Abstract

We investigate the power control behavior of odd-order multiwave mixing in an electromagnetically induced transparency window. We successfully obtain the evolution from pure enhancement (bright state), half-enhancement, and half-suppression, to pure suppression (dark state) in a four-wave mixing (FWM) channel. The correlations of two bright and two dark states of FWM are studied under four different kinds of power configurations. Moreover, the power-controlled quantum interference among multiple dark states is also studied in FWM and six-wave mixing channels. Such selective switching among multiple frequency channels could have potential applications in optical switching, optical communication, and quantum information processing.

© 2014 Optical Society of America

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  1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [CrossRef]
  2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  3. A. Imamoglu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
    [CrossRef]
  4. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
    [CrossRef]
  5. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [CrossRef]
  6. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
    [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. 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]
  9. Y.-q. 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]
  10. 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]
  11. 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]
  12. H. Kang, G. Hernandez, and Y. Zhu, “Resonant four-wave mixing with slow light,” Phys. Rev. A. 70, 061804(R) (2004).
    [CrossRef]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. B. S. Hamand and P. R. Hemmer, “Coherence switching in a four-level system: quantum switching,” Phys. Rev. Lett. 84, 4080–4083 (2000).
    [CrossRef]
  18. M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003).
    [CrossRef]
  19. J. Zhang, G. Hernandez, and Y. Zhu, “Optical switching mediated by quantum interference of Raman transitions,” Opt. Express 16, 19112–19117 (2008).
    [CrossRef]
  20. A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasi-degenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
    [CrossRef]
  21. C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Electromagnetically induced absorption due to transfer of coherence and to transfer of population,” Phys. Rev. A 67, 033807 (2003).
    [CrossRef]
  22. B. Wang, Y. Han, J. Xiao, X. Yang, C. Xie, H. Wang, and M. Xiao, “Multi-dark-state resonances in cold multi-Zeeman-sublevel atoms,” Opt. Lett. 31, 3647–3649 (2006).
    [CrossRef]
  23. H. Zheng, Y. Zhang, U. Khadka, R. Wang, C. Li, Z. Nie, and M. Xiao, “Modulating the multi-wave mixing processes via the polarizable dark states,” Opt. Express 17, 15468–15480 (2009).
    [CrossRef]
  24. U. Khadka, Y. P. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A 81, 023830 (2010).
    [CrossRef]
  25. A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802(R) (2002).
    [CrossRef]

2010 (1)

U. Khadka, Y. P. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A 81, 023830 (2010).
[CrossRef]

2009 (1)

2008 (1)

2006 (2)

B. Wang, Y. Han, J. Xiao, X. Yang, C. Xie, H. Wang, and M. Xiao, “Multi-dark-state resonances in cold multi-Zeeman-sublevel atoms,” Opt. Lett. 31, 3647–3649 (2006).
[CrossRef]

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]

2005 (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

2004 (2)

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]

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

2003 (2)

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Electromagnetically induced absorption due to transfer of coherence and to transfer of population,” Phys. Rev. A 67, 033807 (2003).
[CrossRef]

M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003).
[CrossRef]

2002 (1)

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802(R) (2002).
[CrossRef]

2001 (2)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef]

2000 (1)

B. S. Hamand and P. R. Hemmer, “Coherence switching in a four-level system: quantum switching,” Phys. Rev. Lett. 84, 4080–4083 (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]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (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]

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]

1998 (2)

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]

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasi-degenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

1996 (1)

1995 (1)

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]

1989 (1)

Akulshin, A. M.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasi-degenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
[CrossRef]

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]

Barreiro, S.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasi-degenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
[CrossRef]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

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]

Cirac, J. I.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef]

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]

Donoghue, J.

Duan, L. M.

