OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 19 — Sep. 15, 2008
  • pp: 14629–14634

Sorting photons of different rotational Doppler shifts (RDS) by orbital angular momentum of single-photon with spin-orbit-RDS entanglement

Lixiang Chen and Weilong She  »View Author Affiliations

Optics Express, Vol. 16, Issue 19, pp. 14629-14634 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (317 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We demonstrate that single photons from a rotating q-plate exhibit an entanglement in three degrees of freedom of spin, orbital angular momentum, and the rotational Doppler shift (RDS) due to the nonconservation of total spin and orbital angular momenta. We find that the rotational Doppler shift Δω=Ω(Δsl), where s, l and Ω are quantum numbers of spin, orbital angular momentum, and rotating velocity of the q-plate, respectively. Of interest is that the rotational Doppler shift directly reflects the rotational symmetry of q-plates and can be also expressed as Δωn, where n=2(q-1) denotes the fold number of rotational symmetry. Besides, based on this single-photon spin-orbit-RDS entanglement, we propose an experimental scheme to sort photons of different frequency shifts according to individual orbital angular momentum.

© 2008 Optical Society of America

OCIS Codes
(230.5440) Optical devices : Polarization-selective devices
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

Original Manuscript: June 3, 2008
Revised Manuscript: August 13, 2008
Manuscript Accepted: August 13, 2008
Published: September 3, 2008

Lixiang Chen and Weilong She, "Sorting photons of different rotational Doppler shifts (RDS) by orbital angular momentum of single-photon with spin-orbit-RDS entanglement," Opt. Express 16, 14629-14634 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. Allen, M. J. Padgett, and M. Babiker, "The orbital angular momentum of light," Prog. Opt. 39, 291-372 (1999). [CrossRef]
  2. L. Allen, "Induction to the atoms and angular momentum of light special issue," J. Opt. B: Quantum Semiclass. Opt. 4, S1-S6 (2002). [CrossRef]
  3. M. J. Padgett, J. Courtial, and L. Allen, "Light??s orbital angular momentum," Phys. Today 57, 35-40 (2004). [CrossRef]
  4. J. Courtial and K. O'Holleran, "Experiments with twisted light. Some of the mechanical and quantum-mechanical properties of optical vorteicest," Eur. Phys. J. Special Topics 145, 35-47 (2007). [CrossRef]
  5. G. Molina-Terriza, J. P. Torres, and L. Torner, "Twisted photons," Nature Phys. 3, 305-310 (2007). [CrossRef]
  6. M. J. Padgett, "Electromagnetism: Like a speeding watch," Nature 443, 924-925 (2006). [CrossRef] [PubMed]
  7. B. A. Garetz and S. Arnold, "Variable frequency shifting of circularly polarized laser radiation via a rotating half-wave retardation plate," Opt. Commun. 31, 1-3 (1979). [CrossRef]
  8. R. Simon, H. J. Kimble, and E. C. G. Sudarshan, "Evolving geometric phase and its dynamical manifestation as a frequency shift: an optical experiment," Phys. Rev. Lett. 61, 19-22 (1988). [CrossRef] [PubMed]
  9. F. Bretenaker and A. Le Floch, "Energy exchanges between a rotating retardation plate and a laser beam," Phys. Rev. Lett. 65, 2316 (1990). [CrossRef] [PubMed]
  10. L. Allen and M. Padgett, "Equivalent geometric transformations for spin and orbital angular momentum of light," J. Mod. Opt. 54, 487-491 (2007). [CrossRef]
  11. 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]
  12. L. Allen, M. Babiker, and W. L. Power, "Azimuthal Doppler shift in light beams with orbital angular momentum," Opt. Commun. 112, 141-144 (1994). [CrossRef]
  13. J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, and M. J. Padgett, "Measurement of the rotational frequency shift imparted to a rotating light beams possessing orbital angular momentum," Phys. Rev. Lett. 80, 3217-3219 (1998). [CrossRef]
  14. J. Courtial, D. A. Robertson, K. Dholakia, L. Allen, and M. J. Padgett, "Rotational frequency shift of a light beam," Phys. Rev. Lett. 81, 4828-4830 (1998). [CrossRef]
  15. M. J. Padgett and J. Courtial, "Poincaré-sphere equivalent for light beams containing orbital angular momentum," Opt. Lett. 24, 430-432 (1999). [CrossRef]
  16. I. Bialynicki-Birula and Z. Bialynicka-Birula, "Rotational Frequency shift," Phys. Rev. Lett. 78, 2539-2542 (1997). [CrossRef]
  17. I. V. Basistiy, V. V. Slyusar, M. S. Soskin, M. V. Vasnetsov, and A. Ya. Bekshaev, "Manifestation of the rotational Doppler effect by use of an off-axis optical vortex beam," Opt. Lett. 28, 1185-1187 (2003). [CrossRef] [PubMed]
  18. S. Barreiro, J. W. R. Tabosa, H. Failache, and A. Lezama, "Spectroscopic observation of the rotational Doppler effect," Phys. Rev. Lett. 97, 113601 (2006). [CrossRef] [PubMed]
  19. S. J. van Enk and G. Nienhuis, "Photons in polychromatic rotating modes," Phys. Rev. A 76, 053825 (2007). [CrossRef]
  20. N. J. Cerf, C. Adami, and P. G. Kwiat, "Optical simulation of quantum logic," Phys. Rev. A 57, 1477-1480 (1998). [CrossRef]
  21. B. G. Englert, C. Kurtsiefer, and H. Weinfurter, "Universal unitary gate for single-photon two-qubit states," Phys. Rev. A 63, 032303 (2001). [CrossRef]
  22. Y.-H. Kim, "Single-photon two-qubit entangled states: Preparation and measurement," Phys. Rev. A 67, 040301 (2003). [CrossRef]
  23. A. Beige, B. G. Englert, C. Kurtsiefer, and H. Weinfurter, "Secure communication with single-photon two-qubit states," J. Phys. A: Math. Gen. 35, L407-L413 (2002). [CrossRef]
  24. J. T. Barreiro, T. -C. Wei, and P. G. Kwiat, "Beating the channel capacity limit for linear photonic superdense coding," Nature Phys. 4, 282-286 (2008). [CrossRef]
  25. L. Marrucci, C. Manzo, and D. Paparo, "Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media," Phys. Rev. Lett. 96, 163905 (2006). [CrossRef] [PubMed]
  26. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995). [CrossRef] [PubMed]
  27. E. Schmidt, "Zur Theorie der linearen und nicht linearen Integralgleichungen," Math. Ann. 63, 433-466 (1907). [CrossRef]
  28. Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, and H. Rauch, "Violation of a Bell-like inequality in single-neutron interferometry," Nature 425, 45-48 (2003). [CrossRef] [PubMed]
  29. S. J. van Enk, "Single-particle entanglement," Phys. Rev. A 72, 064306 (2005). [CrossRef]
  30. S. J. van Enk, "Entanglement of electromagnetic fields," Phys. Rev. A 67, 022303 (2003). [CrossRef]
  31. L. Marrucci, "Rotating light with light: Generation of helical modes of light by spin-to-orbital angular momentum conversion in inhomogeneous liquid crystals," Proc. of SPIE 6587, 658708 (2007). [CrossRef]
  32. L. Deng, H. Wang, and K. Wang, "Quantum CNOT gates with orbital angular momentum and polarization of single-photon quantum logic," J. Opt. Soc. Am. B 24, 2517-2520 (2007). [CrossRef]
  33. L. Chen and W. She, "Electro-optically forbidden or enhanced spin-to-orbital angular momentum conversion in a focused light beam," Opt. Lett. 33, 696-698 (2008). [CrossRef] [PubMed]
  34. A. N. de Oliveira, S. P. Walborn, and C. H. Monken, "Implementing the Deutsch algorithm with polarization and transverse spatical modes," J. Opt. B: Quantum Semiclass. Opt. 7, 288-292 (2005). [CrossRef]
  35. R. J. C. Spreeuw, "A classical analogy of entanglement," Found. Phys. 28, 361-374 (1998). [CrossRef]
  36. M. J. Padgett, "The mechanism for energy transfer in the rotational frequency shift of a light beam," J. Opt. A: Pure Appl. Opt. 6, S263-S265 (2004). [CrossRef]
  37. I. V. Basistiy, A. Ya. Bakshaev, M. V. Vasnetsov, V. V. Slyusar, and M. S. Soskin, "Observation of the rotational doppler effect for optical beams with helical wave front using spiral zone plate," JETP Lett. 76, 486-489 (2002). [CrossRef]
  38. S. M. Barnett, "Optical angular-momentum flux," J. Opt. B: Quantum Semiclass. Opt. 4, S7-S16 (2002). [CrossRef]
  39. S. C. McEldowney, D. M. Shemo, and R. A. Chipman, "Vortex retarders produced from photo-aligned liquid crystal polymers," Opt. Express 16, 7295-7308 (2008). [CrossRef] [PubMed]
  40. 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1. Fig. 2. Fig. 3.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited