OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 1 — Jan. 1, 2008
  • pp: 40–47

Four-wave parametric oscillation: theory and observations

Ken-ichi Harada, Nobuhito Hayashi, Kenji Mori, and Masaharu Mitsunaga  »View Author Affiliations

JOSA B, Vol. 25, Issue 1, pp. 40-47 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (709 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We present theoretically and experimentally a novel type of parametric fluorescence and oscillation in which four optical waves in off-axis, diagonal directions simultaneously build up under resonant counterpropagating pump-laser excitation in atomic sodium vapor. Two of the four are anti-Stokes shifted and the other two are Stokes shifted, and they are strongly coupled owing to electromagnetically induced diffraction. Theoretically, the Liouville–Maxwell equations are solved to derive four-wave propagation equations. Experimentally, we have observed four-wave parametric oscillation when a weak off-axis seed beam is introduced into otherwise axially symmetric parametric fluorescence patterns. Temporal waveforms are also analyzed, and strong correlations between any pairs of the four emissions are identified.

© 2008 Optical Society of America

OCIS Codes
(020.1670) Atomic and molecular physics : Coherent optical effects
(020.2930) Atomic and molecular physics : Hyperfine structure
(270.1670) Quantum optics : Coherent optical effects
(300.6320) Spectroscopy : Spectroscopy, high-resolution
(300.6420) Spectroscopy : Spectroscopy, nonlinear

ToC Category:

Original Manuscript: June 5, 2007
Revised Manuscript: October 3, 2007
Manuscript Accepted: October 10, 2007
Published: December 19, 2007

Ken-ichi Harada, Nobuhito Hayashi, Kenji Mori, and Masaharu Mitsunaga, "Four-wave parametric oscillation: theory and observations," J. Opt. Soc. Am. B 25, 40-47 (2008)

Sort:  Year  |  Journal  |  Reset  


  1. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997).
  2. J. A. Giormaine and R. C. Miller, "Tunable coherent parametric oscillation in LiNbO3 at optical frequencies," Phys. Rev. Lett. 14, 973-976 (1965). [CrossRef]
  3. M. D. Lukin, P. R. Hemmer, M. Löffler, and M. O. Scully, "Resonant enhancement of parametric processes via radiative interference and induced coherence," Phys. Rev. Lett. 81, 2675-2678 (1998). [CrossRef]
  4. A. S. Zibrov, M. D. Lukin, and M. O. Scully, "Nondegenerate parametric self-oscillation via multiwave mixing in coherent atomic media," Phys. Rev. Lett. 83, 4049-4052 (1999). [CrossRef]
  5. M. D. Lukin, A. B. Matsko, M. Fleischhauer, and M. O. Scully, "Quantum noise and correlations in resonantly enhanced wave mixing based on atomic coherence," Phys. Rev. Lett. 82, 1847-1850 (1999). [CrossRef]
  6. R. E. Slusher, L. W. Hollberg, B. Yurke, J. C. Mertz, and J. F. Valley, "Observation of squeezed states generated by four-wave mixing in an optical cavity," Phys. Rev. Lett. 55, 2409-2412 (1985). [CrossRef] [PubMed]
  7. C. F. McCormick, V. Boyer, E. Arimondo, and P. D. Lett, "Strong relative intensity squeezing by four-wave mixing in rubidium vapor," Opt. Lett. 32, 178-180 (2007). [CrossRef]
  8. A. Heidmann, R. J. Horowicz, S. Reynaud, E. Giacobino, and C. Fabre, "Observation of quantum noise reduction on twin laser beams," Phys. Rev. Lett. 59, 2555-2557 (1987). [CrossRef] [PubMed]
  9. O. Aytür and P. Kumar, "Pulsed twin beams of light," Phys. Rev. Lett. 65, 1551-1554 (1990). [CrossRef] [PubMed]
  10. H. Zou, A. Zhai, J. Guo, R. Yang, and J. Gao, "Preparation and measurement of tunable high-power sub-Poissonian light using twin beams," Opt. Lett. 31, 1735-1737 (2006). [CrossRef] [PubMed]
  11. M. Fleischhauer and M. D. Lukin, "Quantum memory for photons: dark-state polaritons," Phys. Rev. A 65, 022314 (2002). [CrossRef]
  12. C. H. van der Wal, M. D. Eisaman, A. André, R. L. Walsworth, D. F. Phillips, A. S. Zibrov, and M. D. Lukin, "Atomic memory for correlated photon states," Science 301, 196-200 (2003). [CrossRef] [PubMed]
  13. A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L.-M. Duan, and H. J. Kimble, "Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles," Nature 423, 731-734 (2003). [CrossRef] [PubMed]
  14. K. Harada, M. Ogata, and M. Mitsunaga, "Four-wave parametric oscillation in sodium vapor by electromagnetically induced diffraction," Opt. Lett. 32, 1111-1113 (2007). [CrossRef] [PubMed]
  15. K. Harada, S. Tanaka, T. Kanbashi, M. Mitsunaga, and K. Motomura, "Electromagnetically induced diffraction in sodium vapor," Opt. Lett. 30, 2004-2006 (2005). [CrossRef] [PubMed]
  16. K.-J. Boller, A. Imamoglu, and S. E. Harris, "Observation of electromagnetically induced transparency," Phys. Rev. Lett. 66, 2593-2596 (1991). [CrossRef] [PubMed]
  17. J. E. Field, K. H. Hahn, and S. E. Harris, "Observation of electromagnetically induced transparency in collisionally broadened lead vapor," Phys. Rev. Lett. 67, 3062-3065 (1991). [CrossRef] [PubMed]
  18. A. F. Huss, N. Peer, R. Lammegger, E. A. Korsunsky, and L. Windholz, "Efficient Raman sideband generation in a coherent atomic medium," Phys. Rev. A 63, 013802 (2000). [CrossRef]
  19. V. Wong, R. S. Bennink, A. M. Marino, R. W. Boyd, C. R. Stroud, Jr., and F. A. Narducci, "Influence of coherent Raman scattering on coherent population trapping in atomic sodium vapor," Phys. Rev. A 70, 053811 (2004). [CrossRef]
  20. K. Harada, K. Motomura, T. Koshimizu, H. Ueno, and M. Mitsunaga, "Coherent Raman beats from dark states," J. Opt. Soc. Am. B 22, 1105-1111 (2005). [CrossRef]
  21. K. Harada, T. Kanbashi, M. Mitsunaga, and K. Motomura, "Competition between electromagnetically induced transparency and stimulated Raman scattering," Phys. Rev. A 73, 013807 (2006). [CrossRef]
  22. G. S. Agarwal, T. N. Dey, and D. J. Gauthier, "Competition between electromagnetically induced transparency and Raman processes," Phys. Rev. A 74, 043805 (2006). [CrossRef]
  23. P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, "Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium," Opt. Lett. 20, 982-984 (1995). [CrossRef] [PubMed]
  24. D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electomagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004). [CrossRef] [PubMed]
  25. V. Balic, D. A. Braje, P. Kolchin, G. Y. Yin, and S. E. Harris, "Generation of paired photons with controllable waveforms," Phys. Rev. Lett. 94, 183601 (2005). [CrossRef] [PubMed]
  26. D. N. Matsukevich, T. Chanelière, M. Bhattacharya, S.-Y. Lan, S. D. Jenkins, T. A. B. Kennedy, and A. Kuzmich, "Entanglement of a photon and a collective atomic excitation," Phys. Rev. Lett. 95, 040405 (2005). [CrossRef] [PubMed]
  27. T. Chanelière, D. N. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, "Storage and retrieval of single photons transmitted between remote quantum memories," Nature 438, 833-836 (2005). [CrossRef] [PubMed]
  28. A. Petrossian, M. Pinard, A. Maître, J.-Y. Courtois, and G. Grynberg, "Transverse-pattern formation for counterpropagating laser beams in rubidium vapour," Europhys. Lett. 18, 689-695 (1992). [CrossRef]
  29. A. Maître, A. Petrossian, A. Blouin, M. Panard, and G. Grynberg, "Spatio-temporal instability for counterpropagating beams in rubidium vapor," Opt. Commun. 116, 153-158 (1995). [CrossRef]
  30. A. M. C. Dawes, L. Illing, S. M. Clark, and D. J. Gauthier, "All-optical switching in rubidium vapor," Science 308, 672-674 (2005). [CrossRef] [PubMed]
  31. K. Motomura, M. Tsukamoto, A. Wakiyama, K. Harada, and M. Mitsunaga, "Observation of correlated anti-Stokes emissions by multiwave mixing in sodium vapor," Phys. Rev. A 71, 043817 (2005). [CrossRef]
  32. Similar results were obtained if another definition of correlation function G(2)(τ)=⟨δf1(t)δf2(t+τ)⟩/⟨δf1(t)2⟩⟨δf2(t+τ)2⟩ was employed, where δf1,2(t)≡f1,2(t)−⟨f1,2⟩. See V. A. Sautenkov, Y. V. Rostovtsev, and M. O. Scully, "Switching between photon-photon correlations and Raman anticorrelations in a coherently prepared Rb vapor," Phys. Rev. A 72, 065801 (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