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Detector Models for the Quantum Time of Arrival

  • Andreas RuschhauptEmail author
  • J. Gonzalo Muga
  • Gerhard C. Hegerfeldt
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 789)

Abstract

Quantum particles are characterized, for a given preparation, by a fundamental stochasticity of their observable features, such as positions, momenta, energies, or times, e.g., times of arrival at a detector in time-of-flight experiments. In quantum theory the preparation stage is encoded in a wave function, whereas averages or statistical moments of the observables are calculated by a well-known prescription (the expectation value integral) from self-adjoint operators and their powers: this is at least the case for position, momentum, or energy. In fact, the entire statistical distributions are given by the square modulus of the overlap of the wave function with the corresponding eigenstates.

Keywords

Arrival Time Wave Packet Detector Model Kinetic Energy Density Quantum Time 
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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Notes

Acknowledgments

This work could not have been completed without the aid of A. del Campo, J. A. Damborenea, J. Echanobe, I. L. Egusquiza, V. Hannstein, B. Navarro, and D. Seidel. We also acknowledge "Acciones Integradas" of the German Academic Exchange Service (DAAD) and Ministerio de Educaci´on y Ciencia and additional support from the Max Planck Institute for the Physics of Complex Systems; MEC (FIS2006-10268-C03-01); and UPV-EHU (GIU07/40). AR acknowledges support by the German Research Foundation (DFG).

