Orbital Angular Momentum: Testbed for Quantum Mechanics

Part of the Scottish Graduate Series book series (SGS)


Entanglement of light’s orbital angular momentum (OAM) is firmly established both theoretically and experimentally. For Laguerrre-Gaussian beams, the OAM of a photon can take on any value \(\ell \hbar \), where \(\ell \) is an integer. Within communication systems, this higher dimensionality suggests an increase in the information density of the photon. But no less than this communications application is the relevance of OAM to more fundamental aspects of quantum mechanics. This chapter starts with a brief survey of the history of OAM and its physical origin. We then proceed to describe how a fundamental Gaussian mode can be transformed to an OAM-carrying beam. Capitalising on the analogy between photon polarisation and OAM, we present results of Bell-type experiments which test against local hidden variable theories. Finally, we exploit the higher dimensional OAM space in an Einstien-Podolsky-Rosen experiment for OAM and its conjugate variable, angle.


Angular Momentum Orbital Angular Momentum Bell Inequality Spatial Light Modulator Spin Angular Momentum 
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  1. 1.
    Allen, L., Barnett, S.M., Padgett, M.J.: Optical Angular Momentum. Taylor & Francis, London (2003)Google Scholar
  2. 2.
    Allen, L., Beijersbergen, M.W., Spreeuw, R.J.C., Woerdman, J.P.: Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185–8189 (1992)ADSCrossRefGoogle Scholar
  3. 3.
    Allen, L., Courtial, J., Padgett, M.J.: Matrix formulation for the propagation of light beams with orbital and spin angular momenta. Phys. Rev. E 60, 7497–7503 (1999)ADSCrossRefGoogle Scholar
  4. 4.
    Allen, L., Padgett, M.J., Babiker, M.: IV the orbital angular momentum of light. Prog. Opt. 39, 291–372 (1999)Google Scholar
  5. 5.
    Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    Aspect, A., Grangier, P., Roger, G.: Experimental tests of realistic local theories via Bell’s theorem. Phys. Rev. Lett. 47, 460–463 (1981)ADSCrossRefGoogle Scholar
  7. 7.
    Bazhenov, V., Vasnetsov, M.V., Soskin, M.S.: Laser beams with screw dislocations in their wavefronts. JETP Lett. 52, 429–431 (1990)Google Scholar
  8. 8.
    Beijersbergen, M.W., Allen, L., Van der Veen, H., Woerdman, J.P.: Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun. 96(1–3), 123–132 (1993)ADSCrossRefGoogle Scholar
  9. 9.
    Bell, J.: Speakable and unspeakable in quantum mechanics. Cambridge University Press, Cambridge (1987)Google Scholar
  10. 10.
    Berkhout, G.C.G., Lavery, M.P.J., Courtial, J., Beijersbergen, M.W., Padgett, M.J.: Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett. 105(15), 153601 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    Beth, R.A.: Mechanical detection and measurement of the angular momentum of light. Phys. Rev. 50(2), 115 (1936)ADSCrossRefMathSciNetGoogle Scholar
  12. 12.
    Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88(4), 40404 (2002)ADSCrossRefMathSciNetGoogle Scholar
  13. 13.
    Dada, V., Leach, J., Buller, G., Padgett, M.J., Andersson, E.: Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities. Nat. Phys. 7, 677–680 (2011)Google Scholar
  14. 14.
    Darwin, C.G.: Notes on the theory of radiation. Proc. R. Soc. Lond. A. (Containing papers of a mathematical and physical character) 136(829), 36–52 (1932)Google Scholar
  15. 15.
    Franke-Arnold, S., Allen, L., Padgett, M.: Advances in optical angular momentum. Laser & Photonics Rev. 2(4), 299–313 (2008)CrossRefGoogle Scholar
  16. 16.
    Freedman, S.J., Clauser, J.F.: Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938–941 (1972)ADSCrossRefGoogle Scholar
  17. 17.
    He, H., Friese, M., Heckenberg, N.R., Rubinzstein-Dunlop, H.: Direct observation of transfer of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Phys. Rev. Lett. 75, 826–829 (1995)ADSCrossRefGoogle Scholar
  18. 18.
    Howell, J.C, Bennink, R.S, Bentley, S.J, Boyd, R.W.: Realization of the Einstein-Podolsky-Rosen paradox using momentum-and position-entangled photons from spontaneous parametric down conversion. Phys. Rev. Lett. 92(21), 210403 (2004)Google Scholar
  19. 19.
    Jack, B., Yao, A.M., Leach, J., Romero, J., Franke-Arnold, S., Ireland, D.G., Barnett, S.M., Padgett, M.J.: Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces. Phys. Rev. A 81(4), 43844 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    Langford, N.K., Dalton, R.B., Harvey, M.D., O’Brien, J.L., Pryde, G.J., Gilchrist, A., Bartlett, S.D., White, A.G.: Measuring entangled qutrits and their use for quantum bit commitment. Phys. Rev. Lett. 93(5), 53601 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    Leach, J., Jack, B., Romero, J., Jha, A., Yao, A., Franke-Arnold, S., Ireland, D., Boyd, R., Barnett, S., Padgett, M.: Quantum correlations in optical angle-orbital angular momentum variables. Science 329, 662 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    Leach, J., Jack, B., Romero, J., Ritsch-Marte, M., Boyd, R.W., Jha, A.K., Barnett, S.M., Franke-Arnold, S., Padgett, M.J.: Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces. Opt. Express 10, 8287–8293 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    Mair, A., Vaziri, A., Weihs, G., Zeilinger, A.: Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001)ADSCrossRefGoogle Scholar
  24. 24.
    Nye, J.F, Berry, M.V: Dislocations in wave trains. Proc. R. Soc. Lond. A. Math. Phys. Sci. 336(1605), 165 (1974)Google Scholar
  25. 25.
    O’neil, A.T., MacVicar, I., Allen, L., Padgett, M.J.: Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. Phys. Rev. Lett. 88(5), 53601 (2002)CrossRefGoogle Scholar
  26. 26.
    Ou, Z.Y., Pereira, S.F., Kimble, H.J., Peng, K.C.: Realization of the Einstein-Podolsky-Rosen paradox for continuous variables. Phys. Rev. Lett. 68(25), 3663–3666 (1992)ADSCrossRefGoogle Scholar
  27. 27.
    Padgett, M.J., Courtial, J.: Poincaré-sphere equivalent for light beams containing orbital angular momentum. Opt. Lett. 24(7), 430–432 (1999)ADSCrossRefGoogle Scholar
  28. 28.
    Poynting, J.H: The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light. Proc. R. Soc. Lond. A. (Containing papers of a mathematical and physical character) 82(557), 560–567 (1909)Google Scholar
  29. 29.
    Romero, J., Leach, J., Jack, B., Barnett, S.M., Padgett, M.J., Franke-Arnold, S.: Violation of Leggett inequalities in orbital angular momentum subspaces. New J. Phys. 12, 123007 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    Romero, J., Leach, J., Jack, B., Dennis, M.R., Franke-Arnold, S., Barnett, S.M., Padgett, M.J.: Entangled optical vortex links. Phys. Rev. Lett. 106(10), 100407 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    Simpson, N.B., Dholakia, K., Allen, L., Padgett, M.J.: Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner. Opt. Lett. 22(1), 52–54 (1997)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.School of Physics and AstronomyUniversity of GlasgowGlasgowUK

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