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  • Open Access

Entanglement harvesting in the presence of cavities

Jannik Ströhle* and Nikolija Momčilović

  • Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany

  • *Contact author: jannik.stroehle@uni-ulm.de

Phys. Rev. Research 8, 023198 – Published 21 May, 2026

DOI: https://doi.org/10.1103/ltdq-y4mf

Abstract

So far, entanglement harvesting has been extensively studied in free-space setups. Here, we provide a detailed analytical and numerical analysis of entanglement harvesting in cavities. Specifically, we couple the quantized electromagnetic field to two identical Gaussian detectors located on the symmetry axis of a cylindrical cavity via Gaussian switching. Our numerical investigations reveal a strong dependence on the cavity length, while showing invariance under changes in the cavity radius in regimes of maximal entanglement. Moreover, we identify different scalings of the detector system parameters for entanglement inside and outside the light cone. Finally, we uncover a strong dependence of the harvested correlations on the cavity-induced parity of the electromagnetic field.

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References (56)

  1. S. J. Summers and R. Werner, The vacuum violates Bell’s inequalities, Phys. Lett. A 110, 257 (1985).
  2. S. J. Summers and R. Werner, Bell’s inequalities and quantum field theory. i. General setting, J. Math. Phys. 28, 2440 (1987).
  3. A. Valentini, Non-local correlations in quantum electrodynamics, Phys. Lett. A 153, 321 (1991).
  4. B. Reznik, A. Retzker, and J. Silman, Violating Bell’s inequalities in vacuum, Phys. Rev. A 71, 042104 (2005).
  5. B. Reznik, Entanglement from the vacuum, Found. Phys. 33, 167 (2003).
  6. A. Pozas-Kerstjens and E. Martin-Martinez, Harvesting correlations from the quantum vacuum, Phys. Rev. D 92, 064042 (2015).
  7. E. Martín-Martínez, A. R. Smith, and D. R. Terno, Spacetime structure and vacuum entanglement, Phys. Rev. D 93, 044001 (2016).
  8. E. P. Gale and M. Zych, Relativistic Unruh-DeWitt detectors with quantized center of mass, Phys. Rev. D 107, 056023 (2023).
  9. N. Stritzelberger, L. J. Henderson, V. Baccetti, N. C. Menicucci, and A. Kempf, Entanglement harvesting with coherently delocalized matter, Phys. Rev. D 103, 016007 (2021).
  10. C. Sabín, B. Peropadre, M. del Rey, and E. Martín-Martínez, Extracting past-future vacuum correlations using circuit QED, Phys. Rev. Lett. 109, 033602 (2012).
  11. F. Benatti and R. Floreanini, Entanglement generation in uniformly accelerating atoms: Reexamination of the Unruh effect, Phys. Rev. A 70, 012112 (2004).
  12. G. Salton, R. B. Mann, and N. C. Menicucci, Acceleration-assisted entanglement harvesting and rangefinding, New J. Phys. 17, 035001 (2015).
  13. Z. Liu, J. Zhang, R. B. Mann, and H. Yu, Does acceleration assist entanglement harvesting? Phys. Rev. D 105, 085012 (2022).
  14. J. Zhang and H. Yu, Entanglement harvesting for Unruh-DeWitt detectors in circular motion, Phys. Rev. D 102, 065013 (2020).
  15. A. Pozas-Kerstjens and E. Martín-Martínez, Entanglement harvesting from the electromagnetic vacuum with hydrogenlike atoms, Phys. Rev. D 94, 064074 (2016).
  16. F. Lindel, A. Herter, V. Gebhart, J. Faist, and S. Y. Buhmann, Entanglement harvesting from electromagnetic quantum fields, Phys. Rev. A 110, 022414 (2024).
  17. J. Foo, R. B. Mann, and M. Zych, Entanglement amplification between superposed detectors in flat and curved spacetimes, Phys. Rev. D 103, 065013 (2021).
  18. K. Gallock-Yoshimura and R. B. Mann, Entangled detectors nonperturbatively harvest mutual information, Phys. Rev. D 104, 125017 (2021).
  19. M. Naeem, K. Gallock-Yoshimura, and R. B. Mann, Mutual information harvested by uniformly accelerated particle detectors, Phys. Rev. D 107, 065016 (2023).
  20. A. Reiserer and G. Rempe, Cavity-based quantum networks with single atoms and optical photons, Rev. Mod. Phys. 87, 1379 (2015).
  21. A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys. 93, 025005 (2021).
  22. K. Joulain, R. Carminati, J.-P. Mulet, and J.-J. Greffet, Definition and measurement of the local density of electromagnetic states close to an interface, Phys. Rev. B 68, 245405 (2003).
  23. A. Cazé, R. Pierrat, and R. Carminati, Spatial coherence in complex photonic and plasmonic systems, Phys. Rev. Lett. 110, 063903 (2013).
  24. D. Kleppner, Inhibited spontaneous emission, Phys. Rev. Lett. 47, 233 (1981).
  25. S. Haroche, Entanglement, decoherence and the quantum/classical boundary, Phys. Today 51(7), 36 (1998).
  26. J.-M. Raimond, M. Brune, and S. Haroche, Manipulating quantum entanglement with atoms and photons in a cavity, Rev. Mod. Phys. 73, 565 (2001).
  27. A. Reiserer, Colloquium: Cavity-enhanced quantum network nodes, Rev. Mod. Phys. 94, 041003 (2022).
  28. M. J. Kastoryano, F. Reiter, and A. S. Sørensen, Dissipative preparation of entanglement in optical cavities, Phys. Rev. Lett. 106, 090502 (2011).
  29. E. Martín-Martínez, E. G. Brown, W. Donnelly, and A. Kempf, Sustainable entanglement production from a quantum field, Phys. Rev. A 88, 052310 (2013).
  30. Z. Liu, J. Zhang, and H. Yu, Entanglement harvesting in the presence of a reflecting boundary, Adv. High Energy Phys. 2021, 1 (2021).
  31. D. Barman and B. R. Majhi, Are multiple reflecting boundaries capable of enhancing entanglement harvesting? Phys. Rev. D 108, 085007 (2023).
  32. G. Morigi, J. Eschner, S. Mancini, and D. Vitali, Coherent generation of EPR-entangled light pulses mediated by a single trapped atom, Phys. Rev. A 73, 033822 (2006).
  33. P. Shi, L.-B. Chen, Y.-J. Gu, and W.-D. Li, Generation of multilevel maximally entangled states under large atom-cavity detuning, J. Opt. Soc. Am. B 30, 889 (2013).
  34. F. Arreyes, F. Escudero, J. S. Ardenghi, and A. Juan, Entanglement harvesting in buckled honeycomb lattices by vacuum fluctuations in a microcavity, J. Phys.: Condens. Matter 36, 505701 (2024).
  35. J. S. Ardenghi, Entanglement harvesting in double-layer graphene by vacuum fluctuations in a microcavity, Phys. Rev. D 98, 045006 (2018).
  36. T. C. H. Liew and V. Savona, Multimode entanglement in coupled cavity arrays, New J. Phys. 15, 025015 (2013).
  37. C.-J. Yang, J.-H. An, W. Yang, and Y. Li, Generation of stable entanglement between two cavity mirrors by squeezed-reservoir engineering, Phys. Rev. A 92, 062311 (2015).
  38. Q.-G. Chen, M.-Y. Liu, X.-X. Huang, J. Chen, and W. Xiong, Hybrid cavity-magnon optomechanics: Tailoring bipartite and tripartite macroscopic entanglement, Chaos Solitons Fractals 202, 117472 (2026).
  39. M.-Y. Liu, Y. Gong, J. Chen, Y.-W. Wang, and W. Xiong, Nonreciprocal microwave–optical entanglement in Kerr-modified cavity optomagnomechanics, Chin. Phys. B 34, 057202 (2025).
  40. J. Chen, X.-G. Fan, W. Xiong, D. Wang, and L. Ye, Nonreciprocal photon-phonon entanglement in Kerr-modified spinning cavity magnomechanics, Phys. Rev. A 109, 043512 (2024).
  41. J. Chen, X.-G. Fan, W. Xiong, D. Wang, and L. Ye, Nonreciprocal entanglement in cavity-magnon optomechanics, Phys. Rev. B 108, 024105 (2023).
  42. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2010).
  43. R. Lopp and E. Martín-Martínez, Quantum delocalization, gauge, and quantum optics: Light-matter interaction in relativistic quantum information, Phys. Rev. A 103, 013703 (2021).
  44. J. Ströhle and R. Lopp, Dimensional reduction in quantum optics, Phys. Rev. Res. 6, 013285 (2024).
  45. This simplified expression is based on the assumption that the local correlations for two identical detectors are identical. This assumption holds inside a cylindrical cavity if, in addition, a symmetric arrangement of the detectors is provided.
  46. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, Theory of Bose-Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463 (1999).
  47. E. McKay, A. Lupascu, and E. Martín-Martínez, Finite sizes and smooth cutoffs in superconducting circuits, Phys. Rev. A 96, 052325 (2017).
  48. L. Guo, A. Grimsmo, A. F. Kockum, M. Pletyukhov, and G. Johansson, Giant acoustic atom: A single quantum system with a deterministic time delay, Phys. Rev. A 95, 053821 (2017).
  49. J. Louko and A. Satz, How often does the Unruh–DeWitt detector click? regularization by a spatial profile, Classical Quantum Gravity 23, 6321 (2006).
  50. Note that J1(χm)−2∼χm.
  51. To observe the Gaussian scaling, it is more suitable to reformulate the erfc terms by means of Faddeeva functions.
  52. Asymptotically, we use the approximation χm/R∼mπ/R, which proves with an error of ∼(4m)−1, cf. [56] (9.5.12), sufficient for our task.
  53. Note that for the local correlations this is, as far as the single detectors do not influence each other by having overlapping wave functions, true not only for two but for an arbitrary number of detectors of arbitrary positioning in the cavity. For the nonlocal correlations, this argument relies heavily on having only two detectors and their axial symmetric alignment.
  54. The quantum numbers can take the values (k,l,m) with k=0,2,4,6,..., l=0,1,2,3,..., and m=−l,−l+1,...,l.
  55. For cylindrical coordinates, we define r=(ρcos(ϕ),ρsin(ϕ),z)T and for spherical coordinates we use r=(rcos(ϕ)sin(ϑ),rsin(ϕ)sin(ϑ),rcos(ϑ))T.
  56. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (US Government Printing Office, Washington DC, 1968), Vol. 55.

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