, 56 (2020)

2020
[69]

Y. Jin, K. Shen, P. Ju, X. Gao, C. Zu, A. J. Grine, and T. Li, Nature Communications 15, 5063 (2024)

2024
[70]

G. P. Conangla, A. W. Schell, R. A. Rica, and R. Quidant, Nano Lett. 18, 3956 (2018)

2018
[71]

A. T. M. A. Rahman, A. C. Frangeskou, M. S. Kim, S. Bose, G. W. Morley, and P. F. Barker, Scientific Reports 6, 21633 (2016)

2016
[72]

A. C. Frangeskou, A. T. M. A. Rahman, L. Gines, S. Mandal, O. A. Williams, P. F. Barker, and G. W. Morley, New Journal of Physics 20, 043016 (2018)

2018
[73]

Di´ osi and J

L. Di´ osi and J. J. Halliwell, Phys. Rev. Lett. 81, 2846 (1998)

1998
[74]

Kafri, J

D. Kafri, J. M. Taylor, and G. J. Milburn, New Journal of Physics 16, 065020 (2014)

2014
[75]

Tilloy and L

A. Tilloy and L. Di´ osi, Physical Review D 93, 024026 (2016)

2016
[76]

Oppenheim and Z

J. Oppenheim and Z. Weller-Davies, Journal of High Energy Physics 2022, 1 (2022)

2022
[77]

Oppenheim, Phys

J. Oppenheim, Phys. Rev. X 13, 041040 (2023)

2023
[78]

Christodoulou, A

M. Christodoulou, A. Di Biagio, R. Howl, and C. Rovelli, Classical and Quantum Gravity 40, 047001 (2023)

2023
[79]

G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986)

1986
[80]

Di´ osi, Physics Letters A 120, 377 (1987)

L. Di´ osi, Physics Letters A 120, 377 (1987)

1987
[81]

Penrose, Gen

R. Penrose, Gen. Relat. Gravit. 28, 581–600 (1996)

1996
[82]

Karolyhazy, Nuovo Cimento A (1965-1970) 42, 390–402 (1966)

F. Karolyhazy, Nuovo Cimento A (1965-1970) 42, 390–402 (1966)

1965
[83]

Bassi, K

A. Bassi, K. Lochan, S. Satin, T. P. Singh, and H. Ulbricht, Rev. Mod. Phys. 85, 471 (2013)

2013
[84]

Fr¨ owis, P

F. Fr¨ owis, P. Sekatski, W. D¨ ur, N. Gisin, and N. Sangouard, Rev. Mod. Phys.90, 025004 (2018)

2018
[85]

R. Howl, R. Penrose, and I. Fuentes, New Journal of Physics 21, 043047 (2019)

2019
[86]

Donadi, K

S. Donadi, K. Piscicchia, C. Curceanu, L. Di´ osi, M. Laubenstein, and A. Bassi, Nature Physics 17, 74 (2021)

2021
[87]

Penrose, in Consciousness and Quantum Mechanics , edited by S

R. Penrose, in Consciousness and Quantum Mechanics , edited by S. Gao (Oxford University Press, 2022)

2022
[88]

T. Zhou, S. Bose, and A. Mazumdar, Phys. Rev. A 112, 013315 (2025)

2025
[89]

Rizaldy, T

R. Rizaldy, T. Zhou, S. Bose, and A. Mazumdar, (2024), 2412.15335 [quant-ph] . 13

2024 arXiv
[90]

Magrini, P

L. Magrini, P. Rosenzweig, C. Bach, A. Deutschmann-Olek, S. G. Hofer, S. Hong, N. Kiesel, K. A., and M. Aspelmeyer, Nature 595, 373 (2021)

2021
[91]

Tebbenjohanns, M

F. Tebbenjohanns, M. L. Mattana, M. Rossi, F. M., and L. Novotny, Nature 595, 378 (2021)

2021
[92]

Kamba, R

M. Kamba, R. Shimizu, and K. Aikawa, Opt. Express 30, 26716 (2022)

2022
[93]

Piotrowski, D

J. Piotrowski, D. Windey, J. Vijayan, C. Gonzalez-Ballestero, A. de los R ´ ıos Sommer, N. Meyer, R. Quidant, O. Romero-Isart, R. Reimann, and L. Novotny, Nat. Phys. (2023)

2023
[94]

Dania, O

L. Dania, O. S. Kremer, J. Piotrowski, D. Candoli, J. Vijayan, O. Romero-Isart, C. Gonzalez- Ballestero, L. Novotny, and M. Frimmer, Nat. Phys. (2025)

2025
[95]

Schut, J

M. Schut, J. Tilly, R. J. Marshman, S. Bose, and A. Mazumdar, Phys. Rev. A 105, 032411 (2022)

2022
[96]

Schut, A

M. Schut, A. Geraci, S. Bose, and A. Mazumdar, Phys. Rev. Res. 6, 013199 (2024)

2024
[97]

Schut and A

M. Schut and A. Mazumdar, (2025), arXiv:2502.12474 [quant-ph]

2025 arXiv
[98]

Toroˇ s, T

M. Toroˇ s, T. W. Van De Kamp, R. J. Marshman, M. S. Kim, A. Mazumdar, and S. Bose, Phys. Rev. Res. 3, 023178 (2021)

2021
[99]

Schut, P

M. Schut, P. Andriolo, M. Toroˇ s, S. Bose, and A. Mazumdar, Phys. Rev. A 111, 042211 (2025)

2025
[100]

Narasimha Moorthy, A

S. Narasimha Moorthy, A. Geraci, S. Bose, and A. Mazumdar, Phys. Rev. A 112, 022416 (2025)

2025
[101]

Romero-Isart, Phys

O. Romero-Isart, Phys. Rev. A 84, 052121 (2011)

2011
[102]

S. R. Nair, S. Tian, G. K. Brennen, S. Bose, and J. Twamley, (2023), 2307.14553 [quant-ph]

2023 arXiv
[103]

Brunner, D

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarani, and S. Wehner, Rev. Mod. Phys. 86, 419 (2014)

2014
[104]

Kent and D

A. Kent and D. Pital´ ua-Garc ´ ıa, Phys. Rev. D104, 126030 (2021)

2021
[105]

Rosskopf, A

T. Rosskopf, A. Dussaux, K. Ohashi, M. Loretz, R. Schirhagl, H. Watanabe, S. Shikata, K. M. Itoh, and C. L. Degen, Phys. Rev. Lett. 112, 147602 (2014)

2014
[106]

J. S. Pedernales, G. W. Morley, and M. B. Plenio, Phys. Rev. Lett. 125, 023602 (2020)

2020
[108]

R. Zhou, R. J. Marshman, S. Bose, and A. Mazumdar, Physica Scripta 99, 055114 (2024)

2024
[109]

R. Zhou, R. J. Marshman, S. Bose, and A. Mazumdar, Phys. Rev. Res. 4, 043157 (2022)

2022
[110]

R. Zhou, R. J. Marshman, S. Bose, and A. Mazumdar, Phys. Rev. A 107, 032212 (2023)

2023
[111]

R. Zhou, Q. Xiang, and A. Mazumdar, (2024), arXiv:2408.11909 [quant-ph]

2024 arXiv
[112]

Braccini, A

L. Braccini, A. Serafini, and S. Bose, (2024), arXiv:2408.11930 [quant-ph]

2024 arXiv
[113]

Henkel and R

C. Henkel and R. Folman, A VS Quantum Sci. 4, 025602 (2022)

2022
[114]

Japha and R

Y. Japha and R. Folman, Phys. Rev. Lett. 130, 113602 (2023)

2023
[115]

C. Wan, M. Scala, G. Morley, A. Rahman, H. Ulbricht, J. Bateman, P. Barker, S. Bose, and M. Kim, Phys. Rev. Lett. 117, 143003 (2016)

2016
[116]

J.-F. Hsu, P. Ji, C. W. Lewandowski, and B. D’Urso, Sci. Rep. 6, 30125 (2016). 14

2016
[117]

Dobkowski, B

O. Dobkowski, B. Trok, P. Skakunenko, Y. Japha, D. Groswasser, M. Efremov, C. Marletto, I. Fuentes, R. Penrose, V. Vedral, W. P. Schleich, and R. Folman, (2025), arXiv:2502.14535 [quant-ph]

2025
[118]

M. Keil, O. Amit, S. Zhou, D. Groswasser, Y. Japha, and R. Folman, Journal of Modern Optics 63, 1840 (2016)

2016
[119]

M. C. O’Brien, S. Dunn, J. E. Downes, and J. Twamley, App. Phys. Lett. 114, 053103 (2019)

2019
[120]

G. Afek, F. Monteiro, B. Siegel, J. Wang, S. Dickson, J. Recoaro, M. Watts, and D. C. Moore, Phys. Rev. A 104, 053512 (2021)

2021
[121]

A. D. Rider, D. C. Moore, C. P. Blakemore, M. Louis, M. Lu, and G. Gratta, Phys. Rev. Lett. 117, 101101 (2016)

2016
[122]

Fragolino, M

P. Fragolino, M. Schut, M. Toroˇ s, S. Bose, and A. Mazumdar, Phys. Rev. A 109, 033301 (2024)

2024
[123]

Schut, H

M. Schut, H. Bosma, M. Wu, M. Toroˇ s, S. Bose, and A. Mazumdar, Phys. Rev. A 110, 022412 (2024)

2024
[124]

J. L. Garrett, J. Kim, and J. N. Munday, Phys. Rev. Res. 2, 023355 (2020)

2020
[125]

Ranjit, M

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, Phys. Rev. A 93, 053801 (2016)

2016
[126]

Montoya, E

C. Montoya, E. Alejandro, W. Eom, D. Grass, N. Clarisse, A. Witherspoon, and A. A. Geraci, Appl. Opt. 61, 3486 (2022)

2022
[127]

H. B. G. Casimir and D. Polder, Phys. Rev. 73, 360 (1948)

1948
[128]

Lambrecht and S

A. Lambrecht and S. Reynaud, The European Physical Journal D 8, 309 (2000)

2000
[129]

D. M. Harber, J. M. Obrecht, J. M. McGuirk, and E. A. Cornell, Phys. Rev. A 72, 033610 (2005)

2005
[130]

S. G. Elahi, M. Schut, A. Dana, A. Grinin, S. Bose, A. Mazumdar, and A. Geraci, (2024), arXiv:2411.02325 [quant-ph]

2024
[131]

Schut, A

M. Schut, A. Grinin, A. Dana, S. Bose, A. Geraci, and A. Mazumdar, Phys. Rev. Res. 5, 043170 (2023)

2023
[132]

R. J. Marshman, A. Mazumdar, R. Folman, and S. Bose, Phys. Rev. Res. 4, 023087 (2022)

2022
[133]

A. A. Geraci, S. J. Smullin, D. M. Weld, J. Chiaverini, and A. Kapitulnik, Phys. Rev. D 78, 022002 (2008)

2008
[134]

P. F. Barker, S. Bose, R. J. Marshman, and A. Mazumdar, Phys. Rev. D 106, L041901 (2022)

2022
[135]

B. D. Wood, G. A. Stimpson, J. E. March, Y. N. D. Lekhai, C. J. Stephen, B. L. Green, A. C. Frangeskou, L. Gin´ es, S. Mandal, O. A. Williams, and G. W. Morley, Phys. Rev. B 105, 205401 (2022)

2022
[136]

Andrich, B

P. Andrich, B. J. Alem´ an, J. C. Lee, K. Ohno, C. F. de las Casas, F. J. Heremans, E. L. Hu, and D. D. Awschalom, Nano Lett. 14, 4959 (2014)

2014
[137]

M. E. Trusheim, L. Li, A. Laraoui, E. H. Chen, H. Bakhru, T. Schr¨ oder, O. Gaathon, C. A. Meriles, and D. Englund, Nano Lett. 14, 32 (2013)

2013
[138]

C. J. Stephen, B. L. Green, Y. N. D. Lekhai, L. Weng, P. Hill, S. Johnson, A. C. Frangeskou, P. L. Diggle, Y.-C. Chen, M. J. Strain, E. Gu, M. E. Newton, J. M. Smith, P. S. Salter, and G. W. Morley, Phys. Rev. Applied 12, 064005 (2019). 15

2019
[139]

Tyler, J

S. Tyler, J. Newland, P. Hepworth, A. Wijesekara, I. R. Gullick, M. L. Markham, M. E. Newton, and B. L. Green, Applied Physics Letters 126, 054001 (2025)

2025
[140]

Pentacene-doped naphthalene for levitated optomechanics,

M. O. E. Steiner, J. S. Pedernales, and M. B. Plenio, “Pentacene-doped naphthalene for levitated optomechanics,” (2024), arXiv:2405.13869 [quant-ph]

2024 arXiv
[142]

A. A. Geraci, S. B. Papp, and J. Kitching, Phys. Rev. Lett. 105, 101101 (2010)

2010
[143]

Carney, G

D. Carney, G. Krnjaic, D. C. Moore, C. A. Regal, G. Afek, S. Bhave, B. Brubaker, T. Corbitt, J. Cripe, N. Crisosto, A. Geraci, S. Ghosh, J. G. E. Harris, A. Hook, E. W. Kolb, J. Kunjummen, R. F. Lang, T. Li, T. Lin, Z. Liu, J. Lykken, L. Magrini, J. Manley, N. Matsumoto, A. Mo...

2021
[144]

G. Afek, D. Carney, and D. C. Moore, Phys. Rev. Lett. 128, 101301 (2022)

2022
[145]

D. C. Moore and A. A. Geraci, Quantum Sci. Technol. 6, 014008 (2021)

2021
[146]

C. J. Riedel, Phys. Rev. D 88, 116005 (2013)

2013
[147]

P. G. Carmona Rufo, A. Kumar, C. Sab ´ ın, and A. Mazumdar, Phys. Rev. D 111, 115005 (2025)

2025
[148]

Liu and K.-D

J. Liu and K.-D. Zhu, Classical and Quantum Gravity 35, 205010 (2018)

2018
[149]

Monteiro, G

F. Monteiro, G. Afek, D. Carney, G. Krnjaic, J. Wang, and D. C. Moore, Phys. Rev. Lett. 125, 181102 (2020)

2020
[150]

Kilian, M

E. Kilian, M. Toroˇ s, F. F. Deppisch, R. Saakyan, and S. Bose, Physical Review Research 5, 023012 (2023)

2023
[151]

Kilian, M

E. Kilian, M. Toroˇ s, P. Barker, and S. Bose, Physical Review Research 6, 023037 (2024)

2024
[152]

Kilian, M

E. Kilian, M. Rademacher, J. M. Gosling, J. H. Iacoponi, F. Alder, M. Toroˇ s, A. Pontin, C. Ghag, S. Bose, T. S. Monteiro, and P. F. Barker, A VS Quantum Science 6 (2024)

2024
[153]

Geraci and H

A. Geraci and H. Goldman, Phys. Rev. D 92, 062002 (2015)

2015
[154]

R. J. Marshman, A. Mazumdar, G. W. Morley, P. F. Barker, S. Hoekstra, and S. Bose, New J. Phys. 22, 083012 (2020)

2020
[155]

M.-Z. Wu, M. Toroˇ s, S. Bose, and A. Mazumdar, Phys. Rev. D 111, 064004 (2025)

2025
[156]

Rademacher, J

M. Rademacher, J. Millen, and Y. L. Li, Advanced Optical Technologies 9, 227–239 (2019)

2019
[157]

Monteiro, W

F. Monteiro, W. Li, G. Afek, C.-l. Li, M. Mossman, and D. C. Moore, Phys. Rev. A 101, 053835 (2020)

2020
[158]

Winstone et al

G. Winstone et al. (LSD Collaboration), Phys. Rev. Lett. 129, 053604 (2022). 16

2022

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

[1] [41]

J. E. March, B. D. Wood, C. J. Stephen, L. D. Fervenza, B. G. Breeze, S. Mandal, A. M. Edmonds, D. J. Twitchen, M. L. Markham, O. A. Williams, and G. W. Morley, Phys. Rev. Appl. 20, 044045 (2023)

2023

[2] [141]

C. E. Bradley, J. Randall, M. H. Abobeih, R. C. Berrevoets, M. J. Degen, M. A. Bakker, M. Markham, D. J. Twitchen, and T. H. Taminiau, Phys. Rev. X 9, 031045 (2019)

2019

[3] [107]

B. D. Wood, S. Bose, and G. W. Morley, Phys. Rev. A 105, 012824 (2022)

work page 2022

[4] [1]

S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroˇ s, M. Paternostro, A. Geraci, P. Barker, M. S. Kim, and G. Milburn, Phys. Rev. Lett. 119, 240401 (2017)

2017

[5] [2]

https://www.youtube.com/watch?v=0Fv-0k13s_k (2016), accessed 31st March 2025

2016

[6] [3]

Marletto and V

C. Marletto and V. Vedral, Phys. Rev. Lett. 119, 240402 (2017)

2017

[7] [4]

S. Bose, I. Fuentes, A. A. Geraci, S. M. Khan, S. Qvarfort, M. Rademacher, M. Rashid, M. Toroˇ s, H. Ulbricht, and C. C. Wanjura, Reviews of Modern Physics 97, 015003 (2025)

2025

[8] [5]

Hanif, D

F. Hanif, D. Das, J. Halliwell, D. Home, A. Mazumdar, H. Ulbricht, and S. Bose, Physical Review Letters 133, 180201 (2024)

2024