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  • Letter
  • Open Access

Probing lambda-gravity with Bose-Einstein condensates

Hector A. Fernandez-Melendez1,*, Alexander Belyaev1,2,†, Vahe Gurzadyan3,‡, and Ivette Fuentes1,4,§,∥

  • *Contact author: h.a.fernandez-melendez@soton.ac.uk
  • †Contact author: a.belyaev@soton.ac.uk
  • ‡Contact author: gurzadyan@yerphi.am
  • §Contact author: i.fuentes-guridi@soton.ac.uk
  • ∥Previously known as Fuentes-Guridi and Fuentes-Schuller.
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Phys. Rev. Research 7, L042051 – Published 3 December, 2025

DOI: https://doi.org/10.1103/7x8h-t1l9

Abstract

We propose a precise test of two fundamental gravitational constants using a detector concept that exploits the dynamics of quantum phononic excitations in a trapped Bose-Einstein condensate (BEC), operable at the scale of tabletop experiments. In this setup, the sensitivity is enhanced by approximately 2 orders of magnitude through the use of a tritter operation, which mixes phononic excitations with the BEC's ground state. The BEC exhibits unique sensitivity to the two key components of the gravitational potential in Λ-gravity: the Newtonian GM/r term and the cosmological constant Λr2, both entering the most general function following from a Gurzadyan's theorem. Using state-of-the-art experimental design, we predict that the gravitational constant G could be measured with an accuracy up to 10−17N m2/kg2, representing an improvement by 2 orders of magnitude over current measurements. Moreover, this experiment aims to establish the best Earth-based upper limit on Λ at <10−31 m−2, marking the first laboratory-based probe of the cosmological constant. Additionally, the setup allows for the measurement of the distance-dependent behavior of each term in the gravitational potential, providing a means to test modified gravity theories.

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References (70)

  1. P. J. E. Peebles, Status of the λCDM theory: Supporting evidence and anomalies, Philos. Trans. R. Soc. A 383, 20240021 (2025).
  2. V. G. Gurzadyan, The cosmological constant in the McCrea-Milne cosmological scheme, Observatory 105, 42 (1985).
  3. V. G. Gurzadyan, On the common nature of dark matter and dark energy: Galaxy groups, Eur. Phys. J. Plus 134, 1 (2019).
  4. V. G. Gurzadyan and A. Stepanian, Two fundamental constants of gravity unifying dark matter and dark energy, Eur. Phys. J. C 78, 1 (2018).
  5. V. G. Gurzadyan and A. Stepanian, The cosmological constant derived via galaxy groups and clusters, Eur. Phys. J. C 79, 169 (2019).
  6. V. G. Gurzadyan and A. Stepanian, H0 tension: Clue to common nature of dark sector? Eur. Phys. J. C 79, 568 (2019).
  7. A. G. Riess et al., Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the Hubble constant and stronger evidence for physics beyond λCDM, Astrophys. J. 876, 85 (2019).
  8. A. G. Riess, The expansion of the universe is faster than expected, Nat. Rev. Phys. 2, 10 (2020).
  9. A. G. Riess et al., A 2024 measurement of the Hubble constant from the Hubble space telescope, Astrophys. J. Lett. 962, L17 (2024).
  10. V. G. Gurzadyan and A. Stepanian, Hubble tension vs two flows, Eur. Phys. J. Plus 136, 1 (2021).
  11. V. G. Gurzadyan and A. Stepanian, Galaxy groups and the Hubble tension, Astrophys. J. Lett. 653, A145 (2021).
  12. A. V. Kravtsov, The size–virial radius relation of galaxies, Astrophys. J. 764, L31 (2013).
  13. A. Einstein, Kosmologische betrachtungen zur allgemeinen relativitätstheorie, Sitzungsber. K. Preuss. Akad. Wiss. 142 (1917) (in German).
  14. A. Einstein, Bemerkung zu Herrn Schrödingers Notiz: Über ein Lösungssystem der allgemein kovarianten gravitationsgleichungen, Z. Angew. Phys. 19, 165 (1918).
  15. V. G. Gurzadyan and A. Stepanian, Cosmological constant as a fundamental constant, Eur. Phys. J. Plus 134, 98 (2019).
  16. R. Penrose, Cycles of Time: An Extraordinary New View of the Universe (Bodley Head, London, 2010).
  17. V. G. Gurzadyan and R. Penrose, On CCC-predicted concentric low-variance circles in the CMB sky, Eur. Phys. J. Plus 128, 22 (2013).
  18. V. G. Gurzadyan and R. Penrose, CCC and the Fermi paradox: Concentric circles in WMAP and Planck data, Eur. Phys. J. Plus 131, 11 (2016).
  19. A. Belenchia, M. Carlesso, Ö. Bayraktar, D. Dequal, I. Derkach, G. Gasbarri, W. Herr, Y. L. Li, M. Rademacher, J. Sidhu, D. K. L. Oi, S. T. Seidel, R. Kaltenbaek, C. Marquardt, H. Ulbricht, V. C. Usenko, L. Wörner, A. Xuereb, M. Paternostro, and A. Bassi, Quantum physics in space, Phys. Rep. 951, 1 (2022).
  20. D. Carney et al., Mechanical quantum sensing in the search for dark matter, Quantum Sci. Technol. 6, 024002 (2021).
  21. P. W. Graham, D. E. Kaplan, J. Mardon, S. Rajendran, and W. A. Terrano, Dark matter direct detection with accelerometers, Phys. Rev. D 93, 075029 (2016).
  22. R. Howl and I. Fuentes, Quantum frequency interferometry: With applications ranging from gravitational wave detection to dark matter searches, AVS Quantum Sci. 5, 014402 (2023).
  23. C. Sabín, D. E. Bruschi, M. Ahmadi, and I. Fuentes, Phonon creation by gravitational waves, New J. Phys. 16, 085003 (2014).
  24. M. Ahmadi, D. E. Bruschi, C. Sabín, G. Adesso, and I. Fuentes, Relativistic quantum metrology: Exploiting relativity to improve quantum measurement technologies, Sci. Rep. 4, 4996 (2014).
  25. C. Sabín, J. Kohlrus, D. E. Bruschi, and I. Fuentes, Thermal noise in BEC-phononic gravitational wave detectors, EPJ Quantum Technol. 3, 8 (2016).
  26. D. Rätzel, R. Howl, J. Lindkvist, and I. Fuentes, Dynamical response of Bose–Einstein condensates to oscillating gravitational fields, New J. Phys. 20, 073044 (2018).
  27. D. Hartley, C. Käding, R. Howl, and I. Fuentes, Quantum-enhanced screened dark energy detection, Eur. Phys. J. C 84, 49 (2024).
  28. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463 (1999).
  29. L. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Oxford University Press, Oxford, 2003).
  30. S. Bose, I. Fuentes, A. A. Geraci, S. M. Khan, S. Qvarfort, M. Rademacher, M. Rashid, M. Toroš, H. Ulbricht, and C. C. Wanjura, Massive quantum systems as interfaces of quantum mechanics and gravity, Rev. Mod. Phys. 97, 015003 (2025).
  31. T. Bravo, R. Dennis, D. E. Bruschi, and I. Fuentes, Quantum gravimeters and gradiometers, Patent EP3983829A1, 2020, https://patents.google.com/patent/EP3983829A1/de.
  32. S. S. Szigeti, R. J. Lewis-Swan, and S. A. Haine, Pumped-up SU(1, 1) interferometry, Phys. Rev. Lett. 118, 150401 (2017).
  33. C. Gross, T. Zibold, E. Nicklas, J. Esteve, and M. K. Oberthaler, Nonlinear atom interferometer surpasses classical precision limit, Nature (London) 464, 1165 (2010).
  34. L. Xin, M. Barrios, J. T. Cohen, and M. S. Chapman, Long-lived squeezed ground states in a quantum spin ensemble, Phys. Rev. Lett. 131, 133402 (2023).
  35. W. Muessel, H. Strobel, D. Linnemann, T. Zibold, B. Juliá-Díaz, and M. K. Oberthaler, Twist-and-turn spin squeezing in Bose-Einstein condensates, Phys. Rev. A 92, 023603 (2015).
  36. P. Juschitz, Two-mode phonon squeezing in Bose-Einstein condensates for gravitational wave detection, arXiv:2101.05051.
  37. C. Gross, Spin squeezing, entanglement and quantum metrology with Bose–Einstein condensates, J. Phys. B: At. Mol. Opt. Phys. 45, 103001 (2012).
  38. T. Tufarelli, A. Retzker, M. B. Plenio, and A. Serafini, Input–output Gaussian channels: Theory and application, New J. Phys. 14, 093046 (2012).
  39. A. L. Gaunt, T. F. Schmidutz, I. Gotlibovych, R. P. Smith, and Z. Hadzibabic, Bose-Einstein condensation of atoms in a uniform potential, Phys. Rev. Lett. 110, 200406 (2013).
  40. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett. 96, 010401 (2006).
  41. M. G. A. Paris, Quantum estimation for quantum technology, Int. J. Quantum Inf. 07, 125 (2009).
  42. V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics 5, 222 (2011).
  43. H. Cramér, Mathematical Methods of Statistics (Princeton University Press, Princeton, 1946).
  44. S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72, 3439 (1994).
  45. D. Šafránek, A. R. Lee, and I. Fuentes, Quantum parameter estimation using multi-mode Gaussian states, New J. Phys. 17, 073016 (2015).
  46. Arvind, B. Dutta, N. Mukunda, and R. Simon, The real symplectic groups in quantum mechanics and optics, Pramana J. Phys. 45, 471 (1995).
  47. A. Monras, Phase space formalism for quantum estimation of Gaussian states, arXiv:1303.3682.
  48. O. Pinel, P. Jian, N. Treps, C. Fabre, and D. Braun, Quantum parameter estimation using general single-mode Gaussian states, Phys. Rev. A 88, 040102 (2013).
  49. D. Šafránek and I. Fuentes, Optimal probe states for the estimation of Gaussian unitary channels, Phys. Rev. A 94, 062313 (2016).
  50. A. Monras, Optimal phase measurements with pure Gaussian states, Phys. Rev. A 73, 033821 (2006).
  51. D. Linnemann, H. Strobel, W. Muessel, J. Schulz, R. J. Lewis-Swan, K. V. Kheruntsyan, and M. K. Oberthaler, Quantum-enhanced sensing based on time reversal of nonlinear dynamics, Phys. Rev. Lett. 117, 013001 (2016).
  52. T.-W. Mao, Q. Liu, X.-W. Li, J.-H. Cao, F. Chen, W.-X. Xu, M. K. Tey, Y.-X. Huang, and L. You, Quantum enhanced sensing by echoing spin-nematic squeezing in atomic Bose-Einstein condensate, arXiv:2212.09124.
  53. S. C. Burd, H. M. Knaack, R. Srinivas, C. Arenz, A. L. Collopy, L. J. Stephenson, A. C. Wilson, D. J. Wineland, D. Leibfried, J. J. Bollinger, D. T. C. Allcock, and D. H. Slichter, Experimental speedup of quantum dynamics through squeezing, PRX Quantum 5, 020314 (2024).
  54. J.-C. Jaskula, G. B. Partridge, M. Bonneau, R. Lopes, J. Ruaudel, D. Boiron, and C. I. Westbrook, Acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate, Phys. Rev. Lett. 109, 220401 (2012).
  55. M. Egorov, B. Opanchuk, P. Drummond, B. V. Hall, P. Hannaford, and A. I. Sidorov, Measurement of s-wave scattering lengths in a two-component Bose-Einstein condensate, Phys. Rev. A 87, 053614 (2013).
  56. I. Shammass, S. Rinott, A. Berkovitz, R. Schley, and J. Steinhauer, Phonon dispersion relation of an atomic Bose-Einstein condensate, Phys. Rev. Lett. 109, 195301 (2012).
  57. T. Kraemer, J. Herbig, M. Mark, T. Weber, C. Chin, H.-C. Nägerl, and R. Grimm, Optimized production of a cesium Bose-Einstein condensate, Appl. Phys. B 79, 1013 (2004).
  58. K. M. R. van der Stam, E. D. van Ooijen, R. Meppelink, J. M. Vogels, and P. van der Straten, Large atom number Bose-Einstein condensate of sodium, Rev. Sci. Instrum. 78, 013102 (2007).
  59. W. Hänsel, P. Hommelhoff, T. W. Hänsch, and J. Reichel, Bose-Einstein condensation on a microelectronic chip, Nature (London) 413, 498 (2001).
  60. R. Meppelink, R. A. Rozendaal, S. B. Koller, J. M. Vogels, and P. van der Straten, Thermodynamics of Bose-Einstein-condensed clouds using phase-contrast imaging, Phys. Rev. A 81, 053632 (2010).
  61. D. G. Fried, T. C. Killian, L. Willmann, D. Landhuis, S. C. Moss, D. Kleppner, and T. J. Greytak, Bose-Einstein condensation of atomic hydrogen, Phys. Rev. Lett. 81, 3811 (1998).
  62. E. A. Burt, R. W. Ghrist, C. J. Myatt, M. J. Holland, E. A. Cornell, and C. E. Wieman, Coherence, correlations, and collisions: What one learns about Bose-Einstein condensates from their decay, Phys. Rev. Lett. 79, 337 (1997).
  63. J. Steinhauer, Observation of quantum Hawking radiation and its entanglement in an analogue black hole, Nat. Phys. 12, 959 (2016).
  64. J. Steinhauer, Observation of self-amplifying Hawking radiation in an analogue black-hole laser, Nat. Phys. 10, 864 (2014).
  65. V. Gondret, C. Lamirault, R. Dias, L. Camier, A. Micheli, C. Leprince, Q. Marolleau, J.-R. Rullier, S. Robertson, D. Boiron, and C. I. Westbrook, Observation of entanglement in a cold atom analog of cosmological preheating, arXiv:2506.22024.
  66. P. Mohr, D. Newell, B. Taylor, and E. Tiesinga, CODATA recommended values of the fundamental physical constants: 2022, arXiv:2409.03787.
  67. N. Aghanim et al., Planck 2018 results. VI. Cosmological parameters, Astron. Astrophys. 641, A6 (2020); 652, C4(E) (2021).
  68. Converted from natural units to SI.
  69. J. Stenger, S. Inouye, A. P. Chikkatur, D. M. Stamper-Kurn, D. E. Pritchard, and W. Ketterle, Bragg spectroscopy of a Bose-Einstein condensate, Phys. Rev. Lett. 82, 4569 (1999).
  70. S. S. Szigeti, J. E. Debs, J. J. Hope, N. P. Robins, and J. D. Close, Why momentum width matters for atom interferometry with Bragg pulses, New J. Phys. 14, 023009 (2012).

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Phys. Rev. Research 7, L042051– Published 3 December, 2025
  • Received 14 October 2024
  • Accepted 22 September 2025
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