Abstract

We present a scheme to measure the orbital angular momentum spectrum of light using a precisely timed optical loop and quantum non-demolition measurements. We also discuss the influence of imperfect optical components.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  2. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
    [CrossRef]
  3. S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).
    [CrossRef]
  4. G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
    [CrossRef]
  5. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
    [CrossRef] [PubMed]
  6. G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).
    [CrossRef] [PubMed]
  7. D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
    [CrossRef] [PubMed]
  8. N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).
    [CrossRef] [PubMed]
  9. B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
    [CrossRef]
  10. J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
    [CrossRef]
  11. J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
    [CrossRef] [PubMed]
  12. Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).
    [CrossRef]
  13. V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).
  14. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
    [CrossRef] [PubMed]
  15. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
    [CrossRef]
  16. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
    [CrossRef] [PubMed]
  17. G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
    [CrossRef]
  18. A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48, 931–932 (1980).
    [CrossRef]
  19. A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).
    [CrossRef]
  20. P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
    [CrossRef]
  21. S0 and S1 are optical switches that can be switched from been transmittive to reflective. S0 needs to transmit the initial incident light, and be switched to be reflective by the end of the first outer-loop cycle. A high repetition rate is not required and it can be implemeted either mechanically or opto-electrically. Alternatively it could also be a static high-reflectance mirror, if the one-time transmission loss at the very beginning can be tolerated. S1 needs to be switched every QZI loop cycle (ΔT) and need to be polarization insensitive. The fastest switches are Pockels cells, which can operate at 10–100 GHz with 99% transmission. One scheme, similar to the one implemented in Ref. [20], is to an interferometer with Pockels cells in one of the arms. The Pockels cells introduce π phase shift in the arm when activated, and thus switch the beam between two output ports of the interferometer. Using two Pockels cells rotated relative to each other will cancel the birefringent effect.
  22. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  23. B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
    [CrossRef]
  24. Technically, each |α|2 is slightly different, but the difference is well within 1%. The |α|2 that matters most is the one corresponding to the QZI loop (including S1), which, without any optimization, consists of 4 beam splitters, 5 mirrors, 1 waveplate and up to three Pockels cells. Assuming all optics are anti-reflection coated so that loss is 1% at each Pockels cell and 0.1% at each other component, we have |α|2 = 0.96.
  25. J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A 59, 2322–2329 (1999).
    [CrossRef]

2010 (2)

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

2009 (2)

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).
[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

2008 (2)

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).
[CrossRef]

2007 (1)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

2005 (1)

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

2004 (1)

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

2002 (1)

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef] [PubMed]

2001 (2)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

2000 (1)

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[CrossRef] [PubMed]

1999 (2)

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A 59, 2322–2329 (1999).
[CrossRef]

1998 (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

1994 (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1993 (1)

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).
[CrossRef]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

1990 (1)

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

1980 (1)

A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48, 931–932 (1980).
[CrossRef]

1977 (1)

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
[CrossRef]

Allen, L.

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Almeida, M. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

Barbieri, M.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Barnett, S. M.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

Barreiro, J. T.

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

Bazhekov, V.

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Beijersbergen, M. W.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Berkhout, G. C. G.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Bourennane, M.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef] [PubMed]

Cerf, N. J.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef] [PubMed]

Chávez-Cerda, S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Courtial, J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

Dholakia, K.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

Elitzur, A. C.

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).
[CrossRef]

Fonseca, E. J. S.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Franke-Arnold, S.

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

Gilchrist, A.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Gisin, N.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef] [PubMed]

Gnacinacuteski, P.

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[CrossRef] [PubMed]

Heckenberg, N. R.

Hickmann, J. M.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Jang, J.

J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A 59, 2322–2329 (1999).
[CrossRef]

Jennewein, T.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Karlsson, A.

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef] [PubMed]

Kaszlikowski, D.

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[CrossRef] [PubMed]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Kwiat, P. G.

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

Lanyon, B. P.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Lavery, M. P. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

Leach, J.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

Lin, Q.

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).
[CrossRef]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

McDuff, R.

Miklaszewski, W.

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[CrossRef] [PubMed]

Misra, B.

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
[CrossRef]

Mitchell, J. R.

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Nairz, O.

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

O’Brien, J. L.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Padgett, M. J.

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).
[CrossRef]

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

Peres, A.

A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48, 931–932 (1980).
[CrossRef]

Pryde, G. J.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Ralph, T. C.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Resch, K. J.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

Skeldon, K.

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

Smith, C. P.

Soares, W. C.

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

Soskin, M. S.

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Sudarshan, E. C. G.

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

Ursin, R.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

Vaidman, L.

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).
[CrossRef]

Vasnetsov, M.

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Vaziri, A.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

Wang, Z.

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).
[CrossRef]

Wei, T.

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

Weinfurter, H.

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

White, A. G.

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).
[CrossRef] [PubMed]

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Zdotukowski, M.

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[CrossRef] [PubMed]

Zeilinger, A.

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[CrossRef] [PubMed]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

Zhang, Z.

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).
[CrossRef]

Am. J. Phys. (1)

A. Peres, “Zeno paradox in quantum theory,” Am. J. Phys. 48, 931–932 (1980).
[CrossRef]

Found. Phys. (1)

A. C. Elitzur and L. Vaidman, “Quantum mechanical interaction-free measurements,” Found. Phys. 7, 987–997 (1993).
[CrossRef]

J. Math. Phys. (1)

B. Misra and E. C. G. Sudarshan, “The Zeno’s paradox in quantum theory,” J. Math. Phys. 18, 756–763 (1977).
[CrossRef]

J. Mod. Opt. (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre–Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231–1237 (1998).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

Z. Wang, Z. Zhang, and Q. Lin, “A novel method to determine the helical phase structure of Laguerre–Gaussian beams,” J. Opt. A, Pure Appl. Opt. 11, 085702 (2009).
[CrossRef]

JETP Lett. (1)

V. Bazhekov, M. Vasnetsov, and M. S. Soskin, “Laser-beams with screw dislocation in their wavefronts,” JETP Lett. 52, 429–431 (1990).

Laser Photonics Rev. (1)

S. Franke-Arnold, L. Allen, and M. J. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2, 299–313 (2008).
[CrossRef]

Nat. Phys. (3)

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007).
[CrossRef]

B. P. Lanyon, M. Barbieri, M. P. Almeida, T. Jennewein, T. C. Ralph, K. J. Resch, G. J. Pryde, J. L. O’Brien, A. Gilchrist, and A. G. White, “Simplifying quantum logic using higher-dimensional hilbert spaces,” Nat. Phys. 5, 134–140 (2009).
[CrossRef]

J. T. Barreiro, T. Wei, and P. G. Kwiat, “Beating the channel capacity limit for linear photonic superdense coding,” Nat. Phys. 4, 282–286 (2008).
[CrossRef]

Nature (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412, 313–316 (2001).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (2)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

J. Jang, “Optical interaction-free measurement of semitransparent objects,” Phys. Rev. A 59, 2322–2329 (1999).
[CrossRef]

Phys. Rev. Lett. (8)

J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, “Interferometric methods to measure orbital and spin, or the total angular momentum of a single photon,” Phys. Rev. Lett. 92, 013601 (2004).
[CrossRef] [PubMed]

G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, “Efficient sorting of orbital angular momentum states of light,” Phys. Rev. Lett. 105, 153601 (2010).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,” Phys. Rev. Lett. 88, 013601 (2001).
[CrossRef]

G. Molina-Terriza, A. Vaziri, R. Ursin, and A. Zeilinger, “Experimental quantum coin tossing,” Phys. Rev. Lett. 94, 040501 (2005).
[CrossRef] [PubMed]

D. Kaszlikowski, P. Gnacinacuteski, M. Zdotukowski, W. Miklaszewski, and A. Zeilinger, “Violations of local realism by two entangled N-Dimensional systems are stronger than for two qubits,” Phys. Rev. Lett. 85, 4418–4421 (2000).
[CrossRef] [PubMed]

N. J. Cerf, M. Bourennane, A. Karlsson, and N. Gisin, “Security of quantum key distribution using d-Level systems,” Phys. Rev. Lett. 88, 127902 (2002).
[CrossRef] [PubMed]

J. M. Hickmann, E. J. S. Fonseca, W. C. Soares, and S. Chávez-Cerda, “Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum,” Phys. Rev. Lett. 105, 053904 (2010).
[CrossRef] [PubMed]

P. G. Kwiat, A. G. White, J. R. Mitchell, O. Nairz, G. Weihs, H. Weinfurter, and A. Zeilinger, “High-efficiency quantum interrogation measurements via the quantum Zeno effect,” Phys. Rev. Lett. 83, 4725–4728 (1999).
[CrossRef]

Other (2)

S0 and S1 are optical switches that can be switched from been transmittive to reflective. S0 needs to transmit the initial incident light, and be switched to be reflective by the end of the first outer-loop cycle. A high repetition rate is not required and it can be implemeted either mechanically or opto-electrically. Alternatively it could also be a static high-reflectance mirror, if the one-time transmission loss at the very beginning can be tolerated. S1 needs to be switched every QZI loop cycle (ΔT) and need to be polarization insensitive. The fastest switches are Pockels cells, which can operate at 10–100 GHz with 99% transmission. One scheme, similar to the one implemented in Ref. [20], is to an interferometer with Pockels cells in one of the arms. The Pockels cells introduce π phase shift in the arm when activated, and thus switch the beam between two output ports of the interferometer. Using two Pockels cells rotated relative to each other will cancel the birefringent effect.

Technically, each |α|2 is slightly different, but the difference is well within 1%. The |α|2 that matters most is the one corresponding to the QZI loop (including S1), which, without any optimization, consists of 4 beam splitters, 5 mirrors, 1 waveplate and up to three Pockels cells. Assuming all optics are anti-reflection coated so that loss is 1% at each Pockels cell and 0.1% at each other component, we have |α|2 = 0.96.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

A schematic of the compact OAM spectrometer. The Quantum Zeno Interrogator (shaded region) distinguishes between zero and nonzero OAM states. The outer loop decreases the OAM value of light by one per round trip. All the beam splitters are polarizing beam splitters (PBSs) that transmits horizontally polarized light and reflects vertically polarized light. The OAM filter transmits states with zero OAM, but blocks states with non-zero OAM. S0 and S1 are switching mirrors that either transmits or reflects incident light [21]. R1 and R2 are fixed polarization rotators, which can be half wave plates. P1 and P2 are fast polarization switches, such as Pockels cells. When activated, P1 and P2 switches horizontal polarization to vertical and vice versa. When de-activated, they are transparent to light. The shaded region is a Quantum Zeno Interrogator [20] which separates OAM components with l = 0 and l ≠ 0 into different polarizations. Hence at PBS3, zero OAM component is sent to the detector while the none-zero OAM component is sent back into the outer-loop. The outer loop decreased OAM by one per round trip via, for example, a vortex phase plate (VPP) [22].

Fig. 2
Fig. 2

The probability of detecting the correct OAM value as a function of the number of loops (N) in the QZI using a perfect OAM filter. (a) Neglect optical loss. (b) Assume |α|2 = 0.96 based on commercially available optics. When optical loss is included, there exists an optimal N for higher order OAM states, due to the compromise between the quantum Zeno enhancement and optical loss.

Fig. 3
Fig. 3

The probabilities of different outcomes of a QZI interrogation as a function of the transmission of the OAM filter, neglecting optical loss. The blue solid line represents detecting OAM=0, the red dashed line is detecting OAM≠ 0, and the orange dotted line, loss. (a) N = 8. (b) N = 2 – 10.

Fig. 4
Fig. 4

Transmission of the pinhole spatial filter (a) as a function of the normalized aperture size a 0, for OAM components with l 0 = 0 – 3 and (b) as a function of l 0 with a 0 = 0.8.

Fig. 5
Fig. 5

(a) Extinction ratio η as a function of the number of loops N for various losses |α|2. Solid symbols are for l 0 = 1 and open symbols are for l 0 = 3. l 0 > 3 are essentially indistinguishable from l 0 = 3. For the l 0 = 0 case, the extinction ratio is over a 1000 for all |α|2 values because no premature measurements are possible. The additional green crosses labeled as |α|2 = 0.95* represents |α|2 = 0.96 but including misalignment of the OAM filter and VPP as discussed in the text. (b) Extinction ratio η as a function of the normalized aperture size a 0 for l 0 = 6, Δl = 1 – 3, N = 8, and |α|2 = 0.96. Skipping OAM states increases the extinction ratio by orders of magnitude.

Fig. 6
Fig. 6

(a) The probability of measuring an OAM value l for a given input state l 0 (Eq. (2)), using pinhole as the OAM filter, N = 8, |α|2 = 0.96, and misalignment of 10% and 1%, respectively, at the pinhole filter and VPP. Despite the decrease in probability for the diagonal elements at large l 0, the off diagonal elements decrease much faster, as implied by the large extinction ratios. (b) The diagonal elements of (a) as a function of N for l 0 = 0 – 10.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

( p H p V ) = α QZI N [ ( 1 0 0 T ( l ) e i ϕ ( l ) ) ( cos ( π 2 N ) sin ( π 2 N ) sin ( π 2 N ) cos ( π 2 N ) ) ] N ( 1 0 ) .
P ( l ; l 0 ) = | α init , final | 2 | p V ( l 0 l ) | 2 m = l 0 l + 1 l 0 ( | α out | 2 | p H ( m ) | 2 ) .
η ( l 0 ) = P ( l 0 ; l 0 ) / l l 0 P ( l ; l 0 ) .
I LG ( l ; ρ ) = I 0 0 du u | l | e u L | l | ( u ) ( 2 ρ w 0 ) | l | L | l | ( 2 ρ w 0 2 ) e ρ 2 w 0 2
T ( l , a 0 ) = 0 a 0 0 2 π ρ d ρ d ϕ I LG ( l ; ρ ) / 0 0 2 π ρ d ρ d ϕ I LG ( l ; ρ )
η ( l 0 ) = P ( l 0 ; l 0 ) / Σ P ( l l 0 ; l 0 ) α out | p V ( 0 ) | 2 p H ( 1 ) | 2 | p V ( 1 ) | 2 .

Metrics