Advertisement

Timescales in Quantum Open Systems: Dynamics of Time Correlation Functions and Stochastic Quantum Trajectory Methods in Non-Markovian Systems

  • Daniel AlonsoEmail author
  • Inés de Vega
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 789)

Abstract

The dynamics of a system in interaction with another system, the later considered as a reservoir, is studied in many different domains in physics. This approach is useful not only to address fundamental questions like quantum decoherence decoherence and the measurement problem [1] but also to deal with practical and theoretical problems appearing in the emerging fields of nanotechnology nanotechnology [2, 3] and quantum computing quantum computing as well as in systems of ultracold atoms [7]. In many of these cases, the basic approximation is the Markov assumption in which there is a clear separation of the typical timescales associated with the system and the reservoir or environment. This separation of timescales, together with other assumptions like the weak coupling between the system and the reservoir, has been central in the development of several fields, in particular in quantum optics [8, 9]. However, in

Keywords

Correlation Function Photonic Crystal Master Equation Reduce Density Matrix Quantum Open System 
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.

Notes

Acknowledgement

We would like to thank J.G. Muga for his kind invitation to contribute to this volume and its invaluable support. We thank H. Carmichael, G.C. Hegerfeldt, A. Ruíz, and L.S. Schulman for their comments at different stages of this work and G. Nicolis, P. Gaspard, J.I. Cirac, and W.T. Strunz for support and encouragement. This work has been supported by Ministerio de Ciencia y Tecnología of Spain (FIS2007-64018) and by the EU projects CONQUEST and SCALA.

References

  1. 1.
    J. Gambetta, H. Wiseman, Phys. Rev. A 66, 012108 (2002)ADSCrossRefGoogle Scholar
  2. 2.
    M. Esposito, P. Gaspard, Phys. Rev. E 76, 041134 (2007)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    C. Flindt, T. Novotny, A. Braggio, M. Sassetti, A.-Pekka Jauho, Phys. Rev. Lett. 100, 150601 (2008)ADSCrossRefGoogle Scholar
  4. 4.
    D. Lidar, Phys. Rev. Lett. 100, 160506 (2008)ADSCrossRefGoogle Scholar
  5. 5.
    F. Verstraete, M.M. Wolf, J.I. Cirac, arXiv:0803.1447 (2008)Google Scholar
  6. 6.
    B. Kraus, H.P. Büchler, S. Diehl, A. Kantian, A. Micheli, P. Zoller, Phys. Rev. A 78, 042307 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    S. Diehl, A. Micheli, A. Kantian, B. Kraus, H.P. Büchler, P. Zoller, arXiv:0803.1482 (2008)Google Scholar
  8. 8.
    H.J. Carmichael, An Open Systems Approach to Quantum Optics, Lecture Notes in Physics, Monographs Series, vol. 18 (Springer-Verlag, Berlin, 1993)Google Scholar
  9. 9.
    H.J. Carmichael, Statistical Methods in Quantum Optics 1. Texts and Monographs in Physics (Springer, Berlin, 1999)Google Scholar
  10. 10.
    B.M. Garraway, B.J. Dalton, J. Phys. B 39, S767 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    H.P. Breuer, F. Petruccione, Phys. Rev. E 76, 016701 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    B. Bellomo, R.L. Franco, G. Compagno, Phys. Rev. Lett. 99, 160502 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    C. Lazarou, G.M. Nikolopoulos, P. Lambropoulos, J. Phys. B: At. Mol. Opt. Phys. 40, 2511 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    E. Purcell, Phys. Rev. 69, 681 (1946)CrossRefGoogle Scholar
  15. 15.
    D. Kleppner, Phys. Rev. Lett. 47, 233 (1981)ADSCrossRefGoogle Scholar
  16. 16.
    E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987)ADSCrossRefGoogle Scholar
  17. 17.
    S. John, Phys. Rev. Lett. 58, 2486 (1987)ADSCrossRefGoogle Scholar
  18. 18.
    S. John, T. Quang, Phys. Rev. A 50, 1764 (1994)ADSCrossRefGoogle Scholar
  19. 19.
    B. Gaveau, L.S. Schulman, J. Phys. A: Math. Gen. 28, 7359 (1995)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    M. Lewenstein, J. Zakrzewski, T.W. Mossberg, Phys. Rev. A 38, 808 (1988)ADSCrossRefGoogle Scholar
  21. 21.
    S. Maniscalco, F. Petruccione, Phys. Rev. A 73, 12111 (2006)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    G. Lindblad, Commun. Math. Phys. 48, 119 (1976)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    G.V. Gorini, A. Kossakowski, E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    A.G. Redfield, IBM J. Res. Dev. 1, 19 (1957)CrossRefGoogle Scholar
  25. 25.
    A.G. Redfield, Adv. Magn. Reson. 1, 1 (1965)CrossRefGoogle Scholar
  26. 26.
    P. Gaspard, M. Nagaoka, J. Chem. Phys. 111, 5676 (1999)ADSCrossRefGoogle Scholar
  27. 27.
    P. Gaspard, M. Nagaoka, J. Chem. Phys. 111, 5668 (1999)ADSCrossRefGoogle Scholar
  28. 28.
    R. Zwanzig, J. Chem. Phys. 33, 1338 (1960)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    S. Nakajima, Prog. Theor. Phys. 20, 948 (1958)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    I. Prigogine, Non-Equilibrium Statistical Mechanics (John Wiley & Sons Inc., New York, 1962)zbMATHGoogle Scholar
  31. 31.
    W.T. Strunz, T. Yu, Phys. Rev. A 69, 052115 (2004)ADSCrossRefGoogle Scholar
  32. 32.
    H.P. Breuer, B. Kappler, F. Petruccione, Ann. Phys. 291, 36 (2001)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    J.D. Cresser, Laser Phys. 10, 337 (2000)Google Scholar
  34. 34.
    D. Alonso, I. de Vega, Phys. Rev. Lett. 94, 200403 (2005)ADSCrossRefGoogle Scholar
  35. 35.
    C. Gardiner, P. Zoller, Quantum Noise. Springer Series in Synergetics (Springer-Verlag, Berlin, 2004)zbMATHGoogle Scholar
  36. 36.
    H. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2002)zbMATHGoogle Scholar
  37. 37.
    M. Orszag, Quantum Optics: Including Noise Reduction, Trapped Ions, Quantum Trajectories, and Decoherence, 2nd edn (Springer, Berlin, 2008)zbMATHGoogle Scholar
  38. 38.
    P. Lambropoulos, D. Petrosyan, Fundamentals of Quantum Optics and Quantum Information (Springer, Berlin, 2006)Google Scholar
  39. 39.
    A. Barchielli, V. Belavkin, J. Phys. A: Math. Gen. 24, 1495 (1991)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    J. Dalibard, Y. Castin, K. Molmer, Phys. Rev. Lett. 68, 580 (1992)ADSCrossRefGoogle Scholar
  41. 41.
    R. Dum, P. Zoller, H. Ritsch, Phys. Rev. A 45, 1879 (1992)CrossRefGoogle Scholar
  42. 42.
    G.C. Hegerfeldt, M.B. Plenio, Phys. Rev. A 56, 2334 (1997)CrossRefGoogle Scholar
  43. 43.
    M.B. Plenio, P.L. Knight, Rev. Mod. Phys. 70, 101 (1998)ADSCrossRefGoogle Scholar
  44. 44.
    N. Gisin, I.C. Percival, J. Phys. A: Math. Gen. 25, 5677 (1992)ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    N. Gisin, I.C. Pecival, J. Phys. A: Math. Gen. 26, 2233 (1993)ADSCrossRefGoogle Scholar
  46. 46.
    N. Gisin, I.C. Percival, J. Phys. A: Math. Gen. 26, 2245 (1993)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    N. Gisin, P. Knight, I. Percival, R. Thompson, D. Wilson, J. Mod. Opt. 40, 1663 (1993)ADSCrossRefGoogle Scholar
  48. 48.
    H.M. Wiseman, G.J. Milburn, Phys. Rev. A 47, 1652 (1993)ADSCrossRefGoogle Scholar
  49. 49.
    H.M. Wiseman, G.J. Milburn, Phys. Rev. A 47, 642 (1993)ADSCrossRefGoogle Scholar
  50. 50.
    T.B.L. Kist, M. Orszag, T.A. Brun, L. Davidovich, J. Opt. B: Quantum Semicl. Opt. 1, 251 (1999)ADSCrossRefGoogle Scholar
  51. 51.
    H. Breuer, F. Petruccione, Fortschr. Phys./Prog. Phys. 45, 39 (1997)ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    W. Strunz, Phys. Lett. A 224, 25 (1996)ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    L. Diósi, W.T. Strunz, Phys. Lett. A 235, 569 (1997)ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    L. Diósi, N. Gisin, W. Strunz, Phys. Rev. A 58, 1699 (1998)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    T. Yu, L. Diósi, N. Gisin, W.T. Strunz, Phys. Rev. A 60, 91 (1999)ADSCrossRefGoogle Scholar
  56. 56.
    W.T. Strunz, L. Diósi, N. Gisin, Phys. Rev. Lett. 82, 1801 (1999)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    W.T. Struntz, L. Diósi, N. Gisin, T. Yu, Phys. Rev. Lett. 83, 4909 (1999)ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    M.W. Jack, M.J. Collet, Phys. Rev. A 61, 062106 (2000)ADSMathSciNetCrossRefGoogle Scholar
  59. 59.
    H.P. Breuer, B. Kappler, F. Petruccione, Phys. Rev. A 59, 1633 (1999)ADSCrossRefGoogle Scholar
  60. 60.
    H.P. Breuer, Eur. Phys. J. D 29, 105 (2004)ADSCrossRefGoogle Scholar
  61. 61.
    L. Diósi, Phys. Rev. Lett. 100, 080401 (2008)ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    H.M. Wiseman, J.M. Gambetta, (2008)Google Scholar
  63. 63.
    L. Diósi, Phys. Rev. Lett. Erratum 101, 149902 (2008)ADSCrossRefGoogle Scholar
  64. 64.
    I. de Vega, D. Alonso, P. Gaspard, W.T. Strunz, J. Chem. Phys. 122, 124106 (2005)ADSCrossRefGoogle Scholar
  65. 65.
    W. Struntz, unpublished (2001)Google Scholar
  66. 66.
    W.T. Strunz, Chem. Phys. 268, 237 (2001)ADSCrossRefGoogle Scholar
  67. 67.
    L. Van Hove, Physica 21, 517 (1955)MathSciNetCrossRefGoogle Scholar
  68. 68.
    R. Zwanzig, Nonequilibrium Statistical Mechanics (Oxford University Press, Oxford, 2001)zbMATHGoogle Scholar
  69. 69.
    I. de Vega, D. Alonso, P. Gaspard, Phys. Rev. A 71, 23812 (2005)CrossRefGoogle Scholar
  70. 70.
    M. Lax, Phys. Rev. 129, 2342 (1963)ADSMathSciNetCrossRefGoogle Scholar
  71. 71.
    M. Lax, Phys. Rev. A 172, 350 (1968)ADSCrossRefGoogle Scholar
  72. 72.
    M. Lax, Opt. Comm. 179, 463 (2000)ADSCrossRefGoogle Scholar
  73. 73.
    G.W. Ford, R.F. O’Connell, Phys. Rev. Lett. 77, 798 (1996)ADSMathSciNetCrossRefGoogle Scholar
  74. 74.
    G.W. Ford, R.F. O’Connell, Opt. Comm. 179, 451 (2000)ADSCrossRefGoogle Scholar
  75. 75.
    I. de Vega, D. Alonso, Phys. Rev. A 73, 22102 (2006)CrossRefGoogle Scholar
  76. 76.
    D. Alonso, I. de Vega, Phys. Rev. A 75, 52108 (2007)ADSCrossRefGoogle Scholar
  77. 77.
    A.A. Budini, J. Stat. Phys. 131, 51 (2008)ADSMathSciNetCrossRefGoogle Scholar
  78. 78.
    A.A. Budini, Phys. Rev. A 63, 012106 (2001)ADSCrossRefGoogle Scholar
  79. 79.
    M.O. Scully, M.S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, 1997)CrossRefzbMATHGoogle Scholar
  80. 80.
    C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Atom-Photon Interactions. Basic Processes and Applications (Willey Interscience, New York, 1992)Google Scholar
  81. 81.
    I. de Vega, D. Alonso, Phys. Rev. A 77, 043836 (2008)ADSCrossRefGoogle Scholar
  82. 82.
    D. Alonso, I. de Vega, E. Hernández-Concepci ón, Comptes Rendus-Physique 8, 684 (2007)ADSCrossRefGoogle Scholar
  83. 83.
    Y. Yang, S.Y. Zhu, Phys. Rev. A 62, 013805 (2000)ADSCrossRefGoogle Scholar
  84. 84.
    M. Florescu, S. John, Phys. Rev. A 64, 033801 (2001)ADSCrossRefGoogle Scholar
  85. 85.
    S. John, T. Quang, Phys. Rev. Lett. 74, 3419 (1995)ADSCrossRefGoogle Scholar
  86. 86.
    S. John, J. Wang, Phys. Rev. Lett. 64(20), 2418 (1990)ADSCrossRefGoogle Scholar
  87. 87.
    S. John, J. Wang, Phys. Rev. B 43, 12772 (1991)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Departamento de Física Fundamentaly Experimental, Electrónica y SistemasInstituto Universitario de Estudios Avanzados (IUDEA) en Fí sicaAtómica, Molecular y Fotónica, Universidad de La LagunaLa LagunaSpain
  2. 2.Max Planck Institute of Quantum OpticsGarchingGermany

Personalised recommendations