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Quantum uncertainty and its role in nonlinear propagation of a nonlinear soliton in a lightguide

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An exact solution of the Schrödinger quantum equation is used to investigate the evolution of a fundamental optical soliton in its proper waveguide having a Kerr nonlinearity. It is established that the quantum fluctuations grow unceasingly over the entire length of the nonlinear propagation, so that the soliton is ultimately annihilated. A four-photon interaction model is used to clarify the physical nature of this phenomenon. It is shown that the effects considered restrict the possibility of producing quantum squeezed states of a light pulse.

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Literature Cited

  1. 1.

    S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Pulses [in Russian], Nauka, Moscow (1988).

  2. 2.

    V. A. Vysloukh and A. V. Ivanov, Izv. Akad. Nauk SSSR, Ser. Fiz.,52, 359 (1988).

  3. 3.

    S. J. Carter, P. D. Drummond, M. D. Reid, and R. M. Shelby, Phys. Rev. Lett.,58, 1841 (1987).

  4. 4.

    P. D. Drummond and S. J. Carter, J. Opt. Soc. Am. B,4, 1565, (1987).

  5. 5.

    K. Watanabe, H. Nakano, A. Honold, and Y. Yamamoto, Phys. Rev. Lett.,62, 2257 (1987).

  6. 6.

    B. Yurke and M. J. Potasek, J. Opt. Soc. Am. B,6, 1227 (1989).

  7. 7.

    H. Haus, K. Watanabe, and Y. Yamamoto, ibid.,6, 1138 (1989).

  8. 8.

    A. V. Belinskii and A. S. Chirkin, Kvantovaya Élektron. (Moscow),16, 2570 (1989).

  9. 9.

    A. V. Belinskii and A. S. Chirkin, Zh. Éksp., Teor. Fiz.,98, 407 (1990).

  10. 10.

    S. A. Akhmanov, A. V. Belinskii, and A. S. Chirkin, in: New Physical Principles of Optical Data Processing [in Russian], S. A. Akhmanov and M. A. Vorontsov, (eds.), Nauka, Moscow (1990), pp. 83–194.

  11. 11.

    Y. Lai and H. A. Haus, Phys. Rev. A,40, 844, 854 (1989).

  12. 12.

    A. V. Belinskii, Izv. Akad. Nauk SSSR, Ser. Fiz.,55, No. 2 (1991).

  13. 13.

    A. V. Belinskii, Zh. Éksp. Teor. Fiz.,99, No. 3 (1991).

  14. 14.

    S. A. Akhmanov, Yu. E. D'yakov, and A. S. Chirkin, Introduction to Statistical Radiophysics and Optics [in Russian], Nauka, Moscow (1981), p. 181.

  15. 15.

    J. P. Gordon and H. A. Haus, Opt. Lett.,11, 665 (1986).

  16. 16.

    D. N. Klyshko, Phys. Letts. A,137, 334 (1989).

  17. 17.

    D. N. Smirnov and A. S. Troshin, Usp. Fiz. Nauk,153, 233 (1987).

  18. 18.

    Yu. M. Golubev and I. V. Sokolov, Zh. Éksp. Teor. Fiz.,87, 408 (1984).

  19. 19.

    S. Ya. Kilin, Quantum Optics. Fields and Their Detection [in Russian], Nauka i tekhnika, Minsk (1990).

  20. 20.

    A. N. Oraevskii, Squeezed States of Electromagnetic Field [in Russian], Lebedev Phys. Inst. Preprint No. 232, Moscow (1988).

  21. 21.

    A. I. Zhiliba, “Quantum statistics of electromagnetic waves in quadratically nonlinear processes,”, Doctoral dissertation Inst. of Atmospheric Optics, Siberian Div., USSR Academy of Sciences, Tomsk (1986).

  22. 22.

    K. Wodkiewicz and M. S. Zubairy, Phys. Rev. A,27, 2003 (1983).

  23. 23.

    A. N. Oraevskii, Kvantovaya Élektron.,14, 1525 (1987).

  24. 24.

    A. N. Oraevskii, Zh. Éksp. Teor. Fiz.,95, 59 (1989).

  25. 25.

    A. B. Grudinin, V. N. Men'shov, and T. N. Fursa, ibid.,97, 449 (1990).

  26. 26.

    V. P. Bykov and V. I. Tatarskii, ibid.,96, 528 (1989).

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Belinskii, A.V. Quantum uncertainty and its role in nonlinear propagation of a nonlinear soliton in a lightguide. J Russ Laser Res 12, 464–479 (1991). https://doi.org/10.1007/BF01140236

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  • Soliton
  • Exact Solution
  • Interaction Model
  • Entire Length
  • Light Pulse