Advertisement

Stern-Gerlach experiment with arbitrary spin: Temporal evolution and entanglement

  • J. A. Mendoza Fierro
  • L. M. Arévalo AguilarEmail author
Regular Article
  • 23 Downloads

Abstract.

Because it has disclosed basic quantum properties and concepts, the Stern-Gerlach experiment (SGE) has been fundamental for the development of quantum mechanics; for example, it was particularly used to model the measurement problem on the quantum world. Despite being almost one hundred years old, the SGE is still providing new valuable insights in the development and understanding of quantum mechanics. In this paper, by using the evolution operator method, we derive the equations that provide the time evolution of the quantum state of a particle with arbitrary spin s in the Stern-Gerlach apparatus. Such temporal evolution shows quantum entanglement between the degrees of freedom of the particle. We theoretically study, through the von Neumann entropy, the entanglement that arose between the degrees of freedom of the system for the case when the particle is polarized with an arbitrary angle \( \theta\), analyzing how the entanglement depends on this angle \( \theta\).

References

  1. 1.
    W. Gerlach, O. Stern, Z. Phys. 8, 110 (1922)ADSCrossRefGoogle Scholar
  2. 2.
    Bretislav Friedrich, Dudley Herschbach, Daedalus 127, 165 (1998)Google Scholar
  3. 3.
    B. Friedrich, D. Herschbach, Phys. Today 56, 53 (2003)ADSCrossRefGoogle Scholar
  4. 4.
    D. Herschbach, Ann. Phys. 10, 163 (2001)CrossRefGoogle Scholar
  5. 5.
    Friedel Weinert, Stud. Hist. Philos. Sci. Part B 26, 75 (1995)CrossRefGoogle Scholar
  6. 6.
    H. Schmidt-Böcking, L. Schmidt, H.J. Lüdde, W. Trageser, A. Templeton, T. Sauer, Eur. Phys. J. H 41, 327 (2016)CrossRefGoogle Scholar
  7. 7.
    Arthur H. Compton, J. Frank. Inst. 192, 145 (1921)CrossRefGoogle Scholar
  8. 8.
    G.E. Uhlenbeck, S. Goudsmit, Nature 117, 264 (1926)ADSCrossRefGoogle Scholar
  9. 9.
    J. Mehra, H. Rechenberg, The Quantum Theory of Planck, Einstein, Bohr and Sommerfeld: Its Foundation and the Rise of Its Difficulties 1900--1925, Vol. 1 (Springer-Verlag, New York, 1982)Google Scholar
  10. 10.
    T.E. Phipps, J.B. Taylor, Phys. Rev. 29, 309 (1927)ADSCrossRefGoogle Scholar
  11. 11.
    Willis E. Lamb, Robert C. Retherford, Phys. Rev. 72, 241 (1947)ADSCrossRefGoogle Scholar
  12. 12.
    E. Benéz Rodríguez, L.M. Arévalo Aguilar, E. Piceno Martínez, Eur. J. Phys. 38, 025403 (2017)CrossRefGoogle Scholar
  13. 13.
    E. Benéz Rodríguez, L.M. Arévalo Aguilar, E. Piceno Martínez, Eur. J. Phys. 38, 069501 (2017)CrossRefGoogle Scholar
  14. 14.
    Alma Elena Piceno Martínez, Ernesto Benéz Rodríguez, Julio Abraham Mendoza Fierro, Marcela Maribel Méndez Otero, Luis Manuel Arévalo Aguilar, Entropy 20, 299 (2018)CrossRefGoogle Scholar
  15. 15.
    E.P. Wigner, Am. J. Phys. 31, 6 (1963)ADSCrossRefGoogle Scholar
  16. 16.
    W.H. Zurek, Phys. Rev. D 24, 1516 (1981)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    M.O. Scullya, Y. Rostovtseva, Z. Sariyanni, M.S. Zubairy, Physica E 29, 29 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    L.M. Arévalo Aguilar, On the stern-gerlach experiment as an entangling device, submitted, 2019Google Scholar
  19. 19.
    N.D. Mermin, Phys. Rev. Lett. 65, 3373 (1990)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    A. Peres, Phys. Lett. A 151, 107 (1990)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    G.B. Roston, M. Casas, A. Plastino, A.R. Plastino, Eur. J. Phys. 26, 657 (2005)CrossRefGoogle Scholar
  22. 22.
    Daniel E. Platt, Am. J. Phys. 60, 306 (1992)ADSCrossRefGoogle Scholar
  23. 23.
    Bailey C. Hsu, Manuel Berrondo, Jean-François S. Van Huele, Phys. Rev. A 83, 012109 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    E.B. Manoukian, Eur. Phys. J. D 25, 253 (2003)ADSCrossRefGoogle Scholar
  25. 25.
    Dipankar Home, Alok Kumar Pan, Md Manirul Ali, A.S. Majumdar., J. Phys. A 40, 13975 (2007)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    F. Jeske, Th. Stöferle, M. DeKieviet, Eur. Phys. J. D 63, 25 (2011)ADSCrossRefGoogle Scholar
  27. 27.
    Anirudh Reddy, Joseph Samuel, Kumar Shivam, Supurna Sinha, Phys. Lett. A 380, 1135 (2016)ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Lamb Scully, Barut, Found. Phys. 17, 575 (1987)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Bayram Tekin, Eur. J. Phys. 37, 035401 (2016)CrossRefGoogle Scholar
  30. 30.
    M.G.A. Paris, Eur. Phys. J. ST 203, 61 (2012)CrossRefGoogle Scholar
  31. 31.
    C. Cohen-Tannoudji, B. Diu, F. Laloë, Quantum Mechanics, Vol. 1 (Wiley, New York, 1991)Google Scholar
  32. 32.
    N.L. Harshman, Quantum Inf. Comput. 7, 273 (2007)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Preben Alstro/m, Poul Hjorth, Richard Mattuck, Am. J. Phys. 50, 697 (1982)CrossRefGoogle Scholar
  34. 34.
    F. Casas, A. Murua, M. Nadinic, Comput. Phys. Commun. 183, 2386 (2012)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    P.C. García Quijas, L.M. Arévalo Aguilar, Phys. Scr. 75, 185 (2007)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    S.M. Blinder, Am. J. Phys. 36, 525 (1968)ADSCrossRefGoogle Scholar
  37. 37.
    P.C. García Quijas, L.M. Arévalo Aguilar, Eur. J. Phys. 28, 147 (2007)CrossRefGoogle Scholar
  38. 38.
    M. Keller, F. Mateusz Kotyrbaand Leupold, Ebner M. Singh, A. Zeilinger, Phys. Rev. A 90, 063607 (2014)ADSCrossRefGoogle Scholar
  39. 39.
    G. Reinisch, Phys. Lett. A 259, 427 (1999)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Facultad de Ciencias Físico MatemáticasBenemérita Universidad de PueblaPueblaMexico

Personalised recommendations