- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Graviton-mediated entanglement due to light bending from a quantum rotor

Dripto Biswas1, Sougato Bose2, Anupam Mazumdar3, and Marko Toroš4

PDF

Phys. Rev. D 114, 062004 – Published 11 September, 2026

DOI: https://doi.org/10.1103/gn67-ksx6

Abstract

One of the key tests of the quantum nature of gravity is to test whether the virtual mediator of gravity between matter and photon gives rise to the quantum light-bending phenomenon. The off-shell degrees of freedom, involving the spin-2 and spin-0 components of graviton, reproduce the classical deviation of light rays, as well as have been predicted to generate entanglement between matter and photon. This paper explores the generation of entanglement due to the quantum gravitational interaction in an optomechanical setup with a quantum rotor and photon. The virtual exchange of a graviton provides entanglement between the photon degrees of freedom and the spatial position of the quantum rotor, with the rotational state affecting its magnitude. We analyze the case of a high spinning rotor, in an approximately classical state of angular momentum, and quantify its effect on the gravitationally induced entanglement between the photon and the position of the quantum rotor. We show that the difference in the linear entanglement entropies, of prograde-and-retrograde motion of the photon with respect to the quantum rotor, provide tangible observable consequences.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (64)

  1. F. W. Dyson, A. S. Eddington, and C. Davidson, A determination of the deflection of light by the Sun’s gravitational field, from observations made at the total eclipse of May 29, 1919, Phil. Trans. R. Soc. A 220, 291 (1920).
  2. S. N. Gupta, Quantization of Einstein’s gravitational field: General treatment, Proc. Phys. Soc. London Sect. A 65, 608 (1952).
  3. M. D. Scadron, Advanced Quantum Theory, 3rd ed. (World Scientific, Singapore, 2007).
  4. J. F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50, 3874 (1994).
  5. https://www.youtube.com/watch?v=0Fv-0k13s_k (2016), accessed November 1, 2022.
  6. S. Bose, A. Mazumdar, G. W. Morley, H. Ulbricht, M. Toroš, M. Paternostro, A. Geraci, P. Barker, M. S. Kim, and G. Milburn, Spin entanglement witness for quantum gravity, Phys. Rev. Lett. 119, 240401 (2017).
  7. C. Marletto and V. Vedral, Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity, Phys. Rev. Lett. 119, 240402 (2017).
  8. D. Biswas, S. Bose, A. Mazumdar, and M. Toroš, Gravitational optomechanics: Photon-matter entanglement via graviton exchange, Phys. Rev. D 108, 064023 (2023).
  9. D. Carney, Newton, entanglement, and the graviton, Phys. Rev. D 105, 024029 (2022).
  10. R. J. Marshman, A. Mazumdar, and S. Bose, Locality and entanglement in table-top testing of the quantum nature of linearized gravity, Phys. Rev. A 101, 052110 (2020).
  11. S. Bose, A. Mazumdar, M. Schut, and M. Toroš, Mechanism for the quantum natured gravitons to entangle masses, Phys. Rev. D 105, 106028 (2022).
  12. A. Belenchia, R. M. Wald, F. Giacomini, E. Castro-Ruiz, Č. Brukner, and M. Aspelmeyer, Quantum superposition of massive objects and the quantization of gravity, Phys. Rev. D 98, 126009 (2018).
  13. D. Kafri, G. J. Milburn, and J. M. Taylor, Bounds on quantum communication via Newtonian gravity, New J. Phys. 17, 015006 (2015).
  14. D. Carney, P. C. E. Stamp, and J. M. Taylor, Tabletop experiments for quantum gravity: A user’s manual, Classical Quantum Gravity 36, 034001 (2019).
  15. D. L. Danielson, G. Satishchandran, and R. M. Wald, Gravitationally mediated entanglement: Newtonian field versus gravitons, Phys. Rev. D 105, 086001 (2022).
  16. M. Christodoulou, A. Di Biagio, M. Aspelmeyer, Č. Brukner, C. Rovelli, and R. Howl, Locally mediated entanglement in linearized quantum gravity, Phys. Rev. Lett. 130, 100202 (2023).
  17. M. Christodoulou and C. Rovelli, On the possibility of laboratory evidence for quantum superposition of geometries, Phys. Lett. B 792, 64 (2019).
  18. U. K. Beckering Vinckers, Á. De La Cruz-Dombriz, and A. Mazumdar, Quantum entanglement of masses with nonlocal gravitational interaction, Phys. Rev. D 107, 124036 (2023).
  19. S. G. Elahi and A. Mazumdar, Probing massless and massive gravitons via entanglement in a warped extra dimension, Phys. Rev. D 108, 035018 (2023).
  20. J. S. Pedernales, G. W. Morley, and M. B. Plenio, Motional dynamical decoupling for interferometry with macroscopic particles, Phys. Rev. Lett. 125, 023602 (2020).
  21. R. J. Marshman, A. Mazumdar, R. Folman, and S. Bose, Constructing nano-object quantum superpositions with a Stern-Gerlach interferometer, Phys. Rev. Res. 4, 023087 (2022).
  22. T. W. van de Kamp, R. J. Marshman, S. Bose, and A. Mazumdar, Quantum gravity witness via entanglement of masses: Casimir screening, Phys. Rev. A 102, 062807 (2020).
  23. H. Chevalier, A. J. Paige, and M. S. Kim, Witnessing the nonclassical nature of gravity in the presence of unknown interactions, Phys. Rev. A 102, 022428 (2020).
  24. T. Krisnanda, G. Y. Tham, M. Paternostro, and T. Paterek, Observable quantum entanglement due to gravity, npj Quantum Inf. 6, 12 (2020).
  25. S. G. Elahi, M. Schut, A. Dana, A. Grinin, S. Bose, A. Mazumdar, and A. Geraci, Diamagnetic micro-chip traps for levitated nanoparticle entanglement experiments, Phys. Rev. A 112, 063508 (2025).
  26. T. Zhou, S. Bose, and A. Mazumdar, Gyroscopic stability for nanoparticles in Stern-Gerlach interferometry and spin contrast, Phys. Rev. A 112, 013315 (2025).
  27. S. Bose et al., A spin-based pathway to testing the quantum nature of gravity, arXiv:2509.01586.
  28. M. Toroš, A. Mazumdar, and S. Bose, Loss of coherence and coherence protection from a graviton bath, Phys. Rev. D 109, 084050 (2024).
  29. A. Mazumdar and T. Zhou, Quantum gravitational contrast in creating Schrödinger cat state, arXiv:2605.05153.
  30. P. G. C. Rufo, A. Mazumdar, and C. Sabín, Genuine tripartite entanglement in graviton-matter interactions, Phys. Rev. A 111, 022444 (2025).
  31. A. Dutta, M. Toroš, S. Bose, and A. Mazumdar, Witnessing entanglement between photon and matter due to graviton exchange, arXiv:2604.24496.
  32. G. Higgins, A. Di Biagio, and M. Christodoulou, Truly relativistic gravity mediated entanglement protocol using superpositions of rotational energies, Phys. Rev. D 110, L101901 (2024).
  33. R. Rizaldy, T. Zhou, S. Bose, and A. Mazumdar, Rotational stability in nanorotor and spin contrast in one-loop interferometry in the Stern-Gerlach setup, Phys. Rev. Res. 7, 043095 (2025).
  34. R. Rizaldy, S. Mishra, and A. Mazumdar, Two-dimensional matter-wave interferometer, rotational dynamics, and spin contrast, arXiv:2603.05595.
  35. R. Rizaldy, T. Zhou, R. Zhou, and A. Mazumdar, Spatial superposition for a two-dimensional matter-wave interferometer in an inverted harmonic potential with gyroscopic rotational stability, arXiv:2601.20949.
  36. V. V. Krishnan, M. Bailes, W. van Straten, N. Wex, P. C. C. Freire, E. F. Keane, T. M. Tauris, P. A. Rosado, N. D. R. Bhat, C. Flynn, A. Jameson, and S. Osłowski, Lense–thirring frame dragging induced by a fast-rotating white dwarf in a binary pulsar system, Science 367, 577 (2020).
  37. S. Kopeikin and B. Mashhoon, Gravitomagnetic effects in the propagation of electromagnetic waves in variable gravitational fields of arbitrary moving and spinning bodies, Phys. Rev. D 65, 064025 (2002).
  38. E. Guadagnini, Gravitational deflection of light and helicity asymmetry, Phys. Lett. B 548, 19 (2002).
  39. J. Bodenner and C. M. Will, Deflection of light to second order: A tool for illustrating principles of general relativity, Am. J. Phys. 71, 770 (2003).
  40. M. Fink, A. Rodriguez-Aramendia, J. Handsteiner, A. Ziarkash, F. Steinlechner, T. Scheidl, I. Fuentes, J. Pienaar, T. C. Ralph, and R. Ursin, Experimental test of photonic entanglement in accelerated reference frames, Nat. Commun. 8, 15304 (2017).
  41. S. Restuccia, M. Toroš, G. M. Gibson, H. Ulbricht, D. Faccio, and M. J. Padgett, Photon bunching in a rotating reference frame, Phys. Rev. Lett. 123, 110401 (2019).
  42. M. Toroš, S. Restuccia, G. M. Gibson, M. Cromb, H. Ulbricht, M. Padgett, and D. Faccio, Revealing and concealing entanglement with noninertial motion, Phys. Rev. A 101, 043837 (2020).
  43. M. Toroš, M. Cromb, M. Paternostro, and D. Faccio, Generation of entanglement from mechanical rotation, Phys. Rev. Lett. 129, 260401 (2022).
  44. T. Biswas, T. Koivisto, and A. Mazumdar, Nonlocal theories of gravity: The flat space propagator, in Proceedings of the Barcelona Postgrad Encounters on Fundamental Physics (2013), pp. 13–24, arXiv:1302.0532.
  45. T. Biswas, E. Gerwick, T. Koivisto, and A. Mazumdar, Towards singularity and ghost free theories of gravity, Phys. Rev. Lett. 108, 031101 (2012).
  46. C. Whittle et al., Approaching the motional ground state of a 10-kg object, Science 372, 1333 (2021).
  47. J. Vovrosh, M. Rashid, D. Hempston, J. Bateman, M. Paternostro, and H. Ulbricht, Parametric feedback cooling of levitated optomechanics in a parabolic mirror trap, J. Opt. Soc. Am. B 34, 1421 (2017).
  48. J. W. Yoon, Y. G. Kim, I. W. Choi, J. H. Sung, H. W. Lee, S. K. Lee, and C. H. Nam, Realization of laser intensity over 1023  W/cm2, Optica 8, 630 (2021).
  49. M. Schuck, D. Steinert, T. Nussbaumer, and J. W. Kolar, Ultrafast rotation of magnetically levitated macroscopic steel spheres, Sci. Adv. 4, e1701519 (2018).
  50. J. Ahn, Z. Xu, J. Bang, Y.-H. Deng, T. M. Hoang, Q. Han, R.-M. Ma, and T. Li, Optically levitated nanodumbbell torsion balance and GHz nanomechanical rotor, Phys. Rev. Lett. 121, 033603 (2018).
  51. K. Hornberger, Introduction to decoherence theory, Lect. Notes Phys. 768, 221 (2009).
  52. O. Romero-Isart, Quantum superposition of massive objects and collapse models, Phys. Rev. A 84, 052121 (2011).
  53. M. Schlosshauer, Quantum decoherence, Phys. Rep. 831, 1 (2019).
  54. M. Schut, P. Andriolo, M. Toroš, S. Bose, and A. Mazumdar, Expression for the decoherence rate due to air-molecule scattering in spatial qubits, Phys. Rev. A 111, 042211 (2025).
  55. J. Tilly, R. J. Marshman, A. Mazumdar, and S. Bose, Qudits for witnessing quantum-gravity-induced entanglement of masses under decoherence, Phys. Rev. A 104, 052416 (2021).
  56. J. Preskill, Notes on noise, http://theory.caltech.edu/preskill/papers/decoherence_notesv2.pdf.
  57. C. M. Caves, Quantum-mechanical noise in an interferometer, Phys. Rev. D 23, 1693 (1981).
  58. P. R. Saulson, Terrestrial gravitational noise on a gravitational wave antenna, Phys. Rev. D 30, 732 (1984).
  59. K. S. Thorne and C. J. Winstein, Human gravity-gradient noise in interferometric gravitational-wave detectors, Phys. Rev. D 60, 082001 (1999).
  60. S. A. Hughes and K. S. Thorne, Seismic gravity-gradient noise in interferometric gravitational-wave detectors, Phys. Rev. D 58, 122002 (1998).
  61. M. Toroš, T. W. Van De Kamp, R. J. Marshman, M. S. Kim, A. Mazumdar, and S. Bose, Relative acceleration noise mitigation for nanocrystal matter-wave interferometry: Applications to entangling masses via quantum gravity, Phys. Rev. Res. 3, 023178 (2021).
  62. B. A. Stickler, K. Hornberger, and M. S. Kim, Quantum rotations of nanoparticles, Nat. Rev. Phys. 3, 589 (2021).
  63. M. Perdriat, C. C. Rusconi, T. Delord, P. Huillery, C. Pellet-Mary, A. Durand, B. A. Stickler, and G. Hétet, Rotational locking of charged microparticles in quadrupole ion traps, Phys. Rev. Lett. 133, 253602 (2024).
  64. M. Perdriat, A. Durand, J. Voisin, and G. Hétet, Spin-dependent force from an NV center ensemble on a microlever, Phys. Rev. B 112, 094419 (2025).

Outline

Information

Phys. Rev. D 114, 062004– Published 11 September, 2026
  • Received 3 July 2026
  • Accepted 31 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation