Coulombic Entanglement: One-Step Single Photoionization of Atoms

  • N. Chandra
  • R. Ghosh
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 67)


Photoionization (1.1) is, probably, the simplest among the basic processes in atomic and molecular physics for generating an entangled state of two flying particles one of which is an electronic qubit. It is simplest for two reasons: First, the whole process is completed in a single step; second, it is based on the well-understood physics of photoelectric effect [1] taking place due to the absorption of a single photon γ r in a target \(\mathfrak{T}\) in the E1 approximation. Here, it is obvious from (1.1), the constituents of a bipartite state are the residual photoion \({\mbox{ $\mathfrak{T}$}}^{1+}\) and the photoelectron e p . Unlike the processes (1.2)-(1.8), the incident photon in (1.1) is absorbed by one of the electrons in the outer most shell of \(\mathfrak{T}\) so that the residual photoion \({\mbox{ $\mathfrak{T}$}}^{1+}\) is left in its ground electronic state \(\vert {1}^{+}\rangle\), which is stable against any decay.


Density Matrix Entangle State Bipartite System Bipartite State Partial Transpose 
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.


  1. 1.
    A. Einstein, Annalen der Physik (Leipzig) 17, 132 (1905)Google Scholar
  2. 10.
    B.H. Bransden, C.J. Joachain, Physics of Atoms and Molecules, 2nd edn. (Benjamin Cummings, New York, 2003)Google Scholar
  3. 43.
    G. Alber, T. Berth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, A. Zeilinger (eds.), Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments (Springer, Berlin, 2001)zbMATHGoogle Scholar
  4. 60.
    M. Weissbluth, Atoms and Molecules (Academic, New York, 1978)Google Scholar
  5. 65.
    A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princeton University Press, Princeton, 1996)zbMATHGoogle Scholar
  6. 67.
    D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, Quantum Theory of Angular Momentum (World Scientific, Singapur, 1988)Google Scholar
  7. 110.
    G. Benenti, G. Casati, G. Strini, Principles of Quantum Computation and Information, Volume I: Basic Concepts (World Scientific, Singapore, 2005)Google Scholar
  8. 124.
    A. Peres, Phys. Rev. Lett. 77, 1413 (1996)MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 125.
    M. Horodecki, P. Horodecki, R. Horodecki, Phys. Lett. A 223, 1 (1996)MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 126.
    R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Revs. Mod. Phys. 81, 865 (2009)MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 127.
    L.M. Ioannou, Quant. Inf. Comput. 7, 335 (2007), quant-ph/0603199v7Google Scholar
  12. 132.
    M. Horodecki, P. Horodecki, R. Horodecki, in Quantum Information: An Introduction to Basic Theoretical Concepts and Experiments, eds. G. Alber, T. Berth, M. Horodecki, P. Horodecki, R. Horodecki, M. Rötteler, H. Weinfurter, R. Werner, A. Zeilinger (Springer, Berlin, 2001)Google Scholar
  13. 138.
    P. Horodecki, Phys. Lett. A 232, 333 (1997)MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. 140.
    P. Horodecki, M. Lewenstein, G. Vidal, I. Cirac, Phys. Rev. A 62, 03231 (2000)MathSciNetGoogle Scholar
  15. 149.
    W.K. Wootters, Quant. Inf. Comput. 1, 27 (2001)MathSciNetzbMATHGoogle Scholar
  16. 156.
    M.A. Nielson, Phys. Rev. Lett. 83, 436 (1999)ADSCrossRefGoogle Scholar
  17. 160.
    F. Mintert, A.R.R. Carvalho, M. Kus, A. Buchleitner, Phys. Rep. 415, 207 (2005)MathSciNetADSCrossRefGoogle Scholar
  18. 161.
    C.H. Bennett, D.P. DiVincenzo, J. Smolin, W.K. Wooters, Phys. Rev. A 54, 3824 (1996)MathSciNetADSCrossRefGoogle Scholar
  19. 168.
    F. Mintert, A. Buchleitner, Phys. Rev. Lett. 98, 140505 (2007)MathSciNetADSCrossRefGoogle Scholar
  20. 170.
    C.-J. Zhang, Y.-X. Gong, Y.-S. Zhang, G.-C. Guo, Phys. Rev. A 78, 042308 (2008)ADSCrossRefGoogle Scholar
  21. 184.
    E.U. Condon, R. Shortley, The Theory of Atomic Spectra, (Cambridge at the University Press, England, 1970)Google Scholar
  22. 186.
    I.I. Sobelman, Atomic Spectra and Radiative Transitions, 2nd ed. (Springer, Germany, 1992)CrossRefGoogle Scholar
  23. 219.
    M. Horodecki, R. Horodecki, Quant. Inf. Comput. 1, 45 (2001)MathSciNetzbMATHGoogle Scholar
  24. 220.
    S. Parida, N. Chandra, Phys. Rev. A 86, 062302 (2012)ADSCrossRefGoogle Scholar
  25. 221.
    A.F. Starace, Handbuch der Physik 31, 1 (1982)ADSCrossRefGoogle Scholar
  26. 222.
    Y.S. Kim, Y.J. Kim, R.H. Pratt, Phys. Scr. T110, 79 (2004)ADSCrossRefGoogle Scholar
  27. 223.
    P. Horodecki, J. Smolin, B. Terhal, A. Tnhaplyial, quant-ph/99101222Google Scholar
  28. 224.
    D. Bruβ, A. Peres, Phys. Rev. A 61, 030301 (2000)Google Scholar
  29. 225.
    H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J.A. Smolin, W.K. Wootters, Phys. Rev. Lett. 76, 722 (1996), ibid 78, 2031 (1997)Google Scholar
  30. 227.
    C.H. Bennett, H.J. Bernstein, S. Popescu, B. Schumacher, Phys. Rev. A 53, 2046 (1996)ADSCrossRefGoogle Scholar
  31. 230.
    M. Murao, M.B. Plenio, S. Popescu, V. Vederal, P.L. Knight Phys. Rev. A 57, 4075 (1998)CrossRefGoogle Scholar
  32. 231.
    D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, A. Sanpera, Phys. Rev. Lett. 77, 2818 (1996)ADSCrossRefGoogle Scholar
  33. 233.
    S.J. van Enk, J.I. Cirac, P. Zoller, Science 279, 205 (1998)ADSCrossRefGoogle Scholar
  34. 234.
    D. Jonathan, M.B. Plenio, Phys. Rev. Lett. 83, 1455 (1999)MathSciNetADSCrossRefGoogle Scholar
  35. 235.
    G. Vidal, Phys. Rev. Lett. 83, 1046 (1999)ADSCrossRefGoogle Scholar
  36. 236.
    M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. Lett. 78, 574 (1997)ADSCrossRefGoogle Scholar
  37. 237.
    P. Horodecki,521 M. Horodecki, R. Horodecki, Phys. Rev. Lett. 82, 1056 (1999)Google Scholar
  38. 238.
    C.H. Bennett, D.P. DiVincenzo, T. Mor, P.W. Shor, J.A. Smolin, B.M. Terhal, Phys. Rev. Lett. 82, 5385 (1999)MathSciNetADSCrossRefGoogle Scholar
  39. 246.
    M. Piani, Phys. Rev. A 73, 012345 (2006)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Physics and MeteorologyIndian Institute of TechnologyKharagpurIndia
  2. 2.c/o B.N. PandaPokhariputIndia

Personalised recommendations