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

Quenched entanglement harvesting

Adrian Lopez-Raven1,2,*, Robert B. Mann1,2,3,†, and Jorma Louko4,‡

  • *Contact author: adrian.lopez@uwaterloo.ca, a22lopez@uwaterloo.ca, alopezraven@perimeterinstitute.ca
  • †Contact author: rbmann@uwaterloo.ca
  • ‡Contact author: jorma.louko@nottingham.ac.uk

Phys. Rev. D 112, 085001 – Published 6 October, 2025

DOI: https://doi.org/10.1103/lyhy-ftxz

Abstract

Ultracold fermionic atoms in an optical lattice, with a sudden position-dependent change (a quench) in the effective dispersion relation, have been proposed by Rodríguez-Laguna et al. as an analog spacetime test of the Unruh effect. We provide new support for this analog by analyzing the entanglement of a scalar field in a (1+1)-dimensional continuum spacetime with a similar quench, and the harvesting of this entanglement by a pair of Unruh-DeWitt detectors. We present numerical evidence that the concurrence and mutual information harvested by the detectors are qualitatively similar to those in Rindler spacetime, but they exhibit a small yet noticeable variation when the energy pulse created by the quench crosses the detectors. These findings provide further motivation to implement the experimental proposal of Rodríguez-Laguna et al.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (56)

  1. S. J. Summers and R. Werner, The vacuum violates Bell’s inequalities, Phys. Lett. 110A, 257 (1985).
  2. S. J. Summers and R. Werner, Bell’s inequalities and quantum field theory. I. General setting, J. Math. Phys. (N.Y.) 28, 2440 (1987).
  3. A. Valentini, Non-local correlations in quantum electrodynamics, Phys. Lett. 153A, 321 (1991).
  4. B. Reznik, Entanglement from the vacuum, Found. Phys. 33, 167 (2003).
  5. B. Reznik, A. Retzker, and J. Silman, Violating Bell’s inequalities in vacuum, Phys. Rev. A 71, 042104 (2005).
  6. A. Pozas-Kerstjens and E. Martín-Martínez, Harvesting correlations from the quantum vacuum, Phys. Rev. D 92, 064042 (2015).
  7. J. Doukas and B. Carson, Entanglement of two qubits in a relativistic orbit, Phys. Rev. A 81, 062320 (2010).
  8. G. Salton, R. B. Mann, and N. C. Menicucci, Acceleration-assisted entanglement harvesting and rangefinding, New J. Phys. 17, 035001 (2015).
  9. J. Zhang and H. Yu, Entanglement harvesting for Unruh-DeWitt detectors in circular motion, Phys. Rev. D 102, 065013 (2020).
  10. Z. Liu, J. Zhang, and H. Yu, Entanglement harvesting in the presence of a reflecting boundary, J. High Energy Phys. 08 (2021) 020.
  11. Z. Liu, J. Zhang, R. B. Mann, and H. Yu, Does acceleration assist entanglement harvesting?, Phys. Rev. D 105, 085012 (2022).
  12. J. Foo, S. Onoe, and M. Zych, Unruh-deWitt detectors in quantum superpositions of trajectories, Phys. Rev. D 102, 085013 (2020).
  13. C. Suryaatmadja, R. B. Mann, and W. Cong, Entanglement harvesting of inertially moving Unruh-DeWitt detectors in Minkowski spacetime, Phys. Rev. D 106, 076002 (2022).
  14. Z. Liu, J. Zhang, and H. Yu, Entanglement harvesting of accelerated detectors versus static ones in a thermal bath, Phys. Rev. D 107, 045010 (2023).
  15. M. Naeem, K. Gallock-Yoshimura, and R. B. Mann, Mutual information harvested by uniformly accelerated particle detectors, Phys. Rev. D 107, 065016 (2023).
  16. G. V. Steeg and N. C. Menicucci, Entangling power of an expanding universe, Phys. Rev. D 79, 044027 (2009).
  17. M. Cliche and A. Kempf, Vacuum entanglement enhancement by a weak gravitational field, Phys. Rev. D 83, 045019 (2011).
  18. E. Martín-Martínez, A. R. H. Smith, and D. R. Terno, Spacetime structure and vacuum entanglement, Phys. Rev. D 93, 044001 (2016).
  19. S. Kukita and Y. Nambu, Harvesting large scale entanglement in de Sitter space with multiple detectors, Entropy 19, 449 (2017).
  20. L. J. Henderson, R. A. Hennigar, R. B. Mann, A. R. H. Smith, and J. Zhang, Harvesting entanglement from the black hole vacuum, Classical Quantum Gravity 35, 21LT02 (2018).
  21. K. K. Ng, R. B. Mann, and E. Martín-Martínez, Unruh-DeWitt detectors and entanglement: The anti–de Sitter space, Phys. Rev. D 98, 125005 (2018).
  22. L. J. Henderson, R. A. Hennigar, R. B. Mann, A. R. Smith, and J. Zhang, Entangling detectors in anti-de Sitter space, J. High Energy Phys. 05 (2019) 178.
  23. W. Cong, C. Qian, M. R. Good, and R. B. Mann, Effects of horizons on entanglement harvesting, J. High Energy Phys. 10 (2020) 067.
  24. M. P. G. Robbins, L. J. Henderson, and R. B. Mann, Entanglement amplification from rotating black holes, Classical Quantum Gravity 39, 02LT01 (2022).
  25. Q. Xu, S. Ali Ahmad, and A. R. H. Smith, Gravitational waves affect vacuum entanglement, Phys. Rev. D 102, 065019 (2020).
  26. E. Tjoa and R. B. Mann, Harvesting correlations in Schwarzschild and collapsing shell spacetimes, J. High Energy Phys. 08 (2020) 155.
  27. K. Gallock-Yoshimura, E. Tjoa, and R. B. Mann, Harvesting entanglement with detectors freely falling into a black hole, Phys. Rev. D 104, 025001 (2021).
  28. F. Gray, D. Kubizňák, T. May, S. Timmerman, and E. Tjoa, Quantum imprints of gravitational shockwaves, J. High Energy Phys. 11 (2021) 054.
  29. K. Bueley, L. Huang, K. Gallock-Yoshimura, and R. B. Mann, Harvesting mutual information from BTZ black hole spacetime, Phys. Rev. D 106, 025010 (2022).
  30. L. J. Henderson, S. Y. Ding, and R. B. Mann, Entanglement harvesting with a twist, AVS Quantum Sci. 4, 014402 (2022).
  31. J. G. A. Caribé, R. H. Jonsson, M. Casals, A. Kempf, and E. Martín-Martínez, Lensing of vacuum entanglement near Schwarzschild black holes, Phys. Rev. D 108, 025016 (2023).
  32. I.-C. Benea-Chelmus, F. F. Settembrini, G. Scalari, and J. Faist, Electric field correlation measurements on the electromagnetic vacuum state, Nature (London) 568, 202 (2019).
  33. F. F. Settembrini, F. Lindel, A. M. Herter, S. Y. Buhmann, and J. Faist, Detection of quantum-vacuum field correlations outside the light cone, Nat. Commun. 13, 3383 (2022).
  34. F. Lindel, A. M. Herter, J. Faist, and S. Y. Buhmann, Probing vacuum field fluctuations and source radiation separately in space and time, Phys. Rev. Res. 5, 043207 (2023).
  35. F. Lindel, A. Herter, V. Gebhart, J. Faist, and S. Y. Buhmann, Entanglement harvesting from electromagnetic quantum fields, Phys. Rev. A 110, 022414 (2024).
  36. C. Gooding, A. Sachs, R. B. Mann, and S. Weinfurtner, Vacuum entanglement probes for ultra-cold atom systems, New J. Phys. 26, 105001 (2024).
  37. J. Rodríguez-Laguna, L. Tarruell, M. Lewenstein, and A. Celi, Synthetic Unruh effect in cold atoms, Phys. Rev. A 95, 013627 (2017).
  38. A. Kosior, M. Lewenstein, and A. Celi, Unruh effect for interacting particles with ultracold atoms, SciPost Phys. 5, 061 (2018).
  39. J. Louko, Thermality from a Rindler quench, Classical Quantum Gravity 35, 205006 (2018).
  40. W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870 (1976).
  41. B. S. DeWitt, Quantum gravity: The new synthesis, in General Relativity: An Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge University Press, Cambridge, England, 1979), pp. 680–745.
  42. B. A. Juárez-Aubry and J. Louko, Onset and decay of the 1+1 Hawking-Unruh effect: What the derivative-coupling detector saw, Classical Quantum Gravity 31, 245007 (2014).
  43. B. A. Juárez-Aubry and J. Louko, Quantum fields during black hole formation: How good an approximation is the Unruh state?, J. High Energy Phys. 05 (2018) 140.
  44. E. Martín-Martínez and P. Rodriguez-Lopez, Relativistic quantum optics: The relativistic invariance of the light-matter interaction models, Phys. Rev. D 97, 105026 (2018).
  45. E. Martín-Martínez, T. R. Perche, and B. de S. L. Torres, General relativistic quantum optics: Finite-size particle detector models in curved spacetimes, Phys. Rev. D 101, 045017 (2020).
  46. S. A. Fulling and S. N. M. Ruijsenaars, Temperature, periodicity and horizons, Phys. Rep. 152, 135 (1987).
  47. B. S. Kay, Application of linear hyperbolic PDE to linear quantum fields in curved space-times: Especially black holes, time machines and a new semilocal vacuum concept, in Journées Équations aux dérivées partielles, Nantes, 5 au 9 juin 2000, GDR 1151 (CNRS), IX-1 (2000), arXiv:gr-qc/0103056.
  48. Y. Décanini and A. Folacci, Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension, Phys. Rev. D 78, 044025 (2008).
  49. W. K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett. 80, 2245 (1998).
  50. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information, Cambridge Series on Information and the Natural Sciences (Cambridge University Press, Cambridge, England, 2000).
  51. M. Horodecki, P. Horodecki, and R. Horodecki, Separability of mixed states: Necessary and sufficient conditions, Phys. Lett. A 223, 1 (1996).
  52. H. Ollivier and W. H. Zurek, Quantum discord: A measure of the quantumness of correlations, Phys. Rev. Lett. 88, 017901 (2001).
  53. L. Henderson and V. Vedral, Classical, quantum and total correlations, J. Phys. A 34, 6899 (2001).
  54. https://github.com/khalil753/quench/.
  55. Alexander R. H. Smith, Detectors, reference frames, and time, Ph.D. thesis, University of Waterloo, 2017.
  56. Z. Liu, J. Zhang, and H. Yu, Entanglement harvesting of accelerated detectors versus static ones in a thermal bath, Phys. Rev. D 107, 045010 (2023).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation