Abstract

We analyze backward four-wave mixing in a four-level system exhibiting electromagnetically induced transparency (EIT). We show that EIT suppression of the linear absorption leads to the resonantly enhanced four-wave mixing process and the conversion efficiency near 100% may be achieved in a dense four-level medium with negligible decoherence decay.

© 2006 Optical Society of America

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  1. S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
    [CrossRef]
  2. S. E. Harris and L. V. Hau, "Nonlinear optics at low light levels," Phys. Rev. Lett. 82, 4611-4614 (1999).
    [CrossRef]
  3. M. M. D. Lukin and A. Imamoglu, "Controlling photons using electromagnetically induced transparency," Nature 413, 273-275 (2001).
    [CrossRef]
  4. M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
    [CrossRef] [PubMed]
  5. A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
    [CrossRef] [PubMed]
  6. K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, "Self-induced phase matching in parametric anti-Stokes stimulated Raman scattering," Phys. Rev. Lett. 79, 209-212 (1997).
    [CrossRef]
  7. 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]
  8. S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Weltch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
    [CrossRef]
  9. B. S. Ham, M. S. Shahriar, and P. R. Hemmer, "Enhancement of four-wave mixing and line narrowing by use of quantum coherence in an optically dense double-Lambda solid," Opt. Lett. 24, 86-88 (1999).
    [CrossRef]
  10. Y. Li and M. Xiao, "Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms," Opt. Lett. 21, 1064-1066 (1996).
    [CrossRef] [PubMed]
  11. B. L. Lu, W. H. Burkett, and M. Xiao, "Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping," Opt. Lett. 23, 804-806 (1998).
    [CrossRef]
  12. W. Harshawardhan and G. S. Agarwal, "Enhancement of nonlinear-optical signals under coherent-population-trapping conditions," Phys. Rev. A 58, 598-604 (1998).
    [CrossRef]
  13. G. S. Agarwal and J. H. Eberly, "Continuous-probe solutions for self-similar pulses in four-level systems," Phys. Rev. A 61, 013404 (2000).
    [CrossRef]
  14. 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]
  15. A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, "Efficient frequency up-conversion in resonant coherent media," Phys. Rev. A 65, 051801 (2002).
    [CrossRef]
  16. M. M. Fleischhauer and T. Richter, "Pulse matching and correlation of phase fluctuations in Lambda systems," Phys. Rev. A 51, 2430-2442 (1995).
    [CrossRef] [PubMed]
  17. T. Johnsson and M. Fleischhauer, "Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions," Phys. Rev. A 66, 043808 (2002).
    [CrossRef]
  18. C. Dorman, I. Kucukkara, and J. P. Marangos, "Measurement of high conversion efficiency to 123.6-nm radiation in a four-wave-mixing scheme enhanced by electromagnetically induced transparency," Phys. Rev. A 61, 013802 (2000).
    [CrossRef]
  19. J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, "Role of electromagnetically induced transparency in resonant four-wave-mixing schemes," Phys. Rev. A 53, 543-561 (1996).
    [CrossRef] [PubMed]
  20. L. Deng and M. G. Payne, "Three-photon destructive interference in ultraslow-propagation-enhanced four-wave mixing," Phys. Rev. A 68, 051801(R) (2003).
    [CrossRef]
  21. M. G. Payne and L. Deng, "Consequences of induced transparency in a double-Lambda scheme: destructive interference in four-wave mixing," Phys. Rev. A 65, 063806 (2002).
    [CrossRef]
  22. M. G. Payne and L. Deng, "Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing," Phys. Rev. Lett. 91, 123602 (2003).
    [CrossRef] [PubMed]
  23. C. H. Keitel, "Exponential gain in resonant four-wave mixing via dressed inversions," Phys. Rev. A 57, 1412-1416 (1998).
    [CrossRef]
  24. A. K. Popov and A. S. Bayev, "Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transitions with control fields," Phys. Rev. A 62, 025801 (2000).
    [CrossRef]
  25. H. Kang, G. Hernandez, and Y. Zhu, "Slow-light six-wave mixing at low light intensities," Phys. Rev. Lett. 93, 073601 (2004).
    [CrossRef] [PubMed]
  26. H. Kang, G. Hernandez, and Y. Zhu, "Resonant four-wave mixing with slow light," Phys. Rev. A 70, 061804(R) (2004).
    [CrossRef]
  27. Y. Wu and X. Yang, "Highly efficient four-wave mixing in double-Lambda system in ultraslow propagation regime," Phys. Rev. A 70, 053818 (2004).
    [CrossRef]
  28. H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, "Efficient parametric amplification in double-Lambda systems without maximal two-photon coherence," Phys. Rev. A 70, 063814 (2005).
    [CrossRef]
  29. M. Fleischhauer, "Mirrorless oscillation based on resonantly enhanced four-wave mixing: all-order analytic solutions," in Frontiers of Laser Physics and Quantum Optics, Z.Xu, S.Xie, S.-Y.Zhu, and M.O.Scully, eds. (Springer, 2000) pp. 97-106.
  30. L. Deng and M. G. Payne, "Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Lambda system," Phys. Rev. A 71, 011803(R) (2005).
    [CrossRef]
  31. 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]
  32. C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]
  33. 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]
  34. 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]

2005 (4)

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, "Efficient parametric amplification in double-Lambda systems without maximal two-photon coherence," Phys. Rev. A 70, 063814 (2005).
[CrossRef]

L. Deng and M. G. Payne, "Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Lambda system," Phys. Rev. A 71, 011803(R) (2005).
[CrossRef]

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]

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]

2004 (3)

H. Kang, G. Hernandez, and Y. Zhu, "Slow-light six-wave mixing at low light intensities," Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

H. Kang, G. Hernandez, and Y. Zhu, "Resonant four-wave mixing with slow light," Phys. Rev. A 70, 061804(R) (2004).
[CrossRef]

Y. Wu and X. Yang, "Highly efficient four-wave mixing in double-Lambda system in ultraslow propagation regime," Phys. Rev. A 70, 053818 (2004).
[CrossRef]

2003 (5)

L. Deng and M. G. Payne, "Three-photon destructive interference in ultraslow-propagation-enhanced four-wave mixing," Phys. Rev. A 68, 051801(R) (2003).
[CrossRef]

M. G. Payne and L. Deng, "Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing," Phys. Rev. Lett. 91, 123602 (2003).
[CrossRef] [PubMed]

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]

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Weltch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

2002 (3)

A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, "Efficient frequency up-conversion in resonant coherent media," Phys. Rev. A 65, 051801 (2002).
[CrossRef]

T. Johnsson and M. Fleischhauer, "Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions," Phys. Rev. A 66, 043808 (2002).
[CrossRef]

M. G. Payne and L. Deng, "Consequences of induced transparency in a double-Lambda scheme: destructive interference in four-wave mixing," Phys. Rev. A 65, 063806 (2002).
[CrossRef]

2001 (1)

M. M. D. Lukin and A. Imamoglu, "Controlling photons using electromagnetically induced transparency," Nature 413, 273-275 (2001).
[CrossRef]

2000 (4)

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
[CrossRef] [PubMed]

C. Dorman, I. Kucukkara, and J. P. Marangos, "Measurement of high conversion efficiency to 123.6-nm radiation in a four-wave-mixing scheme enhanced by electromagnetically induced transparency," Phys. Rev. A 61, 013802 (2000).
[CrossRef]

G. S. Agarwal and J. H. Eberly, "Continuous-probe solutions for self-similar pulses in four-level systems," Phys. Rev. A 61, 013404 (2000).
[CrossRef]

A. K. Popov and A. S. Bayev, "Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transitions with control fields," Phys. Rev. A 62, 025801 (2000).
[CrossRef]

1999 (4)

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]

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]

B. S. Ham, M. S. Shahriar, and P. R. Hemmer, "Enhancement of four-wave mixing and line narrowing by use of quantum coherence in an optically dense double-Lambda solid," Opt. Lett. 24, 86-88 (1999).
[CrossRef]

S. E. Harris and L. V. Hau, "Nonlinear optics at low light levels," Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

1998 (3)

B. L. Lu, W. H. Burkett, and M. Xiao, "Nondegenerate four-wave mixing in a double-Lambda system under the influence of coherent population trapping," Opt. Lett. 23, 804-806 (1998).
[CrossRef]

W. Harshawardhan and G. S. Agarwal, "Enhancement of nonlinear-optical signals under coherent-population-trapping conditions," Phys. Rev. A 58, 598-604 (1998).
[CrossRef]

C. H. Keitel, "Exponential gain in resonant four-wave mixing via dressed inversions," Phys. Rev. A 57, 1412-1416 (1998).
[CrossRef]

1997 (2)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, "Self-induced phase matching in parametric anti-Stokes stimulated Raman scattering," Phys. Rev. Lett. 79, 209-212 (1997).
[CrossRef]

1996 (3)

Y. Li and M. Xiao, "Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms," Opt. Lett. 21, 1064-1066 (1996).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, "Role of electromagnetically induced transparency in resonant four-wave-mixing schemes," Phys. Rev. A 53, 543-561 (1996).
[CrossRef] [PubMed]

1995 (1)

M. M. Fleischhauer and T. Richter, "Pulse matching and correlation of phase fluctuations in Lambda systems," Phys. Rev. A 51, 2430-2442 (1995).
[CrossRef] [PubMed]

Agarwal, G. S.

G. S. Agarwal and J. H. Eberly, "Continuous-probe solutions for self-similar pulses in four-level systems," Phys. Rev. A 61, 013404 (2000).
[CrossRef]

W. Harshawardhan and G. S. Agarwal, "Enhancement of nonlinear-optical signals under coherent-population-trapping conditions," Phys. Rev. A 58, 598-604 (1998).
[CrossRef]

Andre, A.

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

Balic, V.

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]

Bayev, A. S.

A. K. Popov and A. S. Bayev, "Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transitions with control fields," Phys. Rev. A 62, 025801 (2000).
[CrossRef]

Bhattacharya, M.

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]

Boca, A.

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]

Boozer, A. D.

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]

Bowen, W. P.

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]

Braje, D. A.

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]

Burkett, W. H.

Chanelière, T.

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]

Chou, C. W.

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]

Deng, L.

L. Deng and M. G. Payne, "Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Lambda system," Phys. Rev. A 71, 011803(R) (2005).
[CrossRef]

M. G. Payne and L. Deng, "Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing," Phys. Rev. Lett. 91, 123602 (2003).
[CrossRef] [PubMed]

L. Deng and M. G. Payne, "Three-photon destructive interference in ultraslow-propagation-enhanced four-wave mixing," Phys. Rev. A 68, 051801(R) (2003).
[CrossRef]

M. G. Payne and L. Deng, "Consequences of induced transparency in a double-Lambda scheme: destructive interference in four-wave mixing," Phys. Rev. A 65, 063806 (2002).
[CrossRef]

Dorman, C.

C. Dorman, I. Kucukkara, and J. P. Marangos, "Measurement of high conversion efficiency to 123.6-nm radiation in a four-wave-mixing scheme enhanced by electromagnetically induced transparency," Phys. Rev. A 61, 013802 (2000).
[CrossRef]

Duan, L. M.

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]

Eberly, J. H.

G. S. Agarwal and J. H. Eberly, "Continuous-probe solutions for self-similar pulses in four-level systems," Phys. Rev. A 61, 013404 (2000).
[CrossRef]

Eisaman, M. D.

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

Fleischhauer, M.

T. Johnsson and M. Fleischhauer, "Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions," Phys. Rev. A 66, 043808 (2002).
[CrossRef]

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]

M. Fleischhauer, "Mirrorless oscillation based on resonantly enhanced four-wave mixing: all-order analytic solutions," in Frontiers of Laser Physics and Quantum Optics, Z.Xu, S.Xie, S.-Y.Zhu, and M.O.Scully, eds. (Springer, 2000) pp. 97-106.

Fleischhauer, M. M.

M. M. Fleischhauer and T. Richter, "Pulse matching and correlation of phase fluctuations in Lambda systems," Phys. Rev. A 51, 2430-2442 (1995).
[CrossRef] [PubMed]

Friedmann, H.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, "Efficient parametric amplification in double-Lambda systems without maximal two-photon coherence," Phys. Rev. A 70, 063814 (2005).
[CrossRef]

Hakuta, K.

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, "Self-induced phase matching in parametric anti-Stokes stimulated Raman scattering," Phys. Rev. Lett. 79, 209-212 (1997).
[CrossRef]

Ham, B. S.

Harris, S. E.

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]

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
[CrossRef] [PubMed]

S. E. Harris and L. V. Hau, "Nonlinear optics at low light levels," Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

Harshawardhan, W.

W. Harshawardhan and G. S. Agarwal, "Enhancement of nonlinear-optical signals under coherent-population-trapping conditions," Phys. Rev. A 58, 598-604 (1998).
[CrossRef]

Hau, L. V.

S. E. Harris and L. V. Hau, "Nonlinear optics at low light levels," Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

Hemmer, P. R.

Hernandez, G.

H. Kang, G. Hernandez, and Y. Zhu, "Slow-light six-wave mixing at low light intensities," Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

H. Kang, G. Hernandez, and Y. Zhu, "Resonant four-wave mixing with slow light," Phys. Rev. A 70, 061804(R) (2004).
[CrossRef]

Hollberg, L.

A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, "Efficient frequency up-conversion in resonant coherent media," Phys. Rev. A 65, 051801 (2002).
[CrossRef]

Imamoglu, A.

M. M. D. Lukin and A. Imamoglu, "Controlling photons using electromagnetically induced transparency," Nature 413, 273-275 (2001).
[CrossRef]

Jain, M.

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

Jenkins, S. D.

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]

Johnsson, T.

T. Johnsson and M. Fleischhauer, "Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions," Phys. Rev. A 66, 043808 (2002).
[CrossRef]

Kang, H.

H. Kang, G. Hernandez, and Y. Zhu, "Resonant four-wave mixing with slow light," Phys. Rev. A 70, 061804(R) (2004).
[CrossRef]

H. Kang, G. Hernandez, and Y. Zhu, "Slow-light six-wave mixing at low light intensities," Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

Kash, M. M.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Weltch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

Katsuragawa, M.

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, "Self-induced phase matching in parametric anti-Stokes stimulated Raman scattering," Phys. Rev. Lett. 79, 209-212 (1997).
[CrossRef]

Keitel, C. H.

C. H. Keitel, "Exponential gain in resonant four-wave mixing via dressed inversions," Phys. Rev. A 57, 1412-1416 (1998).
[CrossRef]

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, "Role of electromagnetically induced transparency in resonant four-wave-mixing schemes," Phys. Rev. A 53, 543-561 (1996).
[CrossRef] [PubMed]

Kennedy, T. A. B.

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]

Kimble, H. J.

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]

Knight, P. L.

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, "Role of electromagnetically induced transparency in resonant four-wave-mixing schemes," Phys. Rev. A 53, 543-561 (1996).
[CrossRef] [PubMed]

Kolchin, P.

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]

Kucukkara, I.

C. Dorman, I. Kucukkara, and J. P. Marangos, "Measurement of high conversion efficiency to 123.6-nm radiation in a four-wave-mixing scheme enhanced by electromagnetically induced transparency," Phys. Rev. A 61, 013802 (2000).
[CrossRef]

Kuzmich, A.

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]

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]

Lan, S.-Y.

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]

Li, J. Z.

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, "Self-induced phase matching in parametric anti-Stokes stimulated Raman scattering," Phys. Rev. Lett. 79, 209-212 (1997).
[CrossRef]

Li, Y.

Lu, B. L.

Lukin, M. D.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Weltch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, "Efficient frequency up-conversion in resonant coherent media," Phys. Rev. A 65, 051801 (2002).
[CrossRef]

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]

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]

Lukin, M. M. D.

M. M. D. Lukin and A. Imamoglu, "Controlling photons using electromagnetically induced transparency," Nature 413, 273-275 (2001).
[CrossRef]

Manuszak, D.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
[CrossRef] [PubMed]

Marangos, J. P.

C. Dorman, I. Kucukkara, and J. P. Marangos, "Measurement of high conversion efficiency to 123.6-nm radiation in a four-wave-mixing scheme enhanced by electromagnetically induced transparency," Phys. Rev. A 61, 013802 (2000).
[CrossRef]

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, "Role of electromagnetically induced transparency in resonant four-wave-mixing schemes," Phys. Rev. A 53, 543-561 (1996).
[CrossRef] [PubMed]

Matsko, A. B.

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]

Matsukevich, D. N.

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]

Merriam, A. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

Payne, M. G.

L. Deng and M. G. Payne, "Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Lambda system," Phys. Rev. A 71, 011803(R) (2005).
[CrossRef]

M. G. Payne and L. Deng, "Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing," Phys. Rev. Lett. 91, 123602 (2003).
[CrossRef] [PubMed]

L. Deng and M. G. Payne, "Three-photon destructive interference in ultraslow-propagation-enhanced four-wave mixing," Phys. Rev. A 68, 051801(R) (2003).
[CrossRef]

M. G. Payne and L. Deng, "Consequences of induced transparency in a double-Lambda scheme: destructive interference in four-wave mixing," Phys. Rev. A 65, 063806 (2002).
[CrossRef]

Petch, J. C.

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, "Role of electromagnetically induced transparency in resonant four-wave-mixing schemes," Phys. Rev. A 53, 543-561 (1996).
[CrossRef] [PubMed]

Phillips, D. F.

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

Popov, A. K.

A. K. Popov and A. S. Bayev, "Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transitions with control fields," Phys. Rev. A 62, 025801 (2000).
[CrossRef]

Richter, T.

M. M. Fleischhauer and T. Richter, "Pulse matching and correlation of phase fluctuations in Lambda systems," Phys. Rev. A 51, 2430-2442 (1995).
[CrossRef] [PubMed]

Sautenkov, V. A.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Weltch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

Scully, M. O.

A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, "Efficient frequency up-conversion in resonant coherent media," Phys. Rev. A 65, 051801 (2002).
[CrossRef]

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]

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]

Shahriar, M. S.

Sharpe, S. J.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
[CrossRef] [PubMed]

Shpaisman, H.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, "Efficient parametric amplification in double-Lambda systems without maximal two-photon coherence," Phys. Rev. A 70, 063814 (2005).
[CrossRef]

Shverdin, M.

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
[CrossRef] [PubMed]

Suzuki, M.

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, "Self-induced phase matching in parametric anti-Stokes stimulated Raman scattering," Phys. Rev. Lett. 79, 209-212 (1997).
[CrossRef]

Van der Wal, C. H.

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

Walsworth, R. L.

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

Weltch, G. R.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Weltch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

Wilson-Gordon, A. D.

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, "Efficient parametric amplification in double-Lambda systems without maximal two-photon coherence," Phys. Rev. A 70, 063814 (2005).
[CrossRef]

Wu, Y.

Y. Wu and X. Yang, "Highly efficient four-wave mixing in double-Lambda system in ultraslow propagation regime," Phys. Rev. A 70, 053818 (2004).
[CrossRef]

Xia, H.

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

Xiao, M.

Yang, X.

Y. Wu and X. Yang, "Highly efficient four-wave mixing in double-Lambda system in ultraslow propagation regime," Phys. Rev. A 70, 053818 (2004).
[CrossRef]

Yelin, S. F.

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Weltch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

Yin, G. Y.

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]

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
[CrossRef] [PubMed]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

Zhu, Y.

H. Kang, G. Hernandez, and Y. Zhu, "Slow-light six-wave mixing at low light intensities," Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

H. Kang, G. Hernandez, and Y. Zhu, "Resonant four-wave mixing with slow light," Phys. Rev. A 70, 061804(R) (2004).
[CrossRef]

Zibrov, A. S.

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, "Efficient frequency up-conversion in resonant coherent media," Phys. Rev. A 65, 051801 (2002).
[CrossRef]

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]

Nature (2)

M. M. D. Lukin and A. Imamoglu, "Controlling photons using electromagnetically induced transparency," Nature 413, 273-275 (2001).
[CrossRef]

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]

Opt. Lett. (3)

Phys. Rev. A (16)

W. Harshawardhan and G. S. Agarwal, "Enhancement of nonlinear-optical signals under coherent-population-trapping conditions," Phys. Rev. A 58, 598-604 (1998).
[CrossRef]

G. S. Agarwal and J. H. Eberly, "Continuous-probe solutions for self-similar pulses in four-level systems," Phys. Rev. A 61, 013404 (2000).
[CrossRef]

A. S. Zibrov, M. D. Lukin, L. Hollberg, and M. O. Scully, "Efficient frequency up-conversion in resonant coherent media," Phys. Rev. A 65, 051801 (2002).
[CrossRef]

M. M. Fleischhauer and T. Richter, "Pulse matching and correlation of phase fluctuations in Lambda systems," Phys. Rev. A 51, 2430-2442 (1995).
[CrossRef] [PubMed]

T. Johnsson and M. Fleischhauer, "Quantum theory of resonantly enhanced four-wave mixing: mean-field and exact numerical solutions," Phys. Rev. A 66, 043808 (2002).
[CrossRef]

C. Dorman, I. Kucukkara, and J. P. Marangos, "Measurement of high conversion efficiency to 123.6-nm radiation in a four-wave-mixing scheme enhanced by electromagnetically induced transparency," Phys. Rev. A 61, 013802 (2000).
[CrossRef]

J. C. Petch, C. H. Keitel, P. L. Knight, and J. P. Marangos, "Role of electromagnetically induced transparency in resonant four-wave-mixing schemes," Phys. Rev. A 53, 543-561 (1996).
[CrossRef] [PubMed]

L. Deng and M. G. Payne, "Three-photon destructive interference in ultraslow-propagation-enhanced four-wave mixing," Phys. Rev. A 68, 051801(R) (2003).
[CrossRef]

M. G. Payne and L. Deng, "Consequences of induced transparency in a double-Lambda scheme: destructive interference in four-wave mixing," Phys. Rev. A 65, 063806 (2002).
[CrossRef]

S. F. Yelin, V. A. Sautenkov, M. M. Kash, G. R. Weltch, and M. D. Lukin, "Nonlinear optics via double dark resonances," Phys. Rev. A 68, 063801 (2003).
[CrossRef]

L. Deng and M. G. Payne, "Achieving induced transparency with one- and three-photon destructive interference in a two-mode, three-level, double-Lambda system," Phys. Rev. A 71, 011803(R) (2005).
[CrossRef]

C. H. Keitel, "Exponential gain in resonant four-wave mixing via dressed inversions," Phys. Rev. A 57, 1412-1416 (1998).
[CrossRef]

A. K. Popov and A. S. Bayev, "Enhanced four-wave mixing via elimination of inhomogeneous broadening by coherent driving of quantum transitions with control fields," Phys. Rev. A 62, 025801 (2000).
[CrossRef]

H. Kang, G. Hernandez, and Y. Zhu, "Resonant four-wave mixing with slow light," Phys. Rev. A 70, 061804(R) (2004).
[CrossRef]

Y. Wu and X. Yang, "Highly efficient four-wave mixing in double-Lambda system in ultraslow propagation regime," Phys. Rev. A 70, 053818 (2004).
[CrossRef]

H. Shpaisman, A. D. Wilson-Gordon, and H. Friedmann, "Efficient parametric amplification in double-Lambda systems without maximal two-photon coherence," Phys. Rev. A 70, 063814 (2005).
[CrossRef]

Phys. Rev. Lett. (10)

H. Kang, G. Hernandez, and Y. Zhu, "Slow-light six-wave mixing at low light intensities," Phys. Rev. Lett. 93, 073601 (2004).
[CrossRef] [PubMed]

S. E. Harris and L. V. Hau, "Nonlinear optics at low light levels," Phys. Rev. Lett. 82, 4611-4614 (1999).
[CrossRef]

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]

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]

M. G. Payne and L. Deng, "Quantum entanglement of Fock states with perfectly efficient ultraslow single-probe photon four-wave mixing," Phys. Rev. Lett. 91, 123602 (2003).
[CrossRef] [PubMed]

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]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient nonlinear frequency conversion with maximal atomic coherence," Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

A. J. Merriam, S. J. Sharpe, M. Shverdin, D. Manuszak, G. Y. Yin, and S. E. Harris, "Efficient nonlinear frequency conversion in an all-resonant double-Lambda system," Phys. Rev. Lett. 84, 5308-5311 (2000).
[CrossRef] [PubMed]

K. Hakuta, M. Suzuki, M. Katsuragawa, and J. Z. Li, "Self-induced phase matching in parametric anti-Stokes stimulated Raman scattering," Phys. Rev. Lett. 79, 209-212 (1997).
[CrossRef]

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]

Phys. Today (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36-42 (1997).
[CrossRef]

Science (1)

C. H. Van der Wal, M. D. Eisaman, A. Andre, 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]

Other (1)

M. Fleischhauer, "Mirrorless oscillation based on resonantly enhanced four-wave mixing: all-order analytic solutions," in Frontiers of Laser Physics and Quantum Optics, Z.Xu, S.Xie, S.-Y.Zhu, and M.O.Scully, eds. (Springer, 2000) pp. 97-106.

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Figures (4)

Fig. 1
Fig. 1

(Color online) FWM coupling scheme in a four-level system. γ 3 ( γ 4 ) is the spontaneous decay rate.

Fig. 2
Fig. 2

(Color online) (a) Calculated backward FWM intensity and probe intensity in the four-level EIT system versus K 13 γ 3 . (b) Calculated forward FWM intensity and probe intensity in the four-level EIT system versus K 13 γ 3 . The parameters are δ k = 0 , Δ p = Δ c = Δ = 0 , Ω c = Ω = 0.5 γ 3 , K 13 = K 14 , γ 3 = γ 4 , and γ 2 = 0.001 γ 3 .

Fig. 3
Fig. 3

(Color online) (a) Calculated backward FWM intensity and probe intensity versus the pump Rabi frequency Ω. (b) Calculated forward FWM intensity and probe intensity versus the pump Rabi frequency Ω. The maximum efficiency is obtained for Ω = Ω c . The parameters are δ k = 0 , Δ p = Δ c = Δ = 0 , Ω c = γ 3 , K 13 = K 14 , γ 3 = γ 4 , and γ 2 = 0.001 γ 3 .

Fig. 4
Fig. 4

(Color online) (a) Calculated backward FWM intensity and probe intensity versus the decoherence rate γ. (b) Calculated forward FWM intensity and probe intensity versus γ. The parameters are δ k = 0 , Δ p = Δ c = Δ = 0 , Ω c = Ω = γ 3 , K 13 = K 14 , K 13 γ 3 = 10 , and γ 3 = γ 4 .

Equations (20)

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

d Ω p ( b ) d z = i κ p Ω p ( b ) + i κ p s Ω s ( b ) ,
d Ω s ( b ) d z = i κ s Ω s ( b ) i κ s p Ω p ( b ) ,
Ω p ( b ) = Ω p + exp ( i k + z ) + Ω p exp ( i k z ) ,
Ω s ( b ) = Ω s + exp ( i k + z ) + Ω s exp ( i k z ) ,
κ ± = κ p κ s 2 ± [ ( κ p + κ s 2 ) 2 κ p s κ s p ] 1 2
Ω s ( b ) ( z ) = K 14 ( z ) 2 γ 3 + K 14 Ω p ( b ) ( 0 ) ,
Ω p ( b ) ( z ) = 2 γ 3 + K 14 ( z ) 2 γ 3 + K 14 Ω p ( b ) ( 0 ) .
η = I s ( z = 0 ) I p ( z = 0 ) = Ω s ( 0 ) Ω p ( 0 ) 2 = ( K 14 ) 2 ( 2 γ 3 + K 14 ) 2 .
d Ω p ( f ) d z = i κ p Ω p ( f ) + i κ p s Ω s ( f ) ,
d Ω s ( f ) d z = i κ s Ω s ( f ) + i κ s p Ω p ( f ) .
κ ± = κ p + κ s 2 ± [ ( κ p κ s 2 ) 2 κ p s κ s p ] 1 2 ,
Ω p ( f ) = Ω p ( f ) ( z = 0 ) 2 [ 1 + exp ( K 13 z γ 3 ) ] ,
Ω s ( f ) = Ω p ( f ) ( z = 0 ) 2 [ 1 + exp ( K 13 z γ 3 ) ] .
η = I s ( z = ) I p ( z = 0 ) = Ω s ( z = ) 2 Ω s ( z = 0 ) 2 = [ 1 exp ( K 13 γ 3 ) ] 2 4 .
V g ( p ) = c 1 + ω p 2 χ ( ω p ) ω p Δ p = 0 ,
V g ( s ) = c 1 + ω s 2 χ ( ω s ) ω s Δ s = 0 ,
χ ( ω p ) ω p Δ p = 0 = γ 4 K 13 γ 3 Ω 2 + γ 4 Ω c 2 K 13 ( Ω 2 Ω * Ω c Ω s Ω p ) ( Ω 2 + Ω c 2 + γ 3 γ 4 ) ( γ 3 Ω 2 + γ 4 Ω c 2 ) 2 ,
χ ( ω s ) ω s Δ s = 0 = γ 4 K 13 γ 3 Ω 2 + γ 4 Ω c 2 K 13 ( Ω c 2 Ω c * Ω Ω p Ω s ) ( Ω 2 + Ω c 2 + γ 3 γ 4 ) ( γ 3 Ω 2 + γ 4 Ω c 2 ) 2 .
V g ( p ) = c 1 + ω p 2 γ 4 K 13 γ 3 Ω 2 + γ 4 Ω c 2 ,
V g ( s ) = c 1 + ω s 2 γ 3 K 14 γ 3 Ω 2 + γ 4 Ω c 2 .

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