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Orbital Angular Momentum: Testbed for Quantum Mechanics

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Quantum Information and Coherence

Part of the book series: Scottish Graduate Series ((SGS))

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Abstract

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.

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References

  1. Allen, L., Barnett, S.M., Padgett, M.J.: Optical Angular Momentum. Taylor & Francis, London (2003)

    Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  4. Allen, L., Padgett, M.J., Babiker, M.: IV the orbital angular momentum of light. Prog. Opt. 39, 291–372 (1999)

    Google Scholar 

  5. Aspect, A., Dalibard, J., Roger, G.: Experimental test of Bell’s inequalities using time-varying analyzers. Phys. Rev. Lett. 49, 1804–1807 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  6. Aspect, A., Grangier, P., Roger, G.: Experimental tests of realistic local theories via Bell’s theorem. Phys. Rev. Lett. 47, 460–463 (1981)

    Article  ADS  Google Scholar 

  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. 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)

    Article  ADS  Google Scholar 

  9. Bell, J.: Speakable and unspeakable in quantum mechanics. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  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)

    Article  ADS  Google Scholar 

  11. Beth, R.A.: Mechanical detection and measurement of the angular momentum of light. Phys. Rev. 50(2), 115 (1936)

    Article  ADS  MathSciNet  Google Scholar 

  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)

    Article  ADS  MathSciNet  Google Scholar 

  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. 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. Franke-Arnold, S., Allen, L., Padgett, M.: Advances in optical angular momentum. Laser & Photonics Rev. 2(4), 299–313 (2008)

    Article  Google Scholar 

  16. Freedman, S.J., Clauser, J.F.: Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938–941 (1972)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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. 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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  23. Mair, A., Vaziri, A., Weihs, G., Zeilinger, A.: Entanglement of the orbital angular momentum states of photons. Nature 412, 313–316 (2001)

    Article  ADS  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  27. Padgett, M.J., Courtial, J.: Poincaré-sphere equivalent for light beams containing orbital angular momentum. Opt. Lett. 24(7), 430–432 (1999)

    Article  ADS  Google Scholar 

  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. 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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. School of Physics and Astronomy, University of Glasgow, Glasgow, UK

    J. Romero & M. J. Padgett

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  1. J. Romero
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  2. M. J. Padgett
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Correspondence to M. J. Padgett .

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Editors and Affiliations

  1. Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh, United Kingdom

    Erika Andersson

  2. Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh, United Kingdom

    Patrik Öhberg

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Romero, J., Padgett, M.J. (2014). Orbital Angular Momentum: Testbed for Quantum Mechanics. In: Andersson, E., Öhberg, P. (eds) Quantum Information and Coherence. Scottish Graduate Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04063-9_7

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