Abstract

The group index and its lineshape parameters of a relatively weak double-resonance probe pulse (signal) propagating through an open doubly driven M-type five-level atomic system are analytically formulated. It is shown for the first time, to our knowledge, that the group velocity status of the signal can be altered (between superluminal and subluminal propagation) by the combined effect of atomic coherence and linear AC Stark shift through coherent coupling. The distinct feature in this scheme is that, although it does not rely on electromagnetically induced transparency, a double-switching effect (i.e., from superluminal to subluminal and vice versa) is observed with negligible absorption/gain at two different frequency regimes.

© 2013 Optical Society of America

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  1. S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
    [CrossRef]
  2. 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]
  3. M. D. Lukin and A. Imamoglu, “Controlling photons with electromagnetically induced transparency,” Nature 413, 273–276 (2001).
    [CrossRef]
  4. X. Yang and Y. Wu, “Achieving an ultra-slowly propagating maximally entangled state of two light beams via four-wave mixing in a double-λ system,” J. Opt. B 7, 54–56 (2005).
    [CrossRef]
  5. Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
    [CrossRef]
  6. D. F. Philips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
    [CrossRef]
  7. M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
    [CrossRef]
  8. O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
    [CrossRef]
  9. D. Hughes and N. Hansen, “Graded nanostructures produced by sliding and exhibiting universal behavior,” Phys. Rev. Lett. 87, 135503 (2001).
    [CrossRef]
  10. A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).
    [CrossRef]
  11. L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
    [CrossRef]
  12. D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
    [CrossRef]
  13. D. Han, Y. Zeng, Y. Bai, W. Chen, and H. Lu, “Phase effects on group velocity propagation in a V-type system with spontaneously generated coherence,” J. Mod. Opt. 54, 493–500 (2007).
    [CrossRef]
  14. M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Tunable phase control for subluminal to superluminal light propagation,” Phys. Rev. A 70, 023813 (2004).
    [CrossRef]
  15. H. Tajalli and M. Sahrai, “Switching from normal to anomalous dispersion via coherent field,” J. Opt. B 7, 168–173 (2005).
    [CrossRef]
  16. G. S. Agarwal and T. N. Dey, “Knob for changing light propagation from subluminal to superluminal,” Phys. Rev. A 64, 053809 (2001).
    [CrossRef]
  17. A. D. Wilson-Gordon and H. Friedmann, “Positive and negative dispersion in a three-level Λ system driven by a single pump,” J. Mod. Opt. 49, 125–139 (2002).
    [CrossRef]
  18. K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transit line,” Phys. Rev. A 68, 013810 (2003).
    [CrossRef]
  19. H. Kang, L. Wen, and Y. Zhu, “Normal or anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
    [CrossRef]
  20. G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A 70, 023802 (2004).
    [CrossRef]
  21. L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, “Optical-wave group-velocity reduction without electromagnetically induced transparency,” Phys. Rev. A 65, 051805(R) (2002).
    [CrossRef]
  22. S. Stenholm, Foundations of Laser Spectroscopy (Wiley, 1983).
  23. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).
  24. J. Miynek and W. Lange, “A simple method of observing coherent ground state transients,” Opt. Commun. 30, 337–340 (1979).
    [CrossRef]
  25. S. Ghosh and S. Mandal, “Analytical studies on pump-induced optical resonances in an M-type six-level system,” J. Phys. B 43, 245505 (2010).
    [CrossRef]
  26. S. Ghosh and S. Mandal, “Double-control coherent absorption and transparency in a six-level optical gain medium,” Phys. Scr. 84, 045405 (2011).
    [CrossRef]

2011 (1)

S. Ghosh and S. Mandal, “Double-control coherent absorption and transparency in a six-level optical gain medium,” Phys. Scr. 84, 045405 (2011).
[CrossRef]

2010 (1)

S. Ghosh and S. Mandal, “Analytical studies on pump-induced optical resonances in an M-type six-level system,” J. Phys. B 43, 245505 (2010).
[CrossRef]

2007 (1)

D. Han, Y. Zeng, Y. Bai, W. Chen, and H. Lu, “Phase effects on group velocity propagation in a V-type system with spontaneously generated coherence,” J. Mod. Opt. 54, 493–500 (2007).
[CrossRef]

2005 (2)

H. Tajalli and M. Sahrai, “Switching from normal to anomalous dispersion via coherent field,” J. Opt. B 7, 168–173 (2005).
[CrossRef]

X. Yang and Y. Wu, “Achieving an ultra-slowly propagating maximally entangled state of two light beams via four-wave mixing in a double-λ system,” J. Opt. B 7, 54–56 (2005).
[CrossRef]

2004 (3)

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
[CrossRef]

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Tunable phase control for subluminal to superluminal light propagation,” Phys. Rev. A 70, 023813 (2004).
[CrossRef]

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A 70, 023802 (2004).
[CrossRef]

2003 (2)

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transit line,” Phys. Rev. A 68, 013810 (2003).
[CrossRef]

H. Kang, L. Wen, and Y. Zhu, “Normal or anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

2002 (2)

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, “Optical-wave group-velocity reduction without electromagnetically induced transparency,” Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

A. D. Wilson-Gordon and H. Friedmann, “Positive and negative dispersion in a three-level Λ system driven by a single pump,” J. Mod. Opt. 49, 125–139 (2002).
[CrossRef]

2001 (6)

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

G. S. Agarwal and T. N. Dey, “Knob for changing light propagation from subluminal to superluminal,” Phys. Rev. A 64, 053809 (2001).
[CrossRef]

M. D. Lukin and A. Imamoglu, “Controlling photons with electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

D. F. Philips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
[CrossRef]

D. Hughes and N. Hansen, “Graded nanostructures produced by sliding and exhibiting universal behavior,” Phys. Rev. Lett. 87, 135503 (2001).
[CrossRef]

2000 (2)

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[CrossRef]

1999 (1)

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]

1994 (1)

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).
[CrossRef]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

1979 (1)

J. Miynek and W. Lange, “A simple method of observing coherent ground state transients,” Opt. Commun. 30, 337–340 (1979).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A 70, 023802 (2004).
[CrossRef]

G. S. Agarwal and T. N. Dey, “Knob for changing light propagation from subluminal to superluminal,” Phys. Rev. A 64, 053809 (2001).
[CrossRef]

Bai, Y.

D. Han, Y. Zeng, Y. Bai, W. Chen, and H. Lu, “Phase effects on group velocity propagation in a V-type system with spontaneously generated coherence,” J. Mod. Opt. 54, 493–500 (2007).
[CrossRef]

Behroozi, C. H.

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]

Bortman-Arbiv, D.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

Chen, W.

D. Han, Y. Zeng, Y. Bai, W. Chen, and H