References

  1. 1.
    Y. Aharonov, D. Bohm, Phys. Rev. 122, 1649 (1961)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Y. Aharonov, J. Oppenheim, S. Popescu, B. Reznik, W.G. Unruh, Phys. Rev. A 57, 4130 (1998)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    M.M. Ali, D. Home, A.S. Majumdar, A.K. Pan, Phys. Rev. A 75, 042110 (2007)ADSCrossRefGoogle Scholar
  4. 4.
    G.R. Allcock, Ann. Phys. (N.Y.) 53, 253 (1969)ADSCrossRefGoogle Scholar
  5. 5.
    G.R. Allcock, Ann. Phys. (N.Y.) 53, 283 (1969)ADSGoogle Scholar
  6. 6.
    G.R. Allcock, Ann. Phys. (N.Y.) 53, 311 (1969)ADSCrossRefGoogle Scholar
  7. 7.
    D. Alonso, R.S. Mayato, C.R. Leavens, Phys. Rev. A 66, 042108 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    Ch. Anastopoulos, N. Savvidou, J. Math. Phys. 47, 122106 (2006)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    P.W. Ayers, R.G. Parr, A. Nagy, Int. J. Quant. Chem. 90, 309 (2002)CrossRefGoogle Scholar
  10. 10.
    R.F.W. Bader, Atoms in Molecules: A Quantum Theory (Clarendon, Oxford, 1990)Google Scholar
  11. 11.
    R.F.W. Bader, P.M. Beddall, J. Chem. Phys. 56, 3320 (1972)ADSCrossRefGoogle Scholar
  12. 12.
    O. del Barco, M. Ortuño, V. Gasparian, Phys. Rev. A 74, 032104 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    A.D. Baute, R.S. Mayato, J.P. Palao, J.G. Muga, I.L. Egusquiza, Phys. Rev. A 61, 022118 (2000)ADSCrossRefGoogle Scholar
  14. 14.
    A.D. Baute, I.L. Egusquiza, J.G. Muga, R. Sala Mayato, Phys. Rev. A 61, 052111 (2000)ADSCrossRefGoogle Scholar
  15. 15.
    A.D. Baute, I.L. Egusquiza, J.G. Muga, Phys. Rev. A 64, 012501 (2001)ADSCrossRefGoogle Scholar
  16. 16.
    A.D. Baute, I.L. Egusquiza, J.G. Muga, Phys. Rev. A 64, 014101 (2001)ADSCrossRefGoogle Scholar
  17. 17.
    A.D. Baute, I.L. Egusquiza, J.G. Muga, Phys. Rev. A 65, 032114 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    Ph. Blanchard, A. Jadczyk, Phys. Lett. A 175, 157 (1993)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Ph. Blanchard, A. Jadczyk, Ann. Phys. (Lpz.) 4, 583 (1995)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Ph. Blanchard, A. Jadczyk, Phys. Lett. A 203, 260 (1995)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Ph. Blanchard, A. Jadczyk, Helv. Phys. Acta 69, 613 (1996)MathSciNetGoogle Scholar
  22. 22.
    R.S. Bondurant, Phys. Rev. A 69, 062104 (2004)ADSCrossRefGoogle Scholar
  23. 23.
    M. Brack, B.P. van Zyl, Phys. Rev. Lett. 86, 1574 (2001)ADSCrossRefGoogle Scholar
  24. 24.
    R. Brunetti, K. Fredenhagen, Phys. Rev. A 66, 044101 (2002)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    H. Carmichael, An Open Systems Approach to Quantum Optics (Springer, Berlin, 1993)zbMATHGoogle Scholar
  26. 26.
    L. Cohen, P. Loughlin, J. Mod. Opt. 49, 539 (2002)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    L. Cohen, J. Chem. Phys. 70, 788 (1979)ADSCrossRefGoogle Scholar
  28. 28.
    L. Cohen, J. Chem. Phys. 80, 4277 (1984)ADSCrossRefGoogle Scholar
  29. 29.
    C.S. Chuu, F. Schreck, T.P. Meyrath, J.L. Hanssen, G.N. Price, M.G. Raizen, Phys. Rev. Lett. 95, 260403 (2005)ADSCrossRefGoogle Scholar
  30. 30.
    J. Dalibard, Y. Castin, K. Mølmer, Phys. Rev. Lett. 68, 580 (1992)ADSCrossRefGoogle Scholar
  31. 31.
    J.A. Damborenea, I.L. Egusquiza, G.C. Hegerfeldt, J.G. Muga, Phys. Rev. A 66, 052104 (2002)ADSCrossRefGoogle Scholar
  32. 32.
    J.A. Damborenea, I.L. Egusquiza, G.C. Hegerfeldt, J.G. Muga, J. Phys. B: At. Mol. Opt. Phys. 36, 2657 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    J. Echanobe, A. del Campo, J.G. Muga, Phys. Rev. A 77, 032112 (2008)ADSCrossRefGoogle Scholar
  34. 34.
    P. Facchi, S. Pascazio, Prog. Opt. 42, 147 (2001)CrossRefGoogle Scholar
  35. 35.
    P. Facchi, S. Pascazio, A. Scardicchio, L.S. Schulman, Phys. Rev. A 65, 012108 (2001)ADSCrossRefGoogle Scholar
  36. 36.
    P. Facchi, S. Tasaki, S. Pascazio, H. Nakazato, A. Tokuse, D.A. Lidar, Phys. Rev. A 71, 022302 (2005)ADSCrossRefGoogle Scholar
  37. 37.
    H. Feshbach, Ann. Phys. (N.Y.) 5, 357 (1958)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    H. Feshbach Ann. Phys. (N.Y.) 19, 287 (1962)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    E.A. Galapon, R.F. Caballar, R.T. Bahague, Phys. Rev. Lett. 93, 180406 (2004)ADSCrossRefGoogle Scholar
  40. 40.
    E.A. Galapon, F. Delgado, J.G. Muga, I. Egusquiza, Phys. Rev. A 74, 042107 (2005)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    R. Giannitrapani, Int. J. Theor. Phys. 36, 1575 (1997)MathSciNetCrossRefGoogle Scholar
  42. 42.
    R. Golub, S. Felber, R. Gähler, E. Gutsmiedl, Phys. Lett. A 148, 27 (1990)ADSCrossRefGoogle Scholar
  43. 43.
    A. Gozdz, M. Debicki, Phys. Atom. Nucl. 70, 529 (2007)ADSCrossRefGoogle Scholar
  44. 44.
    J.J. Halliwell, Prog. Theor. Phys. 102, 707 (1999)ADSCrossRefGoogle Scholar
  45. 45.
    V. Hannstein, G.C. Hegerfeldt, J.G. Muga, J. Phys. B: At. Mol. Opt. Phys. 38, 409 (2005)ADSCrossRefGoogle Scholar
  46. 46.
    T.E. Hartman, J. Appl. Phys. 33, 3427 (1962)ADSCrossRefGoogle Scholar
  47. 47.
    G.C. Hegerfeldt, D. Seidel, J.G. Muga, Phys. Rev. A 68, 022111 (2003)ADSCrossRefGoogle Scholar
  48. 48.
    G.C. Hegerfeldt, D. Seidel, J.G. Muga, B. Navarro, Phys. Rev. A 70, 012110 (2004)ADSCrossRefGoogle Scholar
  49. 49.
    G.C. Hegerfeldt, J.T. Neumann, L.S. Schulman, J. Phys. A 39, 14447 (2006)ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    G.C. Hegerfeldt, J.T. Neumann, L.S. Schulman, Phys. Rev. A 75, 012108 (2007)ADSCrossRefGoogle Scholar
  51. 51.
    G.C. Hegerfeldt, T.S. Wilser, in Classical and Quantum Systems. Proceedings of the Second International Wigner Symposium, July 1991, H.D. Doebner, W. Scherer, F. Schroeck (eds.) (World Scientific, Singapore, 1992), p. 104Google Scholar
  52. 52.
    G.C. Hegerfeldt, Phys. Rev. A 47, 449 (1993)ADSCrossRefGoogle Scholar
  53. 53.
    G.C. Hegerfeldt, D.G. Sondermann, Quantum Semiclass. Opt. 8, 121 (1996). For a review cf. M.B. Plenio, P.L. Knight, Rev. Mod. Phys. 70, 101 (1998)ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    D. Home, A. Whitaker, Ann. Phys. 258, 237 (1997)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    Y.Z. Huang, C.M. Wang, J. Phys. Condens. Matter 3, 5915 (1991)ADSCrossRefGoogle Scholar
  56. 56.
    J. Kijowski, Rep. Math. Phys. 6, 361 (1974)ADSMathSciNetCrossRefGoogle Scholar
  57. 57.
    M.S. Kim, P.L. Knight, K. Wodkiewicz, Opt. Commun. 62, 385 (1987)ADSCrossRefGoogle Scholar
  58. 58.
    K. Koshino, A. Shimizu, Phys. Rep. 412, 191 (2005)ADSMathSciNetCrossRefGoogle Scholar
  59. 59.
    L. Lamata, J. León, Concepts Phys. 2, 49 (2005)Google Scholar
  60. 60.
    C.R. Leavens, Phys. Rev. A 58, 840 (1998)ADSMathSciNetCrossRefGoogle Scholar
  61. 61.
    J. León, J. Julve, P. Pitanga, F.J. de Urríes, Phys. Rev. A 61, 062101 (2000)ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    R.D. Levine, Quantum Mechanics of Molecular Rate Processes (Oxford, London, 1969)Google Scholar
  63. 63.
    B. Misra, E.C.G. Sudarshan, J. Math. Phys. 18, 756 (1977)ADSMathSciNetCrossRefGoogle Scholar
  64. 64.
    J.G. Muga, C.R. Leavens, Phys. Rep. 338, 353 (2000)ADSMathSciNetCrossRefGoogle Scholar
  65. 65.
    J.G. Muga, A.D. Baute, J.A. Damborenea, I.L. Egusquiza, arXiv: quant-ph/0009111 Google Scholar
  66. 66.
    J.G. Muga, S. Brouard, R. Sala, J. Phys. Condens. Matter 4, L579 (1992)ADSCrossRefGoogle Scholar
  67. 67.
    J.G. Muga, S. Brouard, D. Macías, Ann. Phys. (N.Y.) 240, 351 (1995)ADSCrossRefGoogle Scholar
  68. 68.
    J.G. Muga, J.P. Palao, R. Sala, Phys. Lett. A 238, 90 (1998)ADSMathSciNetCrossRefGoogle Scholar
  69. 69.
    J.G. Muga, R. Leavens, J.P. Palao, Phys. Rev. A 58, 4336 (1998)ADSCrossRefGoogle Scholar
  70. 70.
    J.G. Muga, J.P. Palao, C.R. Leavens, Phys. Lett. A 253, 21 (1999)ADSCrossRefGoogle Scholar
  71. 71.
    J.G. Muga, R. Sala, I.L. Egusquiza (eds.), Time in Quantum Mechanics, vol. 1, Lect. Notes Phys. 734 (Springer, Berlin, 2008)Google Scholar
  72. 72.
    J.G. Muga, D. Seidel, G.C. Hegerfeldt, J. Chem. Phys. 122, 154106 (2005)ADSCrossRefGoogle Scholar
  73. 73.
    B. Navarro, I.L. Egusquiza, J.G. Muga, G.C. Hegerfeldt, J. Phys. B: At. Mol. Opt. Phys. 36, 3899 (2003)ADSCrossRefGoogle Scholar
  74. 74.
    B. Navarro, I.L. Egusquiza, J.G. Muga, G.C. Hegerfeldt, Phys. Rev. A 67, 063819 (2003)ADSCrossRefGoogle Scholar
  75. 75.
    H. Nazakato, T. Takazawa, K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003)ADSCrossRefGoogle Scholar
  76. 76.
    M.K. Oberthaler, R. Abfalterer, S. Bernet, J. Schmiedmayer, A. Zeilinger, Phys. Rev. Lett. 77, 4980 (1996)ADSCrossRefGoogle Scholar
  77. 77.
    J.P. Palao, J.G. Muga, S. Brouard, A. Jadczyk, Phys. Lett. A 233, 227 (1997)ADSCrossRefGoogle Scholar
  78. 78.
    R.W. Robinett, Am. J. Phys. 63, 823 (1995)ADSMathSciNetCrossRefGoogle Scholar
  79. 79.
    A. Ruschhaupt, Phys. Lett. A 250, 249 (1998)ADSCrossRefGoogle Scholar
  80. 80.
    A. Ruschhaupt, in Decoherence: Theoretical, Experimental and Conceptual Problems, Ph. Blanchard et al. (eds.), Lect. Notes Phys. 538 (Springer, Berlin, 2000), p. 259Google Scholar
  81. 81.
    A. Ruschhaupt, J. Phys. A: Math. Gen. 35, 10429 (2002)ADSMathSciNetCrossRefGoogle Scholar
  82. 82.
    A. Ruschhaupt, J.A. Damborenea, B. Navarro, J.G. Muga, G.C. Hegerfeldt, Europhys. Lett. 67, 1 (2004)ADSMathSciNetCrossRefGoogle Scholar
  83. 83.
    A. Ruschhaupt, B. Navarro, J.G. Muga, J. Phys. B: At. Mol. Opt. Phys. 37, L313 (2004)ADSCrossRefGoogle Scholar
  84. 84.
    J. Ruseckas, B. Kaulakys, Phys. Rev. A 66, 052106 (2002)ADSCrossRefGoogle Scholar
  85. 85.
    L.S. Schulman, Phys. Rev. A 57, 1509 (1998)ADSMathSciNetCrossRefGoogle Scholar
  86. 86.
    A.M. Steinberg, P.G. Kwiat, R.Y. Chiao, Phys. Rev. Lett. 71, 708 (1993)ADSCrossRefGoogle Scholar
  87. 87.
    E.W. Streed, J. Mun, M. Boyd, G.K. Campbell, P. Medley, W. Ketterle, D.E. Pritchard, Phys. Rev. Lett. 97, 260402 (2006)ADSCrossRefGoogle Scholar
  88. 88.
    A. Tachibana, J. Chem. Phys. 115, 3497 (2001)ADSCrossRefGoogle Scholar
  89. 89.
    M.W. Thomas, R.F. Snider, J. Stat. Phys. 2, 61 (1970)ADSCrossRefGoogle Scholar
  90. 90.
    G. Torres-Vega, Phys. Rev. A 75, 032112 (2007)ADSCrossRefGoogle Scholar
  91. 91.
    R. Werner, J. Math. Phys. 27, 793 (1986)ADSMathSciNetCrossRefGoogle Scholar
  92. 92.
    R. Werner, Ann. Inst. Henri Poincaré 47, 429 (1987)Google Scholar
  93. 93.
    M. Zwanzig, J. Chem. Phys. 33, 1338 (1960)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andreas Ruschhaupt
    • 1
    Email author
  • J. Gonzalo Muga
    • 2
  • Gerhard C. Hegerfeldt
    • 3
  1. 1.Institut für Mathematische PhysikTU BraunschweigBraunschweigGermany
  2. 2.Departamento de Química Física, UPV-EHUBilbaoSpain
  3. 3.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany

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