Abstract

We present a theoretical treatment for generalized dressed and doubly-dressed multi-wave mixing processes. Co-existing four-wave mixing (FWM), six-wave mixing (SWM) and eight-wave mixing processes have been considered in a closed-cycle five-level system. Due to constructive interference of the secondarily-dressed and primarily-dressed excitation pathways, the FWM and SWM signals are greatly enhanced. The dually enhanced FWM channels are opened simultaneously. The dressing fields provide the energy for such large enhancement.

© 2007 Optical Society of America

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  1. 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]
  2. 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]
  3. B. Lu, W. H. Burkett, and M. Xiao, "Nondegenerate four-wave mixing in a double-L system under the influence of coherent population trapping," Opt. Lett. 23, 804-806 (1998).
    [CrossRef]
  4. V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
    [CrossRef]
  5. D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004).
    [CrossRef] [PubMed]
  6. Y. P. Zhang, A. W. Brown, and M. Xiao, "Observation of interference between four-wave mixing and six-wave mixing," Opt. Lett. 32, 1120-1122 (2007).
    [CrossRef] [PubMed]
  7. Y. P. Zhang and M. Xiao, "Enhancement of six-wave mixing by atomic coherence in a four-level inverted-Y system," Appl. Phys. Lett. 90, 111104 (2007).
    [CrossRef]
  8. H. Kang, G. Hernandez, and Y. F. Zhu, "Slow-light six-wave mixing at low light intensities," Phys. Rev. Lett. 93, 073601 (2004).
    [CrossRef] [PubMed]
  9. Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
    [CrossRef] [PubMed]
  10. H. Ma and C. B. de Araujo, "Interference between third- and fifth-order polarization in semiconductor doped glasses," Phys. Rev. Lett. 71, 3649-3652 (1993).
    [CrossRef] [PubMed]
  11. D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering:Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
    [CrossRef]
  12. R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1992).
  13. S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36 (1997).
  14. J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment," Phys. Rev. A 51, 576-584 (1995).
    [CrossRef] [PubMed]
  15. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
    [CrossRef]
  16. M. Yan, E. G. Rickey, and Y. F. Zhu, "Observation of doubly dressed states in cold atoms," Phys. Rev. A 64, 013412 (2001).
    [CrossRef]
  17. L. Deng and M. G. Payne, "Inhibiting the onset of the three-photon destructive interference in ultraslow propagation-enhanced four-wave mixing with dual induced transparency," Phys. Rev. Lett. 91, 243902 (2003).
    [CrossRef] [PubMed]
  18. Y Wu and L Deng, "Achieving multi-frequency mode entanglement with ultra-slow multi-wave mixing," Opt. Lett. 29, 1144-1146 (2004).
    [CrossRef] [PubMed]
  19. H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
    [CrossRef] [PubMed]

2007 (2)

Y. P. Zhang and M. Xiao, "Enhancement of six-wave mixing by atomic coherence in a four-level inverted-Y system," Appl. Phys. Lett. 90, 111104 (2007).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, "Observation of interference between four-wave mixing and six-wave mixing," Opt. Lett. 32, 1120-1122 (2007).
[CrossRef] [PubMed]

2006 (1)

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

2004 (3)

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

Y Wu and L Deng, "Achieving multi-frequency mode entanglement with ultra-slow multi-wave mixing," Opt. Lett. 29, 1144-1146 (2004).
[CrossRef] [PubMed]

D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

2003 (1)

L. Deng and M. G. Payne, "Inhibiting the onset of the three-photon destructive interference in ultraslow propagation-enhanced four-wave mixing with dual induced transparency," Phys. Rev. Lett. 91, 243902 (2003).
[CrossRef] [PubMed]

2001 (2)

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

M. Yan, E. G. Rickey, and Y. F. Zhu, "Observation of doubly dressed states in cold atoms," Phys. Rev. A 64, 013412 (2001).
[CrossRef]

1999 (2)

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

1998 (2)

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

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering:Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

1997 (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36 (1997).

1996 (1)

1995 (2)

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]

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

1993 (1)

H. Ma and C. B. de Araujo, "Interference between third- and fifth-order polarization in semiconductor doped glasses," Phys. Rev. Lett. 71, 3649-3652 (1993).
[CrossRef] [PubMed]

Albrecht, A. C.

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering:Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

Balic, V.

D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

Braje, D. A.

D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

Brown, A. W.

Burkett, W. H.

Cronin-Golomb, M.

de Araujo, C. B.

H. Ma and C. B. de Araujo, "Interference between third- and fifth-order polarization in semiconductor doped glasses," Phys. Rev. Lett. 71, 3649-3652 (1993).
[CrossRef] [PubMed]

Deng, L

Deng, L.

L. Deng and M. G. Payne, "Inhibiting the onset of the three-photon destructive interference in ultraslow propagation-enhanced four-wave mixing with dual induced transparency," Phys. Rev. Lett. 91, 243902 (2003).
[CrossRef] [PubMed]

Donoghue, J.

Fleischhauer, M.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Fry, E. S.

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Fu, G. S.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

Fu, P. M.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

Gea-Banacloche, J.

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

Goda, S.

D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

Goorskey, D.

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

Harris, S. E.

D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36 (1997).

Hemmer, P. R.

Hernandez, G.

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

Hollberg, L.

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Jiang, Q.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

Jin, S.

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

Kang, H.

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

Katz, D. P.

Kirkwood, J. C.

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering:Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

Kumar, P.

Li, Y.

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]

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

Liu, X.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

Lu, B.

Lukin, M. D.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Ma, H.

H. Ma and C. B. de Araujo, "Interference between third- and fifth-order polarization in semiconductor doped glasses," Phys. Rev. Lett. 71, 3649-3652 (1993).
[CrossRef] [PubMed]

Payne, M. G.

L. Deng and M. G. Payne, "Inhibiting the onset of the three-photon destructive interference in ultraslow propagation-enhanced four-wave mixing with dual induced transparency," Phys. Rev. Lett. 91, 243902 (2003).
[CrossRef] [PubMed]

Rickey, E. G.

M. Yan, E. G. Rickey, and Y. F. Zhu, "Observation of doubly dressed states in cold atoms," Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Rostovtsev, Y.

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Sautenkov, V. A.

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Scully, M. O.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Shahriar, M. S.

Sun, J.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

Ulness, D. J.

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering:Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

Wang, H.

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

Welch, G. R.

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Wu, L. A.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

Wu, Y

Xiao, M.

Y. P. Zhang and M. Xiao, "Enhancement of six-wave mixing by atomic coherence in a four-level inverted-Y system," Appl. Phys. Lett. 90, 111104 (2007).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, "Observation of interference between four-wave mixing and six-wave mixing," Opt. Lett. 32, 1120-1122 (2007).
[CrossRef] [PubMed]

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

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

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]

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

Yan, M.

M. Yan, E. G. Rickey, and Y. F. Zhu, "Observation of doubly dressed states in cold atoms," Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Yelin, S. F.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

Yin, G. Y.

D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

Zhang, Y. P.

Y. P. Zhang and M. Xiao, "Enhancement of six-wave mixing by atomic coherence in a four-level inverted-Y system," Appl. Phys. Lett. 90, 111104 (2007).
[CrossRef]

Y. P. Zhang, A. W. Brown, and M. Xiao, "Observation of interference between four-wave mixing and six-wave mixing," Opt. Lett. 32, 1120-1122 (2007).
[CrossRef] [PubMed]

Zhu, Y. F.

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

M. Yan, E. G. Rickey, and Y. F. Zhu, "Observation of doubly dressed states in cold atoms," Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Zibrov, A. S.

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

Zuo, Z. C.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Y. P. Zhang and M. Xiao, "Enhancement of six-wave mixing by atomic coherence in a four-level inverted-Y system," Appl. Phys. Lett. 90, 111104 (2007).
[CrossRef]

J. Chem. Phys. (1)

D. J. Ulness, J. C. Kirkwood, and A. C. Albrecht, "Competitive events in fifth order time resolved coherent Raman scattering:Direct versus sequential processes," J. Chem. Phys. 108, 3897-3902 (1998).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (3)

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment," Phys. Rev. A 51, 576-584 (1995).
[CrossRef] [PubMed]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, "Quantum interference effects induced by interacting dark resonances," Phys. Rev. A 60, 3225-3228 (1999).
[CrossRef]

M. Yan, E. G. Rickey, and Y. F. Zhu, "Observation of doubly dressed states in cold atoms," Phys. Rev. A 64, 013412 (2001).
[CrossRef]

Phys. Rev. Lett. (7)

L. Deng and M. G. Payne, "Inhibiting the onset of the three-photon destructive interference in ultraslow propagation-enhanced four-wave mixing with dual induced transparency," Phys. Rev. Lett. 91, 243902 (2003).
[CrossRef] [PubMed]

V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas," Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

D. A. Braje, V. Balic, S. Goda, G. Y. Yin, and S. E. Harris, "Frequency mixing using electromagnetically induced transparency in cold atoms," Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

H. Wang, D. Goorskey, and M. Xiao, "Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system," Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef] [PubMed]

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

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, "Generalized n-photon resonant 2n-wave mixing in an (n +1)-level system with phase-conjugate geometry," Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef] [PubMed]

H. Ma and C. B. de Araujo, "Interference between third- and fifth-order polarization in semiconductor doped glasses," Phys. Rev. Lett. 71, 3649-3652 (1993).
[CrossRef] [PubMed]

Phys. Today (1)

S. E. Harris, "Electromagnetically induced transparency," Phys. Today 50, 36 (1997).

Other (1)

R. W. Boyd, Nonlinear Optics (Academic Press, New York, 1992).

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Figures (4)

Fig. 1.
Fig. 1.

(a). Schematic diagram of phase-conjugate doubly-dressed (2n-4)WM. (b) Energy-level diagram for doubly-dressed (2n-4)WM in a closed-cycle (n+1)-level cascade system.

Fig.2.
Fig.2.

(a). Three-dimensional beam geometry to achieve required phase-matching conditions. (b) Five-level atomic system for EWM process with blocking beams E2 and E3. (c) Five-level atomic system for dressed SWM process and (d) the corresponding dressed-state picture, there exist co-existing SWM and EWM processes with blocking beams E2 and E4. (e) Five-level atomic system for doubly-dressed FWM process and (f) the corresponding dressed-state picture which shows the primarily-dressed state ∣-> and the secondarily-dressed states ∣++> and ∣+-> (the primarily-dressed state ∣+> channel is not shown here for simplicity), there exist coexisting FWM, SWM and EWM processes with blocking beams E3 and E4.

Fig. 3.
Fig. 3.

(a). Dressed SWM signal intensity versus Δ a 320 (The maximum is normalized to 1) (Γ3020 = 1, Γ1020 = 0.5, Δ420=6, G 420=0 (black curve), G 420=2 (blue curve), G 420=10 (red curve) , G 420 = 20 (magenta curve)). (b) Dressed SWM signal intensity (normalized by no dressing field (G 4 =0) case, i.e., ρ′(5)10(5) 10 versus Δ4302030 =1, Γ1030 =0.5, G 430=0.5, Δ3a30=0 (black curve), Δ3a30=-0.5 (blue curve), Δ a 330=-2 (red curve), Δ3a30=-6 (magenta curve)). (c) Dressed SWM signal intensity (normalized by no dressing field case) versus Δ4302030 = 1, Γ1030 = 0.5, G 430 = 50, Δ a 330 = -30 (black curve), Δ a 3/ Γ30 = -50 (blue curve), Δ a 330 = -70 (red curve), Δ a 330 = -100 (magenta curve)).

Fig.4.
Fig.4.

(a). Doubly-dressed FWM signal intensity versus Δ a 22030 = Γ2010, G 320 =13, G 420 = 5, Δ320=0, Δ420=200 (black curve), Δ420=10.5 (blue curve), Δ420 = -10.5 (red curve)). (b) Doubly-dressed FWM signal intensity (normalized by the two dressing field G 3=G 4=0 case, i.e., ρ′′(3) 10) versus Δ3302030 = 1, Γ1030 = 0.5, G 330 = 0.5, G 4Γ30 = 50, Δ1 = Δ4 = 0, Δ230 = 0 (black curve), Δ230 = -0.5 (blue curve), Δ230=-2 (red curve), Δ230=-6 (magenta curve)). (c) Doubly-dressed FWM signal intensity (normalized by no dressing field case) versus Δ3302030 = 1, Γ1030=0.5, G 330 = G 430 = 50, Δ14=0, Δ230=-30 (black curve), Δ230=-50 (blue curve), Δ2Γ30 = -70 (red curve), Δ230 = -100 (magenta curve)).

Tables (1)

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Table 1. Phase-matching conditions and perturbation chains of EWM, dressed SWM and doubly-dressed FWM in a closed-cycle five-level system.

Equations (7)

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ρ n 0 t = d n ρ n 0 + i G n e i k n r ρ ( n 1 ) 0
ρ ( n 1 ) 0 t = d n 1 ρ ( n 1 ) 0 + i G n 1 e i k n 1 r ρ ( n 2 ) 0 + i G n * e i k n r ρ n 0
ρ ( n 2 ) 0 t = d n 2 ρ ( n 2 ) 0 + i G n 2 e i k n 2 r ρ ( n 3 ) 0 + i G n 1 * e i k n 1 r ρ ( n 1 ) 0
ρ 10 ( 2 n 5 ) = d n 2 ρ 10 ( 2 n 5 ) ( 1 d n 2 G n 1 2 d n 2 2 d n 1 + G n 1 2 G n 2 d n 2 2 d n 1 2 d n )
( i.e. , ρ 10 ( 2 n 5 ) = ρ 10 ( 2 n 5 ) + ρ 10 ( 2 n 3 ) + ρ 10 ( 2 n 1 ) = ρ 10 ( 2 n 5 ) + ρ 10 ( 2 n 1 ) = ρ 10 ( 2 n 5 ) + ρ 10 ( 2 n 3 ) )
ρ n 0 t = d n ρ n 0 + i G n e i k n r ρ ( n 1 ) 0 and ρ ( n 1 ) 0 t = d n 1 ρ ( n 1 ) 0 + i G n 1 e i k n 1 r ρ ( n 2 ) 0 + i G n * e i k n r ρ n 0
ρ 10 ( 3 ) = G a ( d 3 d 4 + G 4 2 ) d 1 2 [ d 2 ( d 3 d 4 + G 4 2 ) + G 3 2 + d 4 ] G a d 1 2 d 2 + G a G 3 3 d 1 2 d 2 2 d 3 + G a G 3 2 G 4 2 d 1 2 d 2 2 d 3 2 d 4 = ρ 10 ( 3 ) + ρ 10 ( 5 ) + ρ 10 ( 7 ) + ρ 10 ( 3 ) + ρ 10 ( 7 ) = ρ 10 ( 3 ) + ρ 10 ( 5 )

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