Advertisement

Entanglement Manipulation in a Cavity Qed Experiment

Chapter
  • 206 Downloads
Part of the NATO Science Series book series (NAII, volume 51)

Abstract

One of the most important feature of quantum physics is the concept of entanglement. After interaction, two quantum objects usually behave as a single entity, each of the systems can not any more be described separately. A non-separable entangled state must the be introduced for representing the state of the system as a whole. Such a state presents unbelievable correlation from the point of view of classical logic as pointed out by Einstein, Podolsky and Rosen [1] (EPR). Entanglement manifests while performing a measurement on one of the two parts of an EPR pair. It enforces to consider that the other part of the system is instantaneously projected during this measurement independently of the distance separating the two systems. The EPR situation also sits at the heart of quantum measurement theory. While describing quantum mechanically the interaction of a system with a meter, one have to consider at some point a system-meter entangled state whose strangeness was emphasised by the famous Schrödinger cat metaphor [2], [3]. While considering this problem the physics of entangled states provides a new insight in the understanding of the transition between the quantum word of small isolated quantum systems and the classical behaviour of macroscopic meters. The concept of decoherence [4], [5], introduced in this context by considering the entanglement of the meter with its environment also relies on the understanding of the behaviour of complex entangled states.

Keywords

Entangle State Photon Number Rabi Oscillation Atomic Qubit Quantum Phase Gate 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Einstein, A., Podolosky, B., and N. Rosen, (1935) Phys. Rev. 47, 777.ADSzbMATHCrossRefGoogle Scholar
  2. 2.
    Schrödinger, E. (1935) Naturwissenschaften, 23, 807, 823, 844; reprinted in English in [8].ADSCrossRefGoogle Scholar
  3. 3.
    Wheeler, J.A. and Zurek, W.H. (1983) Quantum Theory of Measurement, Princeton Univ. Press.Google Scholar
  4. 4.
    Zurek, W.H. (1991) Physics Today, 44, 10 p. 36.CrossRefGoogle Scholar
  5. 5.
    Zurek, W.H. (1981) Phys. Rev. D 24, 1516 and (1982) Phys. Rev. D 26, 1862; Caldeira, A.O. and Leggett, A.J. (1983) Physica A 121, 587; Joos, E. and Zeh, H.D. (1985) Z Phys. B 59, 2230; Omnès, R. (1994) The Interpretation of Quantum Mechanics, Princeton University Press.Google Scholar
  6. 6.
    Bennett, C.H. and Di Vincenzo, D.P. (2000) Nature 404, 247.ADSCrossRefGoogle Scholar
  7. 7.
    Bennett, C.H., Brassard, G., and Ekert, A. (1992) Scientific American October 1992, p.50.Google Scholar
  8. 8.
    Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., and Wootters, W.K. (1993) Phys. Rev. Lett. 70, 1895.MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 9.
    Bell, J.S., (1964) Physics 1, 195; Clauser, J.F., Horne, M.A., Shimony, A., and Holt, R.A. (1969) Phys. Rev. Lett. 23, 880.Google Scholar
  10. 10.
    Zeilinger, A. (1998) Rev. Mod. Phys. 71, S288.CrossRefGoogle Scholar
  11. 11.
    Rarity, J.G., Owens, P.C.M., and Tapster, P.R. (1994) J. Mod. Opt. 41, 2435.ADSCrossRefGoogle Scholar
  12. 12.
    Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., and Zeilinger, A. (1997) Nature 390, 575.ADSCrossRefGoogle Scholar
  13. 13.
    Boschi, D., Branca, S., De Martini, F., Hardy, L., and Popescu, S. (1998) Phys. Rev. Lett. 80, 1121.MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. 14.
    Furusawa, A., Sorensen, J.L., Braunstein, S.L., Fuchs, C.A., Kimble, H.J., and Polzik, E.S. (1998) Science 282, 106.CrossRefGoogle Scholar
  15. 15.
    Greenberger, D.M., Horne, M.A., and Zeilinger, A. (1990) Am. J. Phys. 58, 1131.MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Pan, J.W., Bouwmeester, D., Daniell, M., Weinfurter, H., and Zeilinger, A. (2000) Nature 403, 515.ADSCrossRefGoogle Scholar
  17. 17.
    Meekhof, D.M., Monroe, C., King, B.E., Itano W.M., and Wineland, DJ. (1996) Phys. Rev. Lett. 76, 1796.ADSCrossRefGoogle Scholar
  18. 18.
    Sackett, C.A., Kielpinski, D., King, B.E., Langer, C., Meyer, V., Myatt, C.J., Rowe, M., Turchette, Q.A., Itano, W.M., Wineland, D.J., and Monroe, C.C. (2000) Nature 404, 256.ADSCrossRefGoogle Scholar
  19. 19.
    Haroche, S. and Raimond, J.M. (1993) Cavity Quantum Electrodynamics, Scientific American 268, 54.ADSCrossRefGoogle Scholar
  20. 20.
    Hulet, R.G. and Kleppner, D. (1983) Phys. Rev. Lett. 51, 1430; Nussenzveig, P., Bernardot, F., Brune, M., Hare, J., Raimond, J.M., Haroche, S., and Gawlik, W. (1993) Phys. Rev. A 48, 3991.ADSCrossRefGoogle Scholar
  21. 21.
    Haroche, S. (1992) in J. Dalibard, J.M. Raimond, and J. Zinn-Justin (eds.), Fundamental systems in quantum optics, Les Houches Summer School Session LIII, North Holland, Amsterdam, p. 767; Haroche, S. (1984) in G. Grynberg and R. Stora (eds.), New Trends in Atomic Physics, Les Houches Summer School Session XXXVIII, North Holland, Amsterdam, p. 347.Google Scholar
  22. 22.
    Raimond, J.M. and Haroche, S. (1997) in S. Reynaud, E. Giaccobino and J. Zinn-Justin (eds.), Quantum fluctuations, Les Houches Summer School Session LXIII, North Holland, Amsterdam, p. 309.Google Scholar
  23. 23.
    Haroche, S. and Raimond, J.M. (1994) in D. Bates and B. Bederson (eds.), Avances in Atomic and Molecular Physics, supplement 2, Academic Press, New York, p.347. Haroche, S. and Raimond, J.M. in P. Berman (ed.), Avances in Atomic and molecular physics, supplement 2, Academic Press, New York, p. 123.Google Scholar
  24. 24.
    Raithel G. Wagner C. Walther H. Narducci L.M. and Scully M.O. 1994 Adv. At. Mol. Phys. Supplement 2 57Google Scholar
  25. 25.
    Bernardot, F., Nussenzveig, P., Brune, M., Raimond, J.M., and Haroche, S. (1992) Euro. Phys. Lett. 17, 33.ADSCrossRefGoogle Scholar
  26. 26.
    Brune, M., Schmidt-Kaler, F., Maali, A., Dreyer, J., Hagley, E., Raimond, J.M., and Haroche, S. (1996) Phys. Rev. Lett. 76, 1800.ADSzbMATHCrossRefGoogle Scholar
  27. 27.
    Maître, X., Hagley, E., Nogues, G., Wunderlich, C., Goy, P., Brune, M., Raimond, J.M., and Haroche, S. (1997) Phys. Rev. Lett. 79, 769.ADSCrossRefGoogle Scholar
  28. 28.
    Nogues, G., Rauschenbeutel, A., Osnaghi, S., Brune, M., Raimond, J.M., and Haroche, S. (1999) Nature 400, 239.ADSCrossRefGoogle Scholar
  29. 29.
    Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J.M., and Haroche, S. (1999) Phys. Rev. Lett. 83, 5166.ADSCrossRefGoogle Scholar
  30. 30.
    Hagley, E., Maître, X., Nogues, G., Wunderlich, C., Brune, M., Raimond, J.M., and Haroche, S. (1997) Phys. Rev. Lett. 79, 1.ADSCrossRefGoogle Scholar
  31. 31.
    Rauschenbeutel, A., Nogues, G., Osnaghi, S., Bertet, P., Brune, M., Raimond, J.M., and Haroche, S. (2000) Science, accepted.Google Scholar
  32. 32.
    Brune, M., Hagley, E., Dreyer, J., Maître, X., Maali, A., Wunderlich, C., Raimond, J.M., and Haroche, S. (1996) Phys. Rev. Lett. 77, 4887.ADSCrossRefGoogle Scholar
  33. 33.
    Gross, M. and Liang, J. (1986) Phys. Rev. Lett. 57, 3160.ADSCrossRefGoogle Scholar
  34. 34.
    Rempe, G., Walther, H., and Klein, N. (1987) Phys. Rev. Lett. 58, 353.ADSCrossRefGoogle Scholar
  35. 35.
    Jaynes, E.T. and Cummings, F.W. (1963) Proc. IEEE 51, 89.CrossRefGoogle Scholar
  36. 36.
    Cohen-Tannoudji, C., Dupont-Roc, J., and Grynberg, G. (1987) Photons et atomes, Introduction à l’électrodynamique quantique, Interéditions et Editions du CNRS; English translation: (1989) Photons and Atoms, Introduction to Quantum Electrodynamics, Wiley, New York.Google Scholar
  37. 37.
    Eberly, J.H., Narozhny, N.B., and Sanchez-Mondragon, J.J. (1980) Phys. Rev. Lett. 44, 1323.MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    Glauber, R. (1963) Phys. Rev. 131 2766.MathSciNetADSCrossRefGoogle Scholar
  39. 39.
    Varcoe, B.T.H., Brattke, S., and Walther, H. (2000) Nature 403, 743–746.ADSCrossRefGoogle Scholar
  40. 40.
    Rauch, H., Zeilinger, A., Badurek, G., and Willing, A. (1975) Phys. Lett. A 54, 425.ADSCrossRefGoogle Scholar
  41. 41.
    Werner, S.A., Colella, R., Overhauser, A.W, and Eagen, C.F. (1975) Phys. Rev. Lett. 35, 1053.ADSCrossRefGoogle Scholar
  42. 42.
    Monroe, C., Meekhof, D.M., King, B.E., Itano, WM., and Wineland, D.J. (1995) Phys. Rev. Lett. 75, 4714.MathSciNetADSzbMATHCrossRefGoogle Scholar
  43. 43.
    Braginsky, V.B. and Vorontsov, Y.I. (1974) Usp. Fiz. Nauk. 114, 41. [(1975) Sov. Phys. Usp. 17, 644].CrossRefGoogle Scholar
  44. 44.
    Braginsky, V.B. and Khalili, F.Y. (1992) Quantum measurement., K.S. Thorne, Cambridge Univ. Press, Cambridge.CrossRefGoogle Scholar
  45. 45.
    Caves, C.M., Thorne, K.S., Drever, R.W.P., Sandberg, V.D., and Zimmermann, M. (1980) Rev. Mod. Phys. 52, 341.ADSCrossRefGoogle Scholar
  46. 46.
    Grangier, P., Levenson, A.L., and Poizat, J.P. (1998) Nature 396, 537 and references therein.ADSCrossRefGoogle Scholar
  47. 47.
    Levenson, M.D., Shelby, R.M., Reid, M., and Walls, D.F. (1986) Phys. Rev. Lett. 57, 2473.ADSCrossRefGoogle Scholar
  48. 48.
    La Porta, A., Slusher, R.E., and Yurke, B. (1989) Phys. Rev. Lett. 62, 28.ADSCrossRefGoogle Scholar
  49. 49.
    Friberg, S.R., Machida, S., and Yamamoto, Y (1992) Phys. Rev. Lett. 69, 3165.ADSCrossRefGoogle Scholar
  50. 50.
    Roch, J.F., Roger, G., Grangier, P., Courty, J.M., and Reynaud, S. (1992) Applied. Phys. B 55, 291.ADSCrossRefGoogle Scholar
  51. 51.
    Poizat, J.P. and Grangier, P. (1993) Phys. Rev. Lett. 70, 271.ADSCrossRefGoogle Scholar
  52. 52.
    Pereira, S.F., Ou, Z.Y., and Kimble, H.J. (1994) Phys. Rev. Lett. 72, 214.ADSCrossRefGoogle Scholar
  53. 53.
    (1997) Quantum non-demolition measurements, Appl. Phys. B 64(suppl.), 123.Google Scholar
  54. 54.
    Roch, J.F., Vigneron, K., Grelu, Ph., Sinatra, A., Poizat, J.-Ph., and Grangier, Ph. (1997) Phys. Rev. Lett. 78, 634.ADSCrossRefGoogle Scholar
  55. 55.
    Bencheick, K., Levenson, J.A., Grangier, P., and Lopez, O. (1995) Phys. Rev. Lett. 75, 3422.ADSCrossRefGoogle Scholar
  56. 56.
    Bruckmeier, R., Hansen, H., and Schiller, S. (1997) Phys. Rev. Lett. 79, 1463.ADSCrossRefGoogle Scholar
  57. 57.
    Ramsey, N.F. (1985) Molecular beams, Oxford Univ. Press, New York.Google Scholar
  58. 58.
    Bragingsky, V.B. and Khalili, F.Ya. (1996) Rev. Mod. Phys. 68, 1.ADSCrossRefGoogle Scholar
  59. 59.
    Meystre, P., Rempe, G. and Walther, H. (1988) Optics Lett. 13, 1078. Weidinger, M. et al. (1999) Phys. Rev. Lett. 82, 3795.ADSCrossRefGoogle Scholar
  60. 60.
    Peil, S. and Gabrielse, G. (1999) Phys. Rev. Lett. 83, 1287.ADSCrossRefGoogle Scholar
  61. 61.
    Brune, M., Nussenzveig, P., Schmidt-Kaler, F., Bernardot, F., Maali, A., Raimond, J.M., and Haroche, S. (1994) Phys. Rev. Lett. 72, 3330.ADSCrossRefGoogle Scholar
  62. 62.
    Brune, M., Haroche, S., Lefèvre, V., Raimond, J.M., and Zagury, N. (1990) Phys. Rev. Lett. 65, 97ADSCrossRefGoogle Scholar
  63. 63.
    Brune, M., Haroche, S., Raimond, J.M., Davidovich, L., and Zagury, N. (1992) Phys. Rev. A 45, 519ADSCrossRefGoogle Scholar
  64. 64.
    Haroche, S., Brune, M., and Raimond, J.M. (1992) Journal de Physique II, Paris 2, 659.ADSCrossRefGoogle Scholar
  65. 65.
    Haroche, S. and Raimond, J.M. (1996) Physics Today 51.Google Scholar
  66. 66.
    Lloyd, S. (1995) Phys. Rev. Lett. 75, 346.ADSCrossRefGoogle Scholar
  67. 67.
    Turchette, Q.A., Hood, C.J., Lange, W., Mabuchi, H., Kimble, H.J. (1995) Phys. Rev. Lett. 75, 4710.MathSciNetADSCrossRefGoogle Scholar
  68. 68.
    Note that a three atom experiment in cavity QED has been recently reported in [74]. It exhibited atomic energy correlations, but did not involve entanglement.Google Scholar
  69. 69.
    Barenco, A. Deutsch, D., and Ekert, A. (1995) Phys. Rev. Lett. 74, 4083; Di Vincenzo, D.P. (1995) Science 270, 255; Ekert, A. and Josza, R. (1997) Rev. Mod. Phys. 68, 3733.Google Scholar
  70. 70.
    Barenco, A., Deutsch, D., Ekert, A., and Jozsa, R. (1995) Phys. Rev. Lett. 74, 4083.ADSCrossRefGoogle Scholar
  71. 71.
    Domokos, P., Raimond, J.M., Brune, M., Haroche, S. (1995) Phys. Rev. A 52, 3554.ADSCrossRefGoogle Scholar
  72. 72.
    Haroche, S. et al. (1999) in R. Blatt, J. Eschner, D. Leibfried, F. Schmidt-Kaler (eds.), Laser spectroscopy 14, World Scientific, New York, p. 140.Google Scholar
  73. 73.
    Zheng, S.B. (1999) J. of Opt. B 1, 534.ADSCrossRefGoogle Scholar
  74. 74.
    Haroche, S. (1995) in D. Greenberger, A. Zeilinger (eds.), Fundamental problems in quantum theory, Ann. N.Y. Acad. Sci. 755, p. 73.Google Scholar
  75. 75.
    Varcoe, B.T.H., Brattke, S., Englert, B.-G., and Walther, H. in R. Blatt, J. Eschner, D. Leibfried, F. Schmidt-Kaler (eds.), Laser spectroscopy 14, World Scientific, New York, p. 130.Google Scholar
  76. 76.
    Merrnin, N.D., (1990) Phys. Rev. Lett. 65, 1838.MathSciNetADSCrossRefGoogle Scholar
  77. 77.
    Gershenfeld, N.A. and Chuang, I.L. (1997) Science 275, 350; Cory, D.G., Fahmy, A.F., and Havel, T.F. (1997) Proc. Natl. Acad. Sci. USA 94, 1634; Jones, J.A., Mosca, M., and Hansen, R.H. (1998) Nature 393, 344; Cory, D.G. et al. (1998) Phys. Rev. Lett. 81, 2152.MathSciNetzbMATHCrossRefGoogle Scholar
  78. 78.
    Braunstein, S.L., Caves, C.M., Jozsa, R., Linden, N., Popescu, S., and Schack, R. (1999) Phys. Rev. Lett. 83, 1054.ADSCrossRefGoogle Scholar
  79. 79.
    Turchette, Q.A., Wood, C.S., King, B.E., Myatt, C.J., Leibfried, D., Itano, W.M., Monroe, C., and Wineland, D.J. (1998) Phys. Rev. Lett. 81, 3631.ADSCrossRefGoogle Scholar
  80. 80.
    Nägerl, H.C., Leibfried, D., Rohde, H., Thalhammer, G., Eschner, J., Schmidt-Kaler, F., and Blatt, R. (1999) Phys. Rev. A 60, 145.ADSCrossRefGoogle Scholar
  81. 81.
    von Neumann, J. (1932) Matematische Grundlagen der Quantenmechanik, Springer, Berlin; reprinted in english in [8].Google Scholar
  82. 82.
    Waals, D.F. and Milburn, G.J. (1985) Phys. Rev. A 31, 2403.ADSCrossRefGoogle Scholar
  83. 83.
    Monroe, C., Meekhof, D.M., King, B.E., and Wineland, D.J. (1996) Science 272, 1131.MathSciNetADSzbMATHCrossRefGoogle Scholar
  84. 84.
    Scully, M.O., Englert, B.-G., and Walther, H. (1991) Nature 351, 111; Haroche, S., Brune, M., and Raimond, J.M. (1992) Appl. Phys. B 54, 355.Google Scholar
  85. 85.
    Pfau, T., Spaelter, S., Kurtsiefer, Ch., Ekstrom, C.R., and Mlynek, J. (1994) Phys. Rev. Lett. 73, 1223; Chapman, M.S., Hammond, T.D., Lenef, A., Schmiedmayer, J., Rubenstein, R.A., Smith, E., and Pritchard, D.E. (1995) Phys. Rev. Lett. 75, 3783.ADSCrossRefGoogle Scholar
  86. 86.
    Davidovich, L., Brune, M., Raimond, J.M., and Haroche, S. (1996) Phys. Rev. A 53, 1295.ADSCrossRefGoogle Scholar
  87. 87.
    Raimond, J.M., Brune, M., and Haroche, S. (1997) Phys. Rev. Lett. 79, 1964.ADSCrossRefGoogle Scholar
  88. 88.
    Lutterbach, L. G. and Davidovich, L. (1997) Phys. Rev. Lett. 78, 2547; Lutterbach, L. G. and Davidovich, L. (1998) Optics Express 3, 147.ADSCrossRefGoogle Scholar
  89. 89.
    Kim, M.S., Antesberger, G., Bodendorf, C.T., and Walther, H. (1998) Phys. Rev. A 58, R65.ADSCrossRefGoogle Scholar
  90. 90.
    Davidovich, L., Zagury, N., Brune, M., Raimond, J. M., and Haroche, S. (1994) Phys. Rev. A 50, R89ADSCrossRefGoogle Scholar
  91. 91.
    We acknowledge support from the European Community and JST (ICORP “Quantum Entanglement” project).Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  1. 1.Département de Physique de L’Ecole Normale SupérieureLaboratoire Kastler BrosselParis Cedex 5France

Personalised recommendations