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[CrossRef]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[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. 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]

Friedmann, H.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Electromagnetically induced absorption due to transfer of coherence and to transfer of population,” Phys. Rev. A 67, 033807 (2003).
[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]

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]

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]

Goren, C.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Electromagnetically induced absorption due to transfer of coherence and to transfer of population,” Phys. Rev. A 67, 033807 (2003).
[CrossRef]

Hager, J.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802(R) (2002).
[CrossRef]

Hamand, B. S.

B. S. Hamand and P. R. Hemmer, “Coherence switching in a four-level system: quantum switching,” Phys. Rev. Lett. 84, 4080–4083 (2000).
[CrossRef]

Han, Y.

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]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

A. Imamoglu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
[CrossRef]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hemmer, P. R.

Hernandez, G.

J. Zhang, G. Hernandez, and Y. Zhu, “Optical switching mediated by quantum interference of Raman transitions,” Opt. Express 16, 19112–19117 (2008).
[CrossRef]

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

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]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

A. Imamoglu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
[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]

Kang, H.

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

Katz, D. P.

Khadka, U.

U. Khadka, Y. P. Zhang, and M. Xiao, “Control of multitransparency windows via dark-state phase manipulation,” Phys. Rev. A 81, 023830 (2010).
[CrossRef]

H. Zheng, Y. Zhang, U. Khadka, R. Wang, C. Li, Z. Nie, and M. Xiao, “Modulating the multi-wave mixing processes via the polarizable dark states,” Opt. Express 17, 15468–15480 (2009).
[CrossRef]

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.

Lezama, A.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Electromagnetically induced absorption and transparency due to resonant two-field excitation of quasi-degenerate levels in Rb vapor,” Phys. Rev. A 57, 2996–3002 (1998).
[CrossRef]

Li, C.

Li, Y.-q.

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef]

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]

Lukin, M. D.

M. D. Lukin, “Trapping and manipulating photon states in atomic ensembles,” Rev. Mod. Phys. 75, 457–472 (2003).
[CrossRef]

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802(R) (2002).
[CrossRef]

L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature 414, 413–418 (2001).
[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. 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]

Mair, A.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802(R) (2002).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

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]

Nie, Z.

Phillips, D. F.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802(R) (2002).
[CrossRef]

Rosenbluh, M.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Electromagnetically induced absorption due to transfer of coherence and to transfer of population,” Phys. Rev. A 67, 033807 (2003).
[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, 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]

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]

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]

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]

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]

Walsworth, R. L.

A. Mair, J. Hager, D. F. Phillips, R. L. Walsworth, and M. D. Lukin, “Phase coherence and control of stored photonic information,” Phys. Rev. A 65, 031802(R) (2002).
[CrossRef]

Wang, B.

Wang, H.

Wang, R.

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]

Wilson-Gordon, A. D.

C. Goren, A. D. Wilson-Gordon, M. Rosenbluh, and H. Friedmann, “Electromagnetically induced absorption due to transfer of coherence and to transfer of population,” Phys. Rev. A 67, 033807 (2003).
[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]

Xiao, J.

Xiao, M.

Xie, C.

Yang, X.

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.

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Figures (6)

Fig. 1.
Fig. 1.

(a) Spatial beam geometry used in the experiment. Diagrams of (b) a ladder-type three-level, (c) a Y-type four-level, and (d) a K-type five-level atomic system.

Fig. 2.
Fig. 2.

(a) Measured intensities (from left to right) of (a1) the probe transmission, (a2) the FWM and (a3) fluorescence signals versus Δ2 at Δ1=80, 40, 20, 0, 20, 40, and 80 MHz, respectively. The powers of the laser beams are I1=2mW, I2=15mW, and I2=2mW, respectively. (b1)–(b3) Theoretical calculations corresponding to (a1)–(a3). (c) Dressed energy level diagrams of the doubly dressing FWM signal at Δ1=80, 20, 0, 20, and 80 MHz, respectively.

Fig. 3.
Fig. 3.

(a) Measured intensities (from top to bottom) of (a1) the probe transmission, (a2) the FWM signal, and (a3) fluorescence signals versus Δ2 with I2=10mW and I2=2mW at Δ1=22.8MHz for I1=0.5, 1, 2, 3, 4, 5, 6, and 7 mW, respectively. (a4)–(a6) Theoretical calculations corresponding to (a1)–(a3). (b) Figure setup is as (a) but with I1=2mW at Δ1=22.8MHz, for I2+I2=2, 4, 6, 8, 10, 12, 14, and 16 mW, respectively.

Fig. 4.
Fig. 4.

(a) Intensity of the suppression and enhancement of the FWM signal EF versus Δ4 at different Δ1 when (a1) I1=3mW and I4=4mW, (a2) I1=8mW and I4=4mW, (a3) I1=3mW and I4=40mW, and (a4) I1=8mW and I4=40mW with I2+I2=8mW. (b) Theoretical calculations corresponding to (a). (c) Dressed energy level diagrams of the triply dressing FWM signal at Δ1=80, 20, 0, 20, and 80 MHz, respectively.

Fig. 5.
Fig. 5.

(a) Measured intensity of the FWM signal versus Δ4 at Δ1=30MHz when (a1) I1=3mW and (a3) I1=8mW for I4=4, 10, 15, 20, 25, 30, 35, and 40 mW. (a2) and (a4) Theoretical calculations corresponding to (a1) and (a3). (b) Figure setup is as (a) but at Δ1=30MHz when (b1) I2=4mW and (b3) I2=40mW, for I1=0.5, 1, 2, 3, 4, 5, 6, and 7 mW. (c) Figure setup is as (a) but at (c1) Δ1=60MHz and (c3) Δ1=120MHz when I1=3mW, for I4=4, 10, 15, 20, 25, 30, 35, and 40 mW. The other parameters are I2+I2=11.3mW.

Fig. 6.
Fig. 6.

(a) Intensity of (a1) experimental results and (a2) theoretical calculations of the quantum interference effect in the FWM signal EF versus Δ4 for I4=4, 8, 15, 25, 35, 45, and 55 mW. Powers of other all laser beams are I1=1mW and I2+I2=20mW. (b) The FWM signal taken at I4=55mW in (a) versus Δ4. (c) Measured SWM signals versus Δ4 for I4=5, 10, 30, 50, 55, 60, and 70 mW. (c1) Signal obtained with all laser beams on. (c2) Signal obtained with the laser beams E2 blocked. (c3) Sum of the pure dressing effect. (c4) Theoretical calculations corresponding to (c3). Powers of other laser beams are I1=3.6mW, I2=1mW, and I3+I3=51mW. (d) The FWM signal taken at I4=70mW in (c) versus Δ4.

Equations (42)

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H=Δ1|11|+(Δ1+Δ2)|22|+(Δ1Δ3)|33|+(Δ1+Δ4)|44|[G1|10|+(G2+G2)|21|+(G3+G3)|31|+G4|41|+H.c.].
ρ/t=i/[H,ρ]+(ρ/t)inc,
ρ00(0)ω1ρ10(1),(probe transmission),ρ00(0)ω1ρ10(1)ω2ρ20(2)ω2ρ10(3),(FWM),ρ00(0)ω1ρ10(1)ω3ρ30(2)ω3ρ10(3)ω2ρ20(4)ω2ρ10S2(5),(SWM2),ρ00(0)ω1ρ10(1)ω3ρ30(2)ω3ρ10(3)ω4ρ40(4)ω4ρ10S4(5),(SWM4),ρ00(0)ω1ρ10(1)ω1ρ11(2),(R0fluorescence),ρ00(0)ω1ρ10(1)ω1ρ11(2)ω4ρ21(3)ω4ρ22(4),(R1fluorescence),
ρ10(1)=iG1/d1,(probe transmission signal),
ρ10(3)=GF/(d12d2),(FWMsignal),
ρ10(S2)(5)=GS2/(d13d2d3),(SWM2signal),
ρ10(S4)(5)=GS4/(d13d4d3),(SWM4signal),
ρ11(2)=|G1|2/(d1Γ11),(R0fluorescence signal),
ρ22(4)=|G1|2|G2|2/(Γ22d1d2d21),(R1fluorescence signal),
ρ10(1)=iG1/(d1+|G1|2/d5+|G2|2/d2),
ρ10(3)=GF/[d2(d1+|G1|2/d5+|G2|2/d2)2],
ρ11(2)=|G1|2/[Γ11(d1+|G1|2/d5+|G2|2/d2)],
ρ22(4)=|G1|2|G2|2/[Γ22d1(d2+|G2|2/d1)d21],
ρ10(3)=GF/[d2(d1+|G1|2/d6+|G2|2/d2+|G4|2/d4)2],
H=Δ1|11|+(Δ1+Δ2)|22|+(Δ1+Δ4)|44|[G1|10|+(G2+G2)|21|+G4|41|+H.c.].
|D1=G2|0G1|2|G1|2+|G2|2|0G1G2|2,
|D2=G4|0G1|4|G4|2+|G1|2|0G1G4|4,
|D4=G4|2G2|4|G2|2+|G4|2=cosθ|2sinθ|4,
|D=|D1+|D2+|D4=2|0+(cosθG1/G2)|2(G1/G4+sinθ)|4.
|ψ=c0|0+c1|1+c2|2+c3|4
|D|ψ|2=4ρ00+(cosθG1G2)2ρ22+(G1G4+sinθ)2ρ44+4Re{(cosθG1G2)ρ20(G1G4+sinθ)ρ40(G1G4+sinθ)(cosθG1G2)*ρ42},
ρ20=iG2d2iG1d1+|G2|2/d2+|G4|2/d4ρ00,
ρ40=iG4d4iG1d1+|G2|2/d2+|G4|2/d4ρ00,
ρ21=iG1*d21+|G4|2/d7*ρ20,
ρ41=iG1*d41+|G2|2/d7ρ40,
ρ42=(iG2*ρ41+iG4ρ12)/d7,
|D1=G2|0G1|2|G1|2+|G2|2|0G1G2|2,
|D2=G3|0G1|3|G3|2+|G1|2|0G1G3|3,
|D3=G4|0G1|4|G4|2+|G1|2|0G1G4|4,
|D4=G3|4G4|3|G3|2+|G4|2=cosθ|4sinθ|3,
|D=|D1+|D2+|D3+|D4=3|0G1G2|2(G1G4cosθ)|4(G1G3+sinθ)|3.
|ψ=c0|0+c1|1+c2|2+c3|3+c4|4.
|D|ψ|2=9ρ00+(G1G2)2ρ22+(G1G3+sinθ)2ρ33+(G1G4cosθ)2ρ44+2Re{3G1G2ρ203(G1G3+sinθ)ρ303(G1G4cosθ)ρ40+G1G2(G1G3+sinθ)ρ32+G1G2(G1G4cosθ)ρ42+(G1G3+sinθ)(G1G4cosθ)ρ43},
ρ20=iG2d2iG1d1+|G2|2/d2+|G3|2/d3+|G4|2/d4ρ00,
ρ30=iG3*d3iG1d1+|G2|2/d2+|G3|2/d3+|G4|2/d4ρ00,
ρ40=iG4d4iG1d1+|G2|2/d2+|G3|2/d3+|G4|2/d4ρ00,
ρ21=iG1*d21+|G3|2/d8+|G4|2/d7ρ20,
ρ31=iG1*d31+|G2|2/d8+|G4|2/d9ρ30,
ρ41=iG1*d41+|G2|2/d7+|G3|2/d9ρ40,
ρ32=(iG2*ρ31+iG3*ρ12)/d8,
ρ42=(iG2*ρ41+iG4ρ12)/d7,
ρ43=(iG3ρ41+iG4ρ13)/d9,

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