A Michelson controlled-not gate with a single-lens astigmatic mode converter

doi:10.1364/OE.18.009207

A Michelson controlled-not gate with a single-lens astigmatic mode converter

C. E. R. Souza and A. Z. Khoury »View Author Affiliations

Optics Express, Vol. 18, Issue 9, pp. 9207-9212 (2010)
http://dx.doi.org/10.1364/OE.18.009207

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Abstract
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References (17)
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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.

OCIS Codes
(270.5565) Quantum optics : Quantum communications
(270.5568) Quantum optics : Quantum cryptography
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

History
Original Manuscript: February 25, 2010
Revised Manuscript: March 20, 2010
Manuscript Accepted: March 29, 2010
Published: April 16, 2010

Citation
C. E. R. Souza and A. Z. Khoury, "A Michelson controlled-not gate with a single-lens astigmatic mode converter," Opt. Express 18, 9207-9212 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9207

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References

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] [PubMed]
G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nature 3, 305–310 (2007).
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] [PubMed]
M. Beijersbergen, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96(1-3), 123–132 (1993). [CrossRef]
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. 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]
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. J. Padgett, and J. Courtial, “Poincaré-sphere equivalent for light beams containing orbital angular momentum,” Opt. Lett. 24(7), 430–432 (1999). [CrossRef]
M. A. Nielsen, and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge, 2000).
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] [PubMed]
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] [PubMed]
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]
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. 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] [PubMed]
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]
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] [PubMed]

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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] [PubMed]

[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] [PubMed]

[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] [PubMed]

[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] [PubMed]

[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] [PubMed]

[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] [PubMed]

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A Michelson controlled-not gate with a single-lens astigmatic mode converter