Optics and Spectroscopy

, Volume 94, Issue 5, pp 651–665 | Cite as

Optical experiments beyond the quantum limit: Squeezing, entanglement, and teleportation

  • R. Schnabel
  • W. P. Bowen
  • N. Treps
  • B. Buchler
  • T. C. Ralph
  • P. K. Lam
  • H. -A. Bachor
Entangled States in Optics


Results of experiments recently performed are reported, in which two optical parametric amplifiers were set up to generate two independently quadrature squeezed continuous wave laser beams. The transformation of quadrature squeezed states into polarization squeezed states and into states with spatial quantum correlations is demonstrated. By utilizing two squeezed laser beams, a polarization squeezed state exhibiting three simultaneously squeezed Stokes operator variances was generated. Continuous variable polarization entanglement was generated and the Einstein-Podolsky-Rosen paradox was observed. A pair of Stokes operators satisfied both the inseparability criterion and the conditional variance criterion. Values of 0.49 and 0.77, respectively, were observed, with entanglement requiring values below unity. The inseparability measure of the observed quadrature entanglement was 0.44. This value is sufficient for a demonstration of quantum teleportation, which is the next experimental goal of the authors.


Second Harmonic Generator Shot Noise Quantum Noise Stokes Parameter Polarize Beam Splitter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    H.-A. Bachor, A Guide to Experiments in Quantum Optics (Wiley-VCH, Weinheim, 1998).zbMATHGoogle Scholar
  2. 2.
    M. Xiao, L.-A. Wu, and H. J. Kimble, Phys. Rev. Lett. 59, 278 (1987).CrossRefADSGoogle Scholar
  3. 3.
    K. McKenzie, D. A. Shaddock, D. E. McClelland, et al., Phys. Rev. Lett. 88, 231102 (2002).Google Scholar
  4. 4.
    P. Grangier, R. E. Slusher, B. Yurke, and A. LaPorta, Phys. Rev. Lett. 59, 2153 (1987).CrossRefADSGoogle Scholar
  5. 5.
    W. Bowen, R. Schnabel, H.-A. Bachor, and P. K. Lam, Phys. Rev. Lett. 88, 093601 (2002).Google Scholar
  6. 6.
    Z. Y. Ou, S. F. Pereira, H. J. Kimble, and K. C. Peng, Phys. Rev. Lett. 68, 3663 (1992).CrossRefADSGoogle Scholar
  7. 7.
    Ch. Silberhorn, P. K. Lam, O. Weiß, et al., Phys. Rev. Lett. 86, 4267 (2001).CrossRefADSGoogle Scholar
  8. 8.
    W. Bowen, N. Treps, R. Schnabel, and P. K. Lam, Phys. Rev. Lett. 89, 253601 (2002).Google Scholar
  9. 9.
    A. Furusawa, J. L. Sørensen, S. L. Braunstein, et al., Science 282, 706 (1998).CrossRefADSGoogle Scholar
  10. 10.
    E. Polzik, J. Carri, and H. J. Kimble, Appl. Phys. B 55, 279 (1992); F. Marin, A. Bramati, V. Jost, and E. Giacobino, Opt. Commun. 140, 146 (1997).CrossRefADSGoogle Scholar
  11. 11.
    C. Fabre, J. B. Fouet, and A. Maítre, Opt. Lett. 25, 76 (1999).CrossRefADSGoogle Scholar
  12. 12.
    S.-T. Ho, P. Kumar, and J. H. Shapiro, Phys. Rev. A 37, 2017 (1988).CrossRefADSGoogle Scholar
  13. 13.
    M. Kolobov and C. Fabre, Phys. Rev. Lett. 85, 3789 (2000).CrossRefADSGoogle Scholar
  14. 14.
    The displacement experiment was done in collaboration with the Université Pierre et Marie Curie, Paris.Google Scholar
  15. 15.
    N. Treps, U. L. Andersen, B. Buchler, et al., Phys. Rev. Lett. 88, 203601 (2002).Google Scholar
  16. 16.
    M. I. Kolobov, Rev. Mod. Phys. 71, 1539 (1999).CrossRefADSGoogle Scholar
  17. 17.
    L. A. Lugiato, A. Gatti, and H. Wiedemann, in Quantum Fluctuations: Proceedings of the Les Houches Summer School of Theoretical Physics, Les Houches, 1995, Ed. by S. Reynaud, E. Giacobino, and J. Zinn-Justin (North-Holland, Amsterdam, 1997), p. 431.Google Scholar
  18. 18.
    M. Kolobov, Rev. Mod. Phys. 71, 1539 (1999).CrossRefADSGoogle Scholar
  19. 19.
    A. Joobeur, B. E. A. Saleh, T. S. Larchuk, and M. C. Teich, Phys. Rev. A 53, 4360 (1996).CrossRefADSGoogle Scholar
  20. 20.
    L. A. Lugiato and I. Marzoli, Phys. Rev. A 52, 4886 (1995); I. Marzoli, A. Gatti, and L. A. Lugiato, Phys. Rev. Lett. 78, 2092 (1997).CrossRefADSGoogle Scholar
  21. 21.
    C. A. J. Putman, B. G. De Grooth, N. F. Van Hulst, and J. Greve, J. Appl. Phys. 72, 6 (1992).CrossRefADSGoogle Scholar
  22. 22.
    C. Boccara, D. Fournier, and J. Badoz, Appl. Phys. Lett. 36, 130 (1980).CrossRefADSGoogle Scholar
  23. 23.
    H. Kojima, E. Muto, H. Higuchi, and T. Yanagida, Biophys. J. 73, 2012 (1997).CrossRefGoogle Scholar
  24. 24.
    D. P. E. Smith, Rev. Sci. Instrum. 66, 3191 (1995).CrossRefADSGoogle Scholar
  25. 25.
    V. Delaubert, D. A. Shaddock, P. K. Lam, et al., J. Opt. A: Pure Appl. Opt. 4, 393 (2002).CrossRefADSGoogle Scholar
  26. 26.
    B. C. Buchler, U. L. Andersen, P. K. Lam, et al., Phys. Rev. A 65, 011803 (2002).Google Scholar
  27. 27.
    J. Hald, J. L. Sørensen, C. Schori, and E. S. Polzik, Phys. Rev. Lett. 83, 1319 (1999).CrossRefADSGoogle Scholar
  28. 28.
    A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Lett. 49, 91 (1982).CrossRefADSGoogle Scholar
  29. 29.
    G. S. Agarwal and R. R. Puri, Phys. Rev. A 40, 5179 (1989).CrossRefADSGoogle Scholar
  30. 30.
    A. S. Chirkin, A. A. Orlov, and D. Y. Paraschuk, Kvantovaya Élektron. (Moscow) 20, 999 (1993).Google Scholar
  31. 31.
    V. P. Karasev and A. V. Masalov, Opt. Spektrosk. 74, 928 (1993) [Opt. Spectrosc. 74, 551 (1993)].Google Scholar
  32. 32.
    N. V. Korolkova and A. S. Chirkin, J. Mod. Opt. 43, 869 (1996).zbMATHMathSciNetADSGoogle Scholar
  33. 33.
    A. S. Chirkin, A. P. Alodjants, and S. M. Arakelian, Opt. Spectrosk. 82, 1001 (1997) [Opt. Spectrosc. 82, 919 (1997)].Google Scholar
  34. 34.
    P. A. Bushev, V. P. Karassiov, A. V. Masalov, and A. A. Putilin, Opt. Spectrosk. 91, 558 (2001) [Opt. Spectrosc. 91, 526 (2001)].Google Scholar
  35. 35.
    A. P. Alodjants, S. M. Arakelian, and A. S. Chirkin, Appl. Phys. B 66, 53 (1998).CrossRefADSGoogle Scholar
  36. 36.
    A. P. Alodjants, A. Y. Leksin, A. V. Prokhorov, and S. M. Arakelian, Laser Phys. 12, 247 (2002).Google Scholar
  37. 37.
    T. C. Ralph, W. J. Munro, and R. E. S. Polkinghorne, Phys. Rev. Lett. 85, 2035 (2000).CrossRefADSGoogle Scholar
  38. 38.
    N. Korolkova, G. Leuchs, R. Loudon, et al., Phys. Rev. A 65, 052306 (2002).Google Scholar
  39. 39.
    J. L. Sørensen, J. Hald, and E. S. Polzik, Phys. Rev. Lett. 80, 3487 (1998).CrossRefADSGoogle Scholar
  40. 40.
    G. G. Stokes, Trans. Cambridge Philos. Soc. 9, 399 (1852).Google Scholar
  41. 41.
    J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons, 2nd ed. (Springer, Berlin, 1976).Google Scholar
  42. 42.
    B. A. Robson, The Theory of Polarization Phenomena (Clarendon, Oxford, 1974).Google Scholar
  43. 43.
    See, for example, M. Kaku}, Quantum Field Theory} (Oxford Univ. Press, New York}, 199Google Scholar
  44. 44.
    D. F. Walls and G. J. Milburn, Quantum Optics (Springer, Berlin, 1995).Google Scholar
  45. 45.
    A. Einstein, B. Podolski, and N. Rosen, Phys. Rev. 47, 777 (1935).zbMATHCrossRefADSGoogle Scholar
  46. 46.
    Special issue of Phys. World, March (1998).Google Scholar
  47. 47.
    Ch. Silberhorn, P. K. Lam, O. Weiß, et al., Phys. Rev. Lett. 86, 4267 (2001).CrossRefADSGoogle Scholar
  48. 48.
    M. D. Reid and P. D. Drummond, Phys. Rev. Lett. 60, 2731 (1988).CrossRefADSGoogle Scholar
  49. 49.
    L.-M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 4002 (2000).CrossRefADSGoogle Scholar
  50. 50.
    H. A. Haus, Electromagnetic Noise and Quantum Optical Measurements (Springer, Berlin, 2000).zbMATHGoogle Scholar
  51. 51.
    C. H. Bennett, G. Brassard, C. Crepeau, et al., Phys. Rev. Lett. 70, 1895 (1993).zbMATHCrossRefADSMathSciNetGoogle Scholar
  52. 52.
    The criteria for successful quantum teleportation has been discussed recently, see F. Grosshans and P. Grangier}, Phys. Rev. A} 64}, 010301(R) (2001}) and references therGoogle Scholar
  53. 53.
    F. Grosshans and P. Grangier, Phys. Rev. A 64, 010301(R) (2001).Google Scholar
  54. 54.
    T. C. Ralph and P. K. Lam, Phys. Rev. Lett. 81, 5668 (1998).CrossRefADSGoogle Scholar

Copyright information

© MAIK "Nauka/Interperiodica" 2003

Authors and Affiliations

  • R. Schnabel
    • 1
    • 2
  • W. P. Bowen
    • 1
  • N. Treps
    • 1
  • B. Buchler
    • 1
  • T. C. Ralph
    • 3
  • P. K. Lam
    • 1
  • H. -A. Bachor
    • 1
  1. 1.Department of Physics, Faculty of ScienceAustralian National UniversityAustralia
  2. 2.Albert-Einstein-InstitutUniversität HannoverHannoverGermany
  3. 3.Department of Physics, Centre for LasersUniversity of QueenslandSt. LuciaAustralia

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