Abstract

We propose and demonstrate experimentally a single lens design for an astigmatic mode converter that transforms the transverse mode of paraxial optical beams. As an application, we implement a controlled-not gate based on a Michelson interferometer in which the photon polarization is the control bit and the first order transverse mode is the target. As a further application, we also build a transverse mode parity sorter which can be useful for quantum information processing as a measurement device for the transverse mode qubit.

© 2010 Optical Society of America

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  1. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
    [CrossRef]
  2. G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature 3, 305–310 (2007).
  3. C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
    [CrossRef]
  4. C. E. R. Souza, J. A. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99(16), 160401 (2007).
    [CrossRef]
  5. M. Beijersbergen, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
    [CrossRef]
  6. V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis, maZh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) (JETP Lett. 52, 429–431 (1990)).
  7. J. A. O. Huguenin, B. Coutinho dos Santos, P. A. M. dos Santos, and A. Z. Khoury, “Topological defects in moire fringes with spiral zone plates,” J. Opt. Soc. Am. A 20(10), 1883–1889 (2003).
    [CrossRef]
  8. S. J. van Enk, “Geometric phase, transformations of gaussian light beams and angular momentum transfer,” Opt. Commun. 102(1-2), 59–64 (1993).
    [CrossRef]
  9. M. J. Padgett, and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999).
    [CrossRef]
  10. M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000).
  11. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
    [CrossRef]
  12. E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
    [CrossRef]
  13. E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
    [CrossRef]
  14. H. Sasada, and M. Okamoto, “Transverse-mode beam spliter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68(1), 012323 (2003).
    [CrossRef]
  15. C. C. Leary, L. A. Baumgardner, and M. G. Raymer, “Stable mode sorting by two-dimensional parity of photonic transverse spatial states,” Opt. Express 17(4), 2435–2452 (2009).
    [CrossRef]
  16. A. N. Oliveira, S. P. Walborn, and C. H. Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B Quantum Semiclassical Opt. 7(9), 288–292 (2005).
    [CrossRef]
  17. M. Fiorentino, and F. N. C. Wong, “Deterministic controlled-NOT gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93(7), 070502 (2004).
    [CrossRef]

2009 (3)

2008 (1)

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[CrossRef]

2007 (2)

C. E. R. Souza, J. A. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99(16), 160401 (2007).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature 3, 305–310 (2007).

2006 (1)

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef]

2005 (1)

A. N. Oliveira, S. P. Walborn, and C. H. Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B Quantum Semiclassical Opt. 7(9), 288–292 (2005).
[CrossRef]

2004 (1)

M. Fiorentino, and F. N. C. Wong, “Deterministic controlled-NOT gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93(7), 070502 (2004).
[CrossRef]

2003 (2)

H. Sasada, and M. Okamoto, “Transverse-mode beam spliter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68(1), 012323 (2003).
[CrossRef]

J. A. O. Huguenin, B. Coutinho dos Santos, P. A. M. dos Santos, and A. Z. Khoury, “Topological defects in moire fringes with spiral zone plates,” J. Opt. Soc. Am. A 20(10), 1883–1889 (2003).
[CrossRef]

2001 (1)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef]

1999 (1)

1993 (2)

S. J. van Enk, “Geometric phase, transformations of gaussian light beams and angular momentum transfer,” Opt. Commun. 102(1-2), 59–64 (1993).
[CrossRef]

M. Beijersbergen, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

1990 (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis, maZh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) (JETP Lett. 52, 429–431 (1990)).

Aolita, L.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[CrossRef]

Baumgardner, L. A.

Bazhenov, V. Y.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis, maZh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) (JETP Lett. 52, 429–431 (1990)).

Beijersbergen, M.

M. Beijersbergen, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

Borges, C. V. S.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[CrossRef]

Courtial, J.

Coutinho dos Santos, B.

De Martini, F.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[CrossRef]

dos Santos, P. A. M.

Fiorentino, M.

M. Fiorentino, and F. N. C. Wong, “Deterministic controlled-NOT gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93(7), 070502 (2004).
[CrossRef]

Huguenin, J. A.

C. E. R. Souza, J. A. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99(16), 160401 (2007).
[CrossRef]

Huguenin, J. A. O.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[CrossRef]

J. A. O. Huguenin, B. Coutinho dos Santos, P. A. M. dos Santos, and A. Z. Khoury, “Topological defects in moire fringes with spiral zone plates,” J. Opt. Soc. Am. A 20(10), 1883–1889 (2003).
[CrossRef]

Karimi, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[CrossRef]

Khoury, A. Z.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[CrossRef]

C. E. R. Souza, J. A. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99(16), 160401 (2007).
[CrossRef]

J. A. O. Huguenin, B. Coutinho dos Santos, P. A. M. dos Santos, and A. Z. Khoury, “Topological defects in moire fringes with spiral zone plates,” J. Opt. Soc. Am. A 20(10), 1883–1889 (2003).
[CrossRef]

Leary, C. C.

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef]

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef]

Marrucci, L.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef]

Milman, P.

C. E. R. Souza, J. A. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99(16), 160401 (2007).
[CrossRef]

Molina-Terriza, G.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature 3, 305–310 (2007).

Monken, C. H.

A. N. Oliveira, S. P. Walborn, and C. H. Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B Quantum Semiclassical Opt. 7(9), 288–292 (2005).
[CrossRef]

Nagali, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[CrossRef]

Okamoto, M.

H. Sasada, and M. Okamoto, “Transverse-mode beam spliter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68(1), 012323 (2003).
[CrossRef]

Oliveira, A. N.

A. N. Oliveira, S. P. Walborn, and C. H. Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B Quantum Semiclassical Opt. 7(9), 288–292 (2005).
[CrossRef]

Padgett, M. J.

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef]

Piccirillo, B.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[CrossRef]

Raymer, M. G.

Santamato, E.

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[CrossRef]

Sasada, H.

H. Sasada, and M. Okamoto, “Transverse-mode beam spliter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68(1), 012323 (2003).
[CrossRef]

Sciarrino, F.

E. Nagali, F. Sciarrino, F. De Martini, B. Piccirillo, E. Karimi, L. Marrucci, and E. Santamato, “Polarization control of single photon quantum orbital angular momentum states,” Opt. Express 17(21), 18745–18759 (2009).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[CrossRef]

Soskin, M. S.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis, maZh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) (JETP Lett. 52, 429–431 (1990)).

Souza, C. E. R.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[CrossRef]

C. E. R. Souza, J. A. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99(16), 160401 (2007).
[CrossRef]

Torner, L.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature 3, 305–310 (2007).

Torres, J. P.

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature 3, 305–310 (2007).

van Enk, S. J.

S. J. van Enk, “Geometric phase, transformations of gaussian light beams and angular momentum transfer,” Opt. Commun. 102(1-2), 59–64 (1993).
[CrossRef]

Vasnetsov, M. V.

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis, maZh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) (JETP Lett. 52, 429–431 (1990)).

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef]

Walborn, S. P.

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[CrossRef]

A. N. Oliveira, S. P. Walborn, and C. H. Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B Quantum Semiclassical Opt. 7(9), 288–292 (2005).
[CrossRef]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef]

Wong, F. N. C.

M. Fiorentino, and F. N. C. Wong, “Deterministic controlled-NOT gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93(7), 070502 (2004).
[CrossRef]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef]

Eksp. Teor. Fiz. (1)

V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis, maZh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) (JETP Lett. 52, 429–431 (1990)).

J. Opt. B Quantum Semiclassical Opt. (1)

A. N. Oliveira, S. P. Walborn, and C. H. Monken, “Implementing the Deutsch algorithm with polarization and transverse spatial modes,” J. Opt. B Quantum Semiclassical Opt. 7(9), 288–292 (2005).
[CrossRef]

J. Opt. Soc. Am. A (1)

Nature (2)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature 412(6844), 313–316 (2001).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature 3, 305–310 (2007).

Opt. Commun. (2)

M. Beijersbergen, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993).
[CrossRef]

S. J. van Enk, “Geometric phase, transformations of gaussian light beams and angular momentum transfer,” Opt. Commun. 102(1-2), 59–64 (1993).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. A (2)

H. Sasada, and M. Okamoto, “Transverse-mode beam spliter of a light beam and its application to quantum cryptography,” Phys. Rev. A 68(1), 012323 (2003).
[CrossRef]

C. E. R. Souza, C. V. S. Borges, A. Z. Khoury, J. A. O. Huguenin, L. Aolita, and S. P. Walborn, “Quantum key distribution without a shared reference frame,” Phys. Rev. A 77(3), 032345 (2008).
[CrossRef]

Phys. Rev. Lett. (4)

C. E. R. Souza, J. A. Huguenin, P. Milman, and A. Z. Khoury, “Topological phase for spin-orbit transformations on a laser beam,” Phys. Rev. Lett. 99(16), 160401 (2007).
[CrossRef]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[CrossRef]

E. Nagali, F. Sciarrino, F. De Martini, L. Marrucci, B. Piccirillo, E. Karimi, and E. Santamato, “Quantum information transfer from spin to orbital angular momentum of photons,” Phys. Rev. Lett. 103(1), 013601 (2009).
[CrossRef]

M. Fiorentino, and F. N. C. Wong, “Deterministic controlled-NOT gate for single-photon two-qubit quantum logic,” Phys. Rev. Lett. 93(7), 070502 (2004).
[CrossRef]

Other (1)

M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000).

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