Perturbative photon production in a dispersive medium

  • Francesco Belgiorno
  • Sergio Luigi Cacciatori
  • Francesco Dalla PiazzaEmail author
Regular Article


We investigate photon pair-creation in a dispersive dielectric medium induced by the presence of a spacetime varying dielectric constant. Our aim is to examine the possibility to observe new phenomena of pair creation induced by travelling dielectric perturbations e.g. created by laser pulses by means of the Kerr effect. In this perspective, we adopt a semi-phenomenological version of the Hopfield model in which a space-time dependent dielectric susceptibility appears. We focus our attention on perturbation theory, and provide general formulas for the photon production induced by a local but arbitrarily spacetime dependent refractive index perturbation. As an example, we further explore the case of a uniformly travelling perturbation, and provide examples of purely time-dependent perturbations.


Quantum Optics 


  1. 1.
    W. Heisenberg, H. Euler, Z. Phys. 98, 714 (1936) English translation in arXiv:physics/0605038ADSCrossRefGoogle Scholar
  2. 2.
    J. Schwinger, Phys. Rev. 82, 664 (1951)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    J. Schwinger, Proc. Natl. Acad. Sci. 89, 4091 (1992)ADSCrossRefMathSciNetGoogle Scholar
  4. 4.
    J. Schwinger, Proc. Natl. Acad. Sci. 89, 11118 (1992)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    J. Schwinger, Proc. Natl. Acad. Sci. 90, 958 (1993)ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    J. Schwinger, Proc. Natl. Acad. Sci. 90, 2105 (1993)ADSCrossRefMathSciNetGoogle Scholar
  7. 7.
    J. Schwinger, Proc. Natl. Acad. Sci. 90, 4505 (1993)ADSCrossRefMathSciNetGoogle Scholar
  8. 8.
    J. Schwinger, Proc. Natl. Acad. Sci. 90, 7285 (1993)ADSCrossRefMathSciNetGoogle Scholar
  9. 9.
    J. Schwinger, Proc. Natl. Acad. Sci. 91, 6473 (1994)ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    J.J. Hopfield, Phys. Rev. 112, 1555 (1958)ADSCrossRefzbMATHGoogle Scholar
  11. 11.
    U. Fano, Rev. Mod. Phys. 29, 74 (1957)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  12. 12.
    C. Kittel, Quantum Theory of Solids (Wiley, New York, 1987)Google Scholar
  13. 13.
    A.S. Davydov, Teoria del solido (Mir, Moscow, 1984)Google Scholar
  14. 14.
    F. Belgiorno, S.L. Cacciatori, F. Dalla Piazza, submittedGoogle Scholar
  15. 15.
    R.W. Boyd, Nonlinear Optics (Academic Press, Boston, 2008)Google Scholar
  16. 16.
    F. Belgiorno, S.L. Cacciatori, G. Ortenzi, V.G. Sala, D. Faccio, Phys. Rev. Lett. 104, 140403 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    F. Dalla Piazza, F. Belgiorno, S.L. Cacciatori, D. Faccio, Phys. Rev. A 85, 033833 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    R. Schützhold, G. Plunien, G. Soff, Phys. Rev. A 58, 1783 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    F. Dalla Piazza, F. Belgiorno, S.L. Cacciatori, D. Faccio, forthcoming.Google Scholar
  20. 20.
    L.G. Suttorp, J. Phys. A 40, 3697 (2007)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    P.W. Milonni, J. Mod. Opt. 42, 1191 (1995)CrossRefMathSciNetGoogle Scholar
  22. 22.
    V.L. Ginzburg, Applications of electrodynamics in theoretical physics and astrophysics (Taylor and Francis Ltd, London, 1989)Google Scholar
  23. 23.
    L.G. Suttorp, A.J. van Wonderen, Europhys. Lett. 67, 766 (2004)ADSCrossRefGoogle Scholar
  24. 24.
    L.G. Suttorp, M. Wubs, Phys. Rev. A 70, 013816 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    A. Luks, V. Perinová, Quantum Aspects of Light Propagation (Springer, Berlin, 2009)Google Scholar
  26. 26.
    H. Minkowski, Die Grundgleichungen für die elektromagnetischen Vorgänge in bewegten Körpern. Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. S. 53111 (1908)Google Scholar
  27. 27.
    E.J. Post, Formal structure of electromagnetics: general covariance and electromagnetics (North-Holland, Amsterdam, 1962)Google Scholar
  28. 28.
    P. Penfield, H.A. Haus, Electrodynamics of moving media (M.I.T. Press, Cambridge, 1967)Google Scholar
  29. 29.
    M. Petev, N. Westerberg, D. Moss, E. Rubino, C. Rimoldi, S.L. Cacciatori, F. Belgiorno, D. Faccio, arXiv:1303.5967 [physics.optics]Google Scholar
  30. 30.
    E. Rubino et al., New J. Phys. 13, 085005 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    S. Finazzi, I. Carusotto, Phys. Rev. A 87, 023803 (2013)ADSCrossRefGoogle Scholar
  32. 32.
    S. Finazzi, I. Carusotto, arXiv:1303.4990 [physics. optics]Google Scholar
  33. 33.
    F. Belgiorno, S.L. Cacciatori, G. Ortenzi, L. Rizzi, V. Gorini, D. Faccio, Phys. Rev. D 83, 024015 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints. Springer Series in Nuclear and Particle Physics (Springer, Berlin, 1990)Google Scholar
  35. 35.
    M. Henneaux, C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, 1994)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Francesco Belgiorno
    • 1
  • Sergio Luigi Cacciatori
    • 2
    • 3
  • Francesco Dalla Piazza
    • 4
    Email author
  1. 1.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly
  2. 2.Dipartimento di Scienza e Alta TecnologiaUniversità dell’InsubriaComoItaly
  3. 3.INFN sezione di MilanoMilanoItaly
  4. 4.Dipartimento di MatematicaUniversità “La Sapienza”RomaItaly

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