Entanglement harvesting with moving mirrors

  • Wan CongEmail author
  • Erickson Tjoa
  • Robert B. Mann
Open Access
Regular Article - Theoretical Physics


We study the phenomenon of entanglement extraction from the vacuum of a massless scalar field in (1 + 1) dimensional spacetime in presence of a moving Dirichlet boundary condition, i.e. mirror spacetime, using two inertial Unruh-DeWitt detectors. We consider a variety of non-trivial trajectories for these accelerating mirrors and find (1) an entanglement inhibition phenomenon similar to that recently seen for black holes, as well as (2) trajectory-independent entanglement enhancement in some regimes. We show that the qualitative result obtained is the same for both linear and derivative couplings of the detector with the field.


2D Gravity Black Holes Models of Quantum Gravity 


Open Access

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  1. [1]
    L. Bombelli, R.K. Koul, J. Lee and R.D. Sorkin, A Quantum Source of Entropy for Black Holes, Phys. Rev. D 34 (1986) 373 [INSPIRE].
  2. [2]
    M. Srednicki, Entropy and area, Phys. Rev. Lett. 71 (1993) 666 [hep-th/9303048] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    S.J. Summers and R. Werner, The vacuum violates bells inequalities, Phys. Lett. A 110 (1985) 257.Google Scholar
  5. [5]
    A. Valentini, Non-local correlations in quantum electrodynamics, Phys. Lett. A 153 (1991) 321.Google Scholar
  6. [6]
    W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
  7. [7]
    B.S. DeWitt, Quantum gravity: the new synthesis, in General Relativity: An Einstein Centenary Survey, pp. 680-745 (1980) [INSPIRE].
  8. [8]
    G. Salton, R.B. Mann and N.C. Menicucci, Acceleration-assisted entanglement harvesting and rangefinding, New J. Phys. 17 (2015) 035001 [arXiv:1408.1395] [INSPIRE].
  9. [9]
    A. Pozas-Kerstjens and E. Martin-Martinez, Harvesting correlations from the quantum vacuum, Phys. Rev. D 92 (2015) 064042 [arXiv:1506.03081] [INSPIRE].
  10. [10]
    E. Martin-Martinez, A.R.H. Smith and D.R. Terno, Spacetime structure and vacuum entanglement, Phys. Rev. D 93 (2016) 044001 [arXiv:1507.02688] [INSPIRE].
  11. [11]
    G.L. Ver Steeg and N.C. Menicucci, Entangling power of an expanding universe, Phys. Rev. D 79 (2009) 044027 [arXiv:0711.3066] [INSPIRE].
  12. [12]
    C.M. Wilson et al., Observation of the dynamical casimir effect in a superconducting circuit, Nature 479 (2011) 376 [arXiv:1105.4714].ADSCrossRefGoogle Scholar
  13. [13]
    P. Lahteenmaki, G.S. Paraoanu, J. Hassel and P.J. Hakonen, Dynamical Casimir effect in a Josephson metamaterial, Proc. Nat. Acad. Sci. 110 (2013) 4234 [arXiv:1111.5608] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    N. Birrell and P. Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics, Cambridge University Press (1984).Google Scholar
  15. [15]
    N. Suzuki, Accelerated detector nonlinearly coupled to a scalar field, Class. Quant. Grav. 14 (1997) 3149 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    P.C.W. Davies, Z.X. Liu and A.C. Ottewill, Particle Detectors in the Presence of Boundaries, Class. Quant. Grav. 6 (1989) 1041 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  17. [17]
    L. Hodgkinson, Particle detectors in curved spacetime quantum field theory, Ph.D. Thesis (2013) [arXiv:1309.7281] [INSPIRE].
  18. [18]
    R.D. Carlitz and R.S. Willey, Reflections on moving mirrors, Phys. Rev. D 36 (1987) 2327 [INSPIRE].
  19. [19]
    M.R.R. Good, P.R. Anderson and C.R. Evans, Time Dependence of Particle Creation from Accelerating Mirrors, Phys. Rev. D 88 (2013) 025023 [arXiv:1303.6756] [INSPIRE].
  20. [20]
    M.R.R. Good, P.R. Anderson and C.R. Evans, Mirror Reflections of a Black Hole, Phys. Rev. D 94 (2016) 065010 [arXiv:1605.06635] [INSPIRE].
  21. [21]
    M.R.R. Good, K. Yelshibekov and Y.C. Ong, On Horizonless Temperature with an Accelerating Mirror, JHEP 03 (2017) 013 [arXiv:1611.00809] [INSPIRE].
  22. [22]
    M.R.R. Good and E.V. Linder, Eternal and evanescent black holes and accelerating mirror analogs, Phys. Rev. D 97 (2018) 065006 [arXiv:1711.09922] [INSPIRE].
  23. [23]
    L.J. Henderson, R.A. Hennigar, R.B. Mann, A.R.H. Smith and J. Zhang, Harvesting Entanglement from the Black Hole Vacuum, Class. Quant. Grav. 35 (2018) 21LT02 [arXiv:1712.10018] [INSPIRE].
  24. [24]
    P.R. Anderson, M.R.R. Good and C.R. Evans, Black hole-moving mirror I: An exact correspondence, in Proceedings, 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories (MG14) (in 4 Volumes), Rome, Italy, July 12-18, 2015, vol. 2, pp. 1701-1704 (2017) [] [arXiv:1507.03489] [INSPIRE].
  25. [25]
    E. Martin-Martinez and J. Louko, (1 + 1)D Calculation provides evidence that quantum entanglement survives a firewall, Phys. Rev. Lett. 115 (2015) 031301 [arXiv:1502.07749] [INSPIRE].
  26. [26]
    R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey and D.E. Knuth, On the lambert-w function, Adv. Comput. Math. 5 (1996) 329.MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    M.R.R. Good, P.R. Anderson and C.R. Evans, Black hole-moving mirror II: Particle creation, in Proceedings, 14th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics and Relativistic Field Theories (MG14) (in 4 Volumes), Rome, Italy, July 12-18, 2015, vol. 2, pp. 1705-1708 (2017) [] [arXiv:1507.05048] [INSPIRE].
  28. [28]
    B.A. Juárez-Aubry and J. Louko, Onset and decay of the 1 + 1 Hawking-Unruh effect: what the derivative-coupling detector saw, Class. Quant. Grav. 31 (2014) 245007 [arXiv:1406.2574] [INSPIRE].
  29. [29]
    A. Sachs, R.B. Mann and E. Martin-Martinez, Entanglement harvesting and divergences in quadratic Unruh-DeWitt detector pairs, Phys. Rev. D 96 (2017) 085012 [arXiv:1704.08263] [INSPIRE].
  30. [30]
    E.G. Brown and J. Louko, Smooth and sharp creation of a Dirichlet wall in 1 + 1 quantum field theory: how singular is the sharp creation limit?, JHEP 08 (2015) 061 [arXiv:1504.05269] [INSPIRE].
  31. [31]
    L. Sriramkumar and T. Padmanabhan, Response of finite time particle detectors in noninertial frames and curved space-time, Class. Quant. Grav. 13 (1996) 2061 [gr-qc/9408037] [INSPIRE].
  32. [32]
    R.B. Mann and S.F. Ross, The D → 2 limit of general relativity, Class. Quant. Grav. 10 (1993) 1405 [gr-qc/9208004] [INSPIRE].
  33. [33]
    T. Ohta and R.B. Mann, Canonical reduction of two-dimensional gravity for particle dynamics, Class. Quant. Grav. 13 (1996) 2585 [gr-qc/9605004] [INSPIRE].
  34. [34]
    C. Romero and F. Dahia, Theories of gravity in (2 + 1)-dimensions, Int. J. Theor. Phys. 33 (1994) 2091 [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of WaterlooWaterlooCanada
  2. 2.Institute for Quantum ComputingUniversity of WaterlooWaterlooCanada

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