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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 20 — Sep. 24, 2012
  • pp: 21977–21991

Entangled photon generation using four-wave mixing in azimuthally symmetric microresonators

Ryan M. Camacho  »View Author Affiliations


Optics Express, Vol. 20, Issue 20, pp. 21977-21991 (2012)
http://dx.doi.org/10.1364/OE.20.021977


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Abstract

A novel quantum mechanical formulation of the bi-photon wavefunction and spectra resulting from four-wave mixing is developed for azimuthally symmetric systems. Numerical calculations are performed verifying the use of the angular group velocity and angular group velocity dispersion in such systems, as opposed their commonly used linear counterparts. The dispersion profile and bi-photon spectra of two illustrative examples are given, emphasizing the physical origin of the effects leading to the conditions for angular momentum and energy conservation. A scheme is proposed in which widely spaced narrowband entangled photons may be produced through a four-wave mixing process in a chip-scale ring resonator. The entangled photon pairs are found to conserve energy and momentum in the four-wave mixing interaction, even though both photon modes lie in spectral regions of steep angular group velocity dispersion.

© 2012 OSA

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Nonlinear Optics

History
Original Manuscript: July 24, 2012
Revised Manuscript: August 17, 2012
Manuscript Accepted: August 17, 2012
Published: September 11, 2012

Citation
Ryan M. Camacho, "Entangled photon generation using four-wave mixing in azimuthally symmetric microresonators," Opt. Express 20, 21977-21991 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-20-21977


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References

  1. J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett.78, 3221–3224 (1997). [CrossRef]
  2. T. C. Ralph and G. J. Pryde, “Optical quantum computation,” in Prog. Optics,vol. 54, E. Wolf, ed. (Elsevier Science2010), pp. 209–269. [CrossRef]
  3. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. Duan, and H. J. Kimble, “Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles,” Nature423, 731–734 (2003). [CrossRef] [PubMed]
  4. A. Haase, N. Piro, J. Eschner, and M. W. Mitchell, “Tunable narrowband entangled photon pair source for resonant single-photon single-atom interaction,” Opt. Lett.34, 55–57 (2009). [CrossRef]
  5. K. Akiba, K. Kashiwagi, M. Arikawa, and M. Kozuma, “Storage and retrieval of nonclassical photon pairs and conditional single photons generated by the parametric down-conversion process,” New J. Phys.11, 013049 (2009). [CrossRef]
  6. Z. Y. Ou and Y. J. Lu, “Cavity enhanced spontaneous parametric Down-Conversion for the prolongation of correlation time between conjugate photons,” Phys. Rev. Lett.83, 2556–2559 (1999). [CrossRef]
  7. S. Clemmen, K. P. Huy, W. Bogaerts, R. G. Baets, P. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators,” Opt. Express17, 16558–16570 (2009). [CrossRef] [PubMed]
  8. L. G. Helt, Z. Yang, M. Liscidini, and J. E. Sipe, “Spontaneous four-wave mixing in microring resonators,” Opt. Lett.35, 3006–3008 (2010). [CrossRef] [PubMed]
  9. J. Chen, Z. H. Levine, J. Fan, and A. L. Migdall, “Frequency-bin entangled comb of photon pairs from a Silicon-on-Insulator micro-resonator,” Opt. Express19, 1470–1483 (2011). [CrossRef] [PubMed]
  10. M. Fiorentino, P. L. Voss, J. E. Sharping, and P. Kumar, “All-fiber photon-pair source for quantum communications,” IEEE Photon. Technol. Lett.14, 983 (2002). [CrossRef]
  11. J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides,” Opt. Express14, 12388–12393 (2006). [CrossRef] [PubMed]
  12. H. Takesue, Y. Tokura, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, and S. I. Itabashi, “Entanglement generation using silicon wire waveguide,” Appl. Phys. Lett.91, 201108 (2007). [CrossRef]
  13. X. Li, P. L. Voss, J. E. Sharping, and P. Kumar, “Optical-Fiber source of Polarization-Entangled photons in the 1550 nm telecom band,” Phys. Rev. Lett.94, 053601 (2005). [CrossRef] [PubMed]
  14. H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S.-i. Itabashi, “Generation of polarization entangledphoton pairs using silicon wirewaveguide,” Opt. Express16, 5721–5727 (2008). [CrossRef] [PubMed]
  15. K.-i. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S.-i. Itabashi, “Generation of high-purity entangled photon pairs using silicon wire waveguide,” Opt. Express16, 20368–20373 (2008). [CrossRef] [PubMed]
  16. P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, “Optical frequency comb generation from a monolithic microresonator,” Nature450, 1214–1217 (2007). [CrossRef]
  17. J. S. Levy, A. Gondarenko, M. A. Foster, A. C. Turner-Foster, A. L. Gaeta, and M. Lipson, “CMOS-compatible multiple-wavelength oscillator for on-chip optical interconnects,” Nat. Photonics4, 37–40 (2010). [CrossRef]
  18. L. Razzari, D. Duchesne, M. Ferrera, R. Morandotti, S. Chu, B. Little, and D. Moss, “CMOS-compatible integrated optical hyper-parametric oscillator,” Nat. Photonics4, 41–45 (2010). [CrossRef]
  19. M. Ferrera, Y. Park, L. Razzari, B. E. Little, S. T. Chu, R. Morandotti, D. J. Moss, and J. Azaa, “On-chip CMOS-compatible all-optical integrator,” Nat. Commun1, 29 (2010). [CrossRef] [PubMed]
  20. T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-Based optical frequency combs,” Science332, 555 –559 (2011). [CrossRef] [PubMed]
  21. F. Ferdous, H. Miao, D. E. Leaird, K. Srinivasan, J. Wang, L. Chen, L. T. Varghese, and A. M. Weiner, “Spectral line-by-line pulse shaping of on-chip microresonator frequency combs,” Nat. Photonics5, 770–776 (2011). [CrossRef]
  22. A. R. Johnson, Y. Okawachi, J. S. Levy, J. Cardenas, K. Saha, M. Lipson, and A. L. Gaeta, “Chip-based frequency combs with sub-100GHz repetition rates,” Opt. Lett.37, 875–877 (2012). [CrossRef] [PubMed]
  23. P. P. Absil, J. V. Hryniewicz, B. E. Little, P. S. Cho, R. A. Wilson, L. G. Joneckis, and P. Ho, “Wavelength conversion in GaAs micro-ring resonators,” Opt. Lett.25, 554–556 (2000). [CrossRef]
  24. A. C. Turner, M. A. Foster, A. L. Gaeta, and M. Lipson, “Ultra-low power parametric frequency conversion in a silicon microring resonator,” Opt. Express16, 4881–4887 (2008). [CrossRef] [PubMed]
  25. Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A82, 033801 (2010). [CrossRef]
  26. Y. K. Chembo, D. V. Strekalov, and N. Yu, “Spectrum and dynamics of optical frequency combs generated with monolithic whispering gallery mode resonators,” Phys. Rev. Lett.104, 103902 (2010). [CrossRef] [PubMed]
  27. M. Scholz, L. Koch, and O. Benson, “Analytical treatment of spectral properties and signal/idler intensity correlations for a double-resonant optical parametric oscillator far below threshold,” Opt. Commun.282, 3518–3523 (2009). [CrossRef]
  28. D. Walls and G. J. Milburn, Quantum Optics (Springer, 2007).
  29. T. Bååk, “Silicon oxynitride; a material for GRIN optics,” Appl. Optics21, 1069–1072 (1982). [CrossRef]
  30. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am.55, 1205–1208 (1965). [CrossRef]
  31. D. A. B. Miller, Quantum Mechanics for Scientists and Engineers (Cambridge University Press, 2008). [CrossRef]
  32. P. Milonni, “Field quantization and radiative processes in dispersive dielectric media,” J. Mod. Optic.42, 1991–2004 (1995). [CrossRef]
  33. B. Huttner, J. J. Baumberg, and S. M. Barnett, “Canonical quantization of light in a linear dielectric,” Europhys. Lett.16, 177–182 (1991). [CrossRef]

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