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Entangled photon states in consecutive nonlinear optical interactions

  • A. V. Rodionov
  • A. S. Chirkin
Nonlinear Dynamics

Abstract

Quantum theory of two consecutive light-wave parametric interactions with aliquant frequencies produced by a common pump wave in a crystal is developed. Using the differentiation method, the unitary evolution operator of the system is reduced to an ordered form that allows the calculation of the field state and the statistical characteristics of interacting waves. It is shown that, for the initial vacuum field state, the created photons obey the super-Poisson statistics at the interacting frequencies and are in a multiparticle entangled state.

PACS numbers

42.50.Dv 42.65.Ky 03.67.Mn 03.65.Ud 

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References

  1. 1.
    L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge Univ. Press, Cambridge, 1995; Nauka, Moscow, 2000).Google Scholar
  2. 2.
    M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988); M. D. Reid, Phys. Rev. A 40, 913 (1989).CrossRefADSGoogle Scholar
  3. 3.
    N. Korolkova, G. Leuchs, R. Loudon, et al., Phys. Rev. A 65, 052306 (2002); R. Schnabel, W. P. Bowen, N. Treps, et al., Phys. Rev. A 67, 012316 (2003).Google Scholar
  4. 4.
    The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation, Ed. by D. Bouwmeester, A. K. Ekert, and A. Zeilinger (Springer, Berlin, 2000; Postmarket, Moscow, 2002).Google Scholar
  5. 5.
    D. N. Klyshko, Photons and Nonlinear Optics (Nauka, Moscow, 1980).Google Scholar
  6. 6.
    J. S. Bell, Physics (Long Island City, N.Y.) 1, 195 (1964).Google Scholar
  7. 7.
    S. J. Freedman and J. S. Clauser, Phys. Rev. Lett. 28, 938 (1972).ADSGoogle Scholar
  8. 8.
    D. M. Greenberger, M. A. Horne, A. Shimony, et al., Am. J. Phys. 58, 1131 (1990); D. M. Greenberger, M. A. Horne, and A. Zeilinger, Phys. Today 46 (8), 22 (1993).CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    D. Bouwmeester, J.-W. Pan, M. Daniell, et al., Phys. Rev. Lett. 82, 1345 (1999).CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    J.-W. Pan, M. Daniell, S. Gasparoni, et al., Phys. Rev. Lett. 86, 4435 (2001).CrossRefADSGoogle Scholar
  11. 11.
    M. Eibl, S. Gaertner, M. Bourennane, et al., Phys. Rev. Lett. 90, 200403 (2003).Google Scholar
  12. 12.
    N. Korolkova and G. Leuchs, in Coherence and Statistics of Photons and Atoms, Ed. by J. Perina (Wiley, New York, 2001), p. 111.Google Scholar
  13. 13.
    E. Yu. Morozov and A. S. Chirkin, J. Opt. A: Pure Appl. Opt. 5, 233 (2003).CrossRefGoogle Scholar
  14. 14.
    A. S. Chirkin, V. V. Volkov, G. D. Laptev, et al., Kvantovaya Élektron. (Moscow) 30, 847 (2000).CrossRefGoogle Scholar
  15. 15.
    N. Ya. Vilenkin, Special Functions and the Theory of Group Representations (Nauka, Moscow, 1965; American Mathematical Society, Providence, R.I., 1968).Google Scholar
  16. 16.
    J. Wei and E. Norman, J. Math. Phys. 4, 575 (1963).MathSciNetGoogle Scholar
  17. 17.
    M. J. Collett, Phys. Rev. A 38, 2233 (1988).ADSMathSciNetGoogle Scholar
  18. 18.
    I. V. Bargatin, B. A. Grishanin, and V. N. Zadkov, Usp. Fiz. Nauk 171, 625 (2001) [Phys. Usp. 44, 597 (2001)].Google Scholar
  19. 19.
    A. V. Burlakov, M. V. Chekhova, O. A. Karabutova, et al., Phys. Rev. A 60, R4209 (1999); L. A. Krivitskii, S. P. Kulik, A. N. Penin, et al., Zh. Éksp. Teor. Fiz. 124, 943 (2003) [JETP 97, 846 (2003)].Google Scholar
  20. 20.
    S. A. Akhmanov, Yu. E. D’yakov, and A. S. Chirkin, Introduction to Statistical Radio Physics and Optics (Nauka, Moscow, 1981).Google Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2004

Authors and Affiliations

  • A. V. Rodionov
    • 1
  • A. S. Chirkin
    • 1
  1. 1.Faculty of PhysicsMoscow State UniversityVorob’evy gory, MoscowRussia

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