Abstract

We propose a scheme to implement the Deutsch’s algorithm through non-degenerate four-wave mixing process. By employing photon topological charges of optical vortices, we demonstrate the ability to realize the necessary four logic gates for all balanced and constant functions. We also analyze the feasibility of the proposed scheme on the single photon level.

© 2012 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. A45(11), 8185–8189 (1992).
    [CrossRef] [PubMed]
  2. X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
    [CrossRef] [PubMed]
  3. P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
    [CrossRef]
  4. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
    [CrossRef] [PubMed]
  5. Q. F. Chen, B. S. Shi, Y. S. Zhang, and G. C. Guo, “Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble,” Phys. Rev. A78(5), 053810 (2008).
    [CrossRef]
  6. J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett.83(24), 4967–4970 (1999).
    [CrossRef]
  7. S. Barreiro and J. W. R. Tabosa, “Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms,” Phys. Rev. Lett.90(13), 133001 (2003).
    [CrossRef] [PubMed]
  8. S. Barreiro, J. W. R. Tabosa, J. P. Torres, Y. Deyanova, and L. Torner, “Four-wave mixing of light beams with engineered orbital angular momentum in cold cesium atoms,” Opt. Lett.29(13), 1515–1517 (2004).
    [CrossRef] [PubMed]
  9. D. Akamatsu and M. Kozuma, “Coherent transfer of orbital angular momentum from an atomic system to a light field,” Phys. Rev. A67(2), 023803 (2003).
    [CrossRef]
  10. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A56(5), 4193–4196 (1997).
    [CrossRef]
  11. H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85(2), 286–289 (2000).
    [CrossRef] [PubMed]
  12. W. Jiang, Q. F. Chen, Y. S. Zhang, and G. C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A74(4), 043811 (2006).
    [CrossRef]
  13. D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. Lond. A Math. Phys. Sci.400(1818), 97–117 (1985).
    [CrossRef]
  14. J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett.74(20), 4091–4094 (1995).
    [CrossRef] [PubMed]
  15. T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Measuring the entanglement between double quantum dot charge qubits,” Phys. Rev. B80, 161309 (2009).
    [CrossRef] [PubMed]
  16. D. Jaksch, “Optical lattices, ultracold atoms and quantum information processing,” Contemp. Phys.45(5), 367–381 (2004).
    [CrossRef]
  17. M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett.91(18), 187903 (2003).
    [CrossRef] [PubMed]
  18. 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]
  19. P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A82(6), 064302 (2010).
    [CrossRef]
  20. H. T. Zhou, D. W. Wang, D. Wang, J. X. Zhang, and S. Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A84(5), 053835 (2011).
    [CrossRef]
  21. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon.3(2), 161–204 (2011).
    [CrossRef]
  22. Y. Q. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett.21(14), 1064–1066 (1996).
    [CrossRef] [PubMed]
  23. R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1992).
  24. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
    [CrossRef] [PubMed]
  25. D. A. Steck, “Rubidium 85 D line data,” http://steck.us/alkalidata .
  26. D. Höckel and O. Benson, “Electromagnetically induced transparency in cesium vapor with probe pulses on the single-photon level,” Phys. Rev. Lett.105(15), 153605 (2010).
    [CrossRef] [PubMed]

2011

H. T. Zhou, D. W. Wang, D. Wang, J. X. Zhang, and S. Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A84(5), 053835 (2011).
[CrossRef]

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon.3(2), 161–204 (2011).
[CrossRef]

2010

D. Höckel and O. Benson, “Electromagnetically induced transparency in cesium vapor with probe pulses on the single-photon level,” Phys. Rev. Lett.105(15), 153605 (2010).
[CrossRef] [PubMed]

P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
[CrossRef]

P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A82(6), 064302 (2010).
[CrossRef]

2009

T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Measuring the entanglement between double quantum dot charge qubits,” Phys. Rev. B80, 161309 (2009).
[CrossRef] [PubMed]

2008

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Q. F. Chen, B. S. Shi, Y. S. Zhang, and G. C. Guo, “Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble,” Phys. Rev. A78(5), 053810 (2008).
[CrossRef]

2006

W. Jiang, Q. F. Chen, Y. S. Zhang, and G. C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A74(4), 043811 (2006).
[CrossRef]

2005

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

2003

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett.91(18), 187903 (2003).
[CrossRef] [PubMed]

S. Barreiro and J. W. R. Tabosa, “Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms,” Phys. Rev. Lett.90(13), 133001 (2003).
[CrossRef] [PubMed]

D. Akamatsu and M. Kozuma, “Coherent transfer of orbital angular momentum from an atomic system to a light field,” Phys. Rev. A67(2), 023803 (2003).
[CrossRef]

2002

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

2001

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

2000

H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85(2), 286–289 (2000).
[CrossRef] [PubMed]

1999

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett.83(24), 4967–4970 (1999).
[CrossRef]

1997

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A56(5), 4193–4196 (1997).
[CrossRef]

1996

1995

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett.74(20), 4091–4094 (1995).
[CrossRef] [PubMed]

1992

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

1985

D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. Lond. A Math. Phys. Sci.400(1818), 97–117 (1985).
[CrossRef]

Akamatsu, D.

D. Akamatsu and M. Kozuma, “Coherent transfer of orbital angular momentum from an atomic system to a light field,” Phys. Rev. A67(2), 023803 (2003).
[CrossRef]

Allen, L.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A56(5), 4193–4196 (1997).
[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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Arnaut, H. H.

H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85(2), 286–289 (2000).
[CrossRef] [PubMed]

Barbosa, G. A.

H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85(2), 286–289 (2000).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Barreiro, S.

S. Barreiro, J. W. R. Tabosa, J. P. Torres, Y. Deyanova, and L. Torner, “Four-wave mixing of light beams with engineered orbital angular momentum in cold cesium atoms,” Opt. Lett.29(13), 1515–1517 (2004).
[CrossRef] [PubMed]

S. Barreiro and J. W. R. Tabosa, “Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms,” Phys. Rev. Lett.90(13), 133001 (2003).
[CrossRef] [PubMed]

Beijersbergen, M. W.

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Benson, O.

D. Höckel and O. Benson, “Electromagnetically induced transparency in cesium vapor with probe pulses on the single-photon level,” Phys. Rev. Lett.105(15), 153605 (2010).
[CrossRef] [PubMed]

Chen, Q. F.

Q. F. Chen, B. S. Shi, Y. S. Zhang, and G. C. Guo, “Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble,” Phys. Rev. A78(5), 053810 (2008).
[CrossRef]

W. Jiang, Q. F. Chen, Y. S. Zhang, and G. C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A74(4), 043811 (2006).
[CrossRef]

Cheong, H. D.

T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Measuring the entanglement between double quantum dot charge qubits,” Phys. Rev. B80, 161309 (2009).
[CrossRef] [PubMed]

Cirac, J. I.

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett.74(20), 4091–4094 (1995).
[CrossRef] [PubMed]

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A56(5), 4193–4196 (1997).
[CrossRef]

Deutsch, D.

D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. Lond. A Math. Phys. Sci.400(1818), 97–117 (1985).
[CrossRef]

Deyanova, Y.

Dholakia, K.

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A56(5), 4193–4196 (1997).
[CrossRef]

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Fujisawa, T.

T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Measuring the entanglement between double quantum dot charge qubits,” Phys. Rev. B80, 161309 (2009).
[CrossRef] [PubMed]

Gao, H.

P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A82(6), 064302 (2010).
[CrossRef]

Guo, G. C.

P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
[CrossRef]

Q. F. Chen, B. S. Shi, Y. S. Zhang, and G. C. Guo, “Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble,” Phys. Rev. A78(5), 053810 (2008).
[CrossRef]

W. Jiang, Q. F. Chen, Y. S. Zhang, and G. C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A74(4), 043811 (2006).
[CrossRef]

Hayashi, T.

T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Measuring the entanglement between double quantum dot charge qubits,” Phys. Rev. B80, 161309 (2009).
[CrossRef] [PubMed]

Hirayama, Y.

T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Measuring the entanglement between double quantum dot charge qubits,” Phys. Rev. B80, 161309 (2009).
[CrossRef] [PubMed]

Höckel, D.

D. Höckel and O. Benson, “Electromagnetically induced transparency in cesium vapor with probe pulses on the single-photon level,” Phys. Rev. Lett.105(15), 153605 (2010).
[CrossRef] [PubMed]

Huang, Y. F.

P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A82(6), 064302 (2010).
[CrossRef]

Jaksch, D.

D. Jaksch, “Optical lattices, ultracold atoms and quantum information processing,” Contemp. Phys.45(5), 367–381 (2004).
[CrossRef]

Jeong, Y. H.

T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Measuring the entanglement between double quantum dot charge qubits,” Phys. Rev. B80, 161309 (2009).
[CrossRef] [PubMed]

Jiang, W.

W. Jiang, Q. F. Chen, Y. S. Zhang, and G. C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A74(4), 043811 (2006).
[CrossRef]

Kozuma, M.

D. Akamatsu and M. Kozuma, “Coherent transfer of orbital angular momentum from an atomic system to a light field,” Phys. Rev. A67(2), 023803 (2003).
[CrossRef]

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Leng, H. Y.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Li, F. L.

P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
[CrossRef]

P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A82(6), 064302 (2010).
[CrossRef]

Li, H. R.

P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
[CrossRef]

Li, Y. Q.

Liu, B. H.

P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
[CrossRef]

Liu, R. F.

P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
[CrossRef]

P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A82(6), 064302 (2010).
[CrossRef]

Lundeen, J. S.

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett.91(18), 187903 (2003).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Ming, N. B.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Mohseni, M.

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett.91(18), 187903 (2003).
[CrossRef] [PubMed]

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]

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.

A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon.3(2), 161–204 (2011).
[CrossRef]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A56(5), 4193–4196 (1997).
[CrossRef]

Petrov, D. V.

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett.83(24), 4967–4970 (1999).
[CrossRef]

Resch, K. J.

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett.91(18), 187903 (2003).
[CrossRef] [PubMed]

Shi, B. S.

Q. F. Chen, B. S. Shi, Y. S. Zhang, and G. C. Guo, “Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble,” Phys. Rev. A78(5), 053810 (2008).
[CrossRef]

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Steinberg, A. M.

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett.91(18), 187903 (2003).
[CrossRef] [PubMed]

Tabosa, J. W. R.

S. Barreiro, J. W. R. Tabosa, J. P. Torres, Y. Deyanova, and L. Torner, “Four-wave mixing of light beams with engineered orbital angular momentum in cold cesium atoms,” Opt. Lett.29(13), 1515–1517 (2004).
[CrossRef] [PubMed]

S. Barreiro and J. W. R. Tabosa, “Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms,” Phys. Rev. Lett.90(13), 133001 (2003).
[CrossRef] [PubMed]

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett.83(24), 4967–4970 (1999).
[CrossRef]

Torner, L.

Torres, J. P.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Walborn, S. P.

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]

Wang, D.

H. T. Zhou, D. W. Wang, D. Wang, J. X. Zhang, and S. Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A84(5), 053835 (2011).
[CrossRef]

Wang, D. W.

H. T. Zhou, D. W. Wang, D. Wang, J. X. Zhang, and S. Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A84(5), 053835 (2011).
[CrossRef]

Wang, J. F.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Woerdman, J. P.

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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

Xiao, M.

Xie, Z. D.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Xu, P.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Yao, A. M.

Yu, X. Q.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Zhang, J. X.

H. T. Zhou, D. W. Wang, D. Wang, J. X. Zhang, and S. Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A84(5), 053835 (2011).
[CrossRef]

Zhang, P.

P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A82(6), 064302 (2010).
[CrossRef]

P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
[CrossRef]

Zhang, Y. S.

Q. F. Chen, B. S. Shi, Y. S. Zhang, and G. C. Guo, “Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble,” Phys. Rev. A78(5), 053810 (2008).
[CrossRef]

W. Jiang, Q. F. Chen, Y. S. Zhang, and G. C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A74(4), 043811 (2006).
[CrossRef]

Zhao, J. S.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Zhou, H. T.

H. T. Zhou, D. W. Wang, D. Wang, J. X. Zhang, and S. Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A84(5), 053835 (2011).
[CrossRef]

Zhu, S. N.

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

Zhu, S. Y.

H. T. Zhou, D. W. Wang, D. Wang, J. X. Zhang, and S. Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A84(5), 053835 (2011).
[CrossRef]

Zoller, P.

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett.74(20), 4091–4094 (1995).
[CrossRef] [PubMed]

Adv. Opt. Photon.

Contemp. Phys.

D. Jaksch, “Optical lattices, ultracold atoms and quantum information processing,” Contemp. Phys.45(5), 367–381 (2004).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt.

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]

Nature

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, “Entanglement of the orbital angular momentum states of photons,” Nature412(6844), 313–316 (2001).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

P. Zhang, R. F. Liu, Y. F. Huang, H. Gao, and F. L. Li, “Demonstration of Deutsch’s algorithm on a stable linear optical quantum computer,” Phys. Rev. A82(6), 064302 (2010).
[CrossRef]

H. T. Zhou, D. W. Wang, D. Wang, J. X. Zhang, and S. Y. Zhu, “Efficient reflection via four-wave mixing in a Doppler-free electromagnetically-induced-transparency gas system,” Phys. Rev. A84(5), 053835 (2011).
[CrossRef]

D. Akamatsu and M. Kozuma, “Coherent transfer of orbital angular momentum from an atomic system to a light field,” Phys. Rev. A67(2), 023803 (2003).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A56(5), 4193–4196 (1997).
[CrossRef]

Q. F. Chen, B. S. Shi, Y. S. Zhang, and G. C. Guo, “Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble,” Phys. Rev. A78(5), 053810 (2008).
[CrossRef]

P. Zhang, B. H. Liu, R. F. Liu, H. R. Li, F. L. Li, and G. C. Guo, “Implementation of one-dimensional quantum walks on spin-orbital angular momentum space of photons,” Phys. Rev. A81(5), 052322 (2010).
[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. A45(11), 8185–8189 (1992).
[CrossRef] [PubMed]

W. Jiang, Q. F. Chen, Y. S. Zhang, and G. C. Guo, “Computation of topological charges of optical vortices via nondegenerate four-wave mixing,” Phys. Rev. A74(4), 043811 (2006).
[CrossRef]

Phys. Rev. B

T. Hayashi, T. Fujisawa, H. D. Cheong, Y. H. Jeong, and Y. Hirayama, “Measuring the entanglement between double quantum dot charge qubits,” Phys. Rev. B80, 161309 (2009).
[CrossRef] [PubMed]

Phys. Rev. Lett.

D. Höckel and O. Benson, “Electromagnetically induced transparency in cesium vapor with probe pulses on the single-photon level,” Phys. Rev. Lett.105(15), 153605 (2010).
[CrossRef] [PubMed]

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the orbital angular momentum of a single photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

X. Q. Yu, P. Xu, Z. D. Xie, J. F. Wang, H. Y. Leng, J. S. Zhao, S. N. Zhu, and N. B. Ming, “Transforming spatial entanglement using a domain-engineering technique,” Phys. Rev. Lett.101(23), 233601 (2008).
[CrossRef] [PubMed]

J. I. Cirac and P. Zoller, “Quantum computations with cold trapped ions,” Phys. Rev. Lett.74(20), 4091–4094 (1995).
[CrossRef] [PubMed]

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett.91(18), 187903 (2003).
[CrossRef] [PubMed]

J. W. R. Tabosa and D. V. Petrov, “Optical pumping of orbital angular momentum of light in cold cesium atoms,” Phys. Rev. Lett.83(24), 4967–4970 (1999).
[CrossRef]

S. Barreiro and J. W. R. Tabosa, “Generation of light carrying orbital angular momentum via induced coherence grating in cold atoms,” Phys. Rev. Lett.90(13), 133001 (2003).
[CrossRef] [PubMed]

H. H. Arnaut and G. A. Barbosa, “Orbital and intrinsic angular momentum of single photons and entangled pairs of photons generated by parametric down-conversion,” Phys. Rev. Lett.85(2), 286–289 (2000).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci.

D. Deutsch, “Quantum theory, the Church-Turing principle and the universal quantum computer,” Proc. R. Soc. Lond. A Math. Phys. Sci.400(1818), 97–117 (1985).
[CrossRef]

Other

D. A. Steck, “Rubidium 85 D line data,” http://steck.us/alkalidata .

R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1992).

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 (5)

Fig. 1
Fig. 1

(a) The experimental setup of the four-wave mixing scheme. P1, P2, P3 field are provided by three lasers. M1, M2 are mirrors. PBS is polarizing beam-splitter, which transmits horizontal polarization and reflects vertical polarization. (b) The energy diagram of atom levels coupled by different laser fields in the scheme.

Fig. 2
Fig. 2

(a) Quantum circuit for Deutsch’s algorithm. H is the Hadamard gate to supply the superposition state, U f is quantum operation, which takes inputs | x,y to | x,yf(x) for the four possible functions and output states | ψ 2 . | ψ 1 is the converted state after Hadamard gate, and | ψ 3 is the final state to be measured. (b) Four basic logical operations for Deutsch’s algorithm.

Fig. 3
Fig. 3

Experimental scheme of Deutsch’s algorithm. DH1, DH2, and DH3 are three displaced holograms, and they are chosen as the Hadamard gate to supply the superposition state. Dashed square area is the experimental implementation of U f operations, in which four logic gates can be realized in different methods. D represents the photon detector.

Fig. 4
Fig. 4

Experimental realization of U f in a FWM process, (a) I gate, (b) NOT gate, (c) C-NOT gate, and (d) Z-CNOT gate. CGH is computer-generated hologram, which is applied to change the photon’s OAM. In the I gate and the NOT gate, an acoustic-optical modulator (AOM) can be introduced to make the frequency shift, so the P1 and P3 fields can be manipulated simultaneously. In the I and the NOT gates, half wave plate (HWP) is placed behind the BS to change the P3 field’s polarization. Mirrors in both gates are introduced to change the sign of OAM. In the C-NOT gate, CGH1 and CGH2 are introduced to prepare the arbitrary initial sates in OAM space.

Fig. 5
Fig. 5

Testing results of two types of function. (a) and (b) are the intensity distributions of constant function and balance function when we detect the testing states of | ψ 2 , respectively. While (c) and (d) are intensity distributions of constant function and balanced function when we detect the testing states of | ψ 3 .

Tables (1)

Tables Icon

Table 1 Encoding protocol using quantum states of OAM to realize the Deutsch’s algorithm.

Equations (10)

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

L G p l = 2p! π(p+| l |)! 1 w(z) [ r 2 w(z) ] | l | exp[ r 2 w 2 (z) ] L p | l | ( 2 r 2 w 2 (z) ) exp[ i k 0 r 2 z 2( z 2 + z R 2 ) ]exp[ i(2p+| l |+1) tan 1 ( z z R ) ]exp[ilϕ],
E P1 = A 1 e i l 1 ϕ , E P2 = A 2 e i l 2 ϕ , E P3 = A 3 e i l 3 ϕ ,
E S = χ (3) E P1 E P2 E P3 * .
E S = χ (3) A 1 A 2 A 3 * exp[ i( l 1 + l 2 l 3 )ϕ ].
| 0,0 =| , I | , =| 0,0 ,| 1,0 =| , I | , =| 1,0 , | 0,1 =| , I | , =| 0,1 ,| 1,1 =| , I | , =| 1,1 .
| 0,0 =| , NOT | , =| 0,1 ,| 1,0 =| , NOT | , =| 1,1 , | 0,1 =| , NOT | , =| 0,0 ,| 1,1 =| , NOT | , =| 1,0 .
P ^ [ α|0+β|1 ]=α| e i(0+11)ϕ +β| e i(0+01)ϕ =α|0+β|1, P ^ '[ α|0+β|1 ]=α| e i(0+10)ϕ +β| e i(0+00)ϕ =α|1+β|0.
| 0,0 =| , CNOT | , =| 0,0 ,| 1,0 =| , CNOT | , =| 1,1 , | 0,1 =| , CNOT | , =| 0,1 ,| 1,1 =| , CNOT | , =| 1,0 .
| 0,0 =| , ZCNOT | , =| 0,1 ,| 1,0 =| , ZCNOT | , =| 1,0 , | 0,1 =| , ZCNOT | , =| 0,0 ,| 1,1 =| , ZCNOT | , =| 1,1 .
| ψ 2 ={ 1 2 ( |0+|1 )( |0|1 ) 1 2 ( |0+|1 )( |0|1 ) 1 2 ( |0|1 )( |0|1 ) 1 2 ( |0|1 )( |0|1 ) H | ψ 3 ={ |0 ( |0|1 ) 2 I gate, |0 ( |0|1 ) 2 NOT gate, |1 ( |0|1 ) 2 C-NOT gate, |1 ( |0|1 ) 2 Z-CNOT gate.

Metrics