OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 14 — Jul. 6, 2009
  • pp: 11505–11514

Macroscopic entanglement and violation of Bell’s inequalities between two spatially separated quantum dots in a planar photonic crystal system

P. Yao and S. Hughes  »View Author Affiliations

Optics Express, Vol. 17, Issue 14, pp. 11505-11514 (2009)

View Full Text Article

Enhanced HTML    Acrobat PDF (456 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present and apply a medium-dependent quantum optics formalism for describing the exciton dynamics of two spatially-separated quantum dots on-chip, in the regime of coupled-cavity quantum electrodynamics. With each dot placed in a spatially-separated cavity and coupled through a periodic waveguide channel, the quantum dot excitons behave as a composite entangled pair, exhibiting pronounced entanglement over distances of 300µm and more. The computed light spectra above the two cavities show clear signatures of pronounced photon coupling including increased vacuum Rabi splitting and cavity-induced transmission and absorption. The macroscopic entanglement is confirmed by investigating the Bell inequality, which is shown to be violated for hundreds of picoseconds.

© 2009 Optical Society of America

OCIS Codes
(270.5580) Quantum optics : Quantum electrodynamics
(350.4238) Other areas of optics : Nanophotonics and photonic crystals

ToC Category:
Quantum Optics

Original Manuscript: April 9, 2009
Revised Manuscript: June 12, 2009
Manuscript Accepted: June 18, 2009
Published: June 24, 2009

P. Yao and S. Hughes, "Macroscopic entanglement and violation of Bell’s inequalities between two spatially separated quantum dots in a planar photonic crystal system," Opt. Express 17, 11505-11514 (2009)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. A. K. Ekert, "Quantum cryptography based on Bell’s theorem," Phys. Rev. Lett. 67, 661 (1991). [CrossRef] [PubMed]
  2. C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels," Phys. Rev. Lett. 70, 1895 (1993). [CrossRef] [PubMed]
  3. C. H. Bennett and S. J. Wiesner, "Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states," Phys. Rev. Lett. 69, 2881 (1992). [CrossRef] [PubMed]
  4. J. Vučković and Y. Yamamoto, "Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot," Appl. Phys. Lett. 82, 2374 (2003). [CrossRef]
  5. W. Chang, W-Y. Chen, H-S. Chang, T-P. Hsieh, J-I. Chyi, and T-M. Hsu, "Efficient single-photon sources based on low-density quantum dots in photonic-crystal nanocavities," Phys. Rev. Lett. 96, 117401 (2006). [CrossRef] [PubMed]
  6. K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, and A. Imamoğlu, "Quantum nature of a strongly coupled single quantum dot cavity system," Nature 445,896 (2007). [CrossRef] [PubMed]
  7. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, "Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal," Phys. Rev. Lett. 95, 013904 (2005). [CrossRef] [PubMed]
  8. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature 432, 200 (2004). [CrossRef] [PubMed]
  9. J. P. Reithmaier, G. Sek, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot semiconductor microcavity system," Nature 432, 197 (2004). [CrossRef] [PubMed]
  10. E. Peter, P. Senellart, D. Martrou, A. Lemaitre, J. Hours, J. M. Gérard, and J. Bloch, "Exciton-photon strongcoupling regime for a single quantum dot embedded in a microcavity," Phys. Rev. Lett. 95, 067401 (2005). [CrossRef] [PubMed]
  11. S. Hughes and H. Kamada, "Single-quantum-dot strong coupling in a semiconductor photonic crystal nanocavity side coupled to a waveguide," Phys. Rev. B 70, 195313 (2004). [CrossRef]
  12. D. Englund, A. Faraon, I. Fushman, N. Stoltz, P. Petroff, and J. Vučković, "Controlling cavity reflectivity with a single quantum dot," Nature 450, 857 (2007). [CrossRef] [PubMed]
  13. S. Hughes, "Modified spontaneous emission and qubit entanglement from dipole-coupled quantum dots in a photonic crystal nanocavity," Phys. Rev. Lett. 94, 227402 (2005) [CrossRef] [PubMed]
  14. M. Bayer, P. Hawrylak, K. Hinzer, S. Fafard, M. Korkusinski, Z. R. Wasilewski, O. Stern, and A. Forchel, "Coupling and entangling of quantum states in quantum dot molecules," Science 291, 451 (2001). [CrossRef] [PubMed]
  15. G. Bester, A. Zunger, and J. Shumway "Broken symmetry and quantum entanglement of an exciton in InxGa1−xAsGaAs quantum dot molecules," Phys. Rev. B 71, 075325 (2005). [CrossRef]
  16. Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944 (2003). [CrossRef] [PubMed]
  17. M. Wubs, L. G. Suttorp, and A. Lagendijk, "Multiple-scattering approach to interatomic interactions and superradiance in inhomogeneous dielectrics," Phys. Rev. A 70, 053823 (2004). [CrossRef]
  18. S. Hughes, "Coupled-cavity QED using planar photonic crystals," Phys. Rev. Lett. 98, 083603 (2007). [CrossRef] [PubMed]
  19. S. Hughes, H. Gotoh, and H. Kamada, "Classical and quantum optical correlation effects between single quantum dots: the role of the hopping photon," Phys. Rev. B 74, 115334 (2006). [CrossRef]
  20. A. Cowan and J. F. Young, "Optical bistability involving photonic crystal microcavities and Fano line shapes," Phys. Rev. E 68, 46606 (2003). [CrossRef]
  21. W. K. Wootters, "Entanglement of formation of an arbitrary state of two qubits," Phys. Rev. Lett. 80, 2245 (1998). [CrossRef]
  22. K. L. Silverman, R. P. Mirin, S. T. Cundiff, and A. G. Norman, "Direct measurement of polarization resolved transition dipole moment in InGaAs/GaAs quantum dots," Appl. Phys. Lett. 82, 4552 (2003). [CrossRef]
  23. T. H. Stievater, Xiaoqin Li, D. G. Steel, D. Gammon, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, "Rabi oscillations of excitons in single quantum dots," Phys. Rev. Lett. 87, 133603 (2001). [CrossRef] [PubMed]
  24. E. Waks and J. Vučković, "Dipole induced transparency in drop-filter cavity-waveguide systems," Phys. Rev. Lett. 96, 153601 (2006). [CrossRef] [PubMed]
  25. B. R. Mollow, "Power spectrum of light scattered by two-level systems," Phys.Rev. 188, 1969 (1969). [CrossRef]
  26. W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, "Radiatively limited dephasing in InAs quantum dots," Phys. Rev. B 70, 033301 (2004). [CrossRef]
  27. J. S. Bell, "On the problem of hidden variables in quantum mechanics," Physics 1, 195 (1964).
  28. A. Einstein, B. Podolsky, and N. Rosen, "Can quantum-mechanical description of physical reality be considered complete?," Phys. Rev. 47, 777 (1935). [CrossRef]
  29. A. Beige, W. J. Munro, and P. L. Knight, "Bell’s inequality test with entangled atoms," Phys. Rev. A 62, 052102 (2000). [CrossRef]
  30. S. Hughes, L. Ramunno, J. F. Young, and J. E. Sipe, "Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity," Phys. Rev. Lett. 94, 33903 (2005). [CrossRef]

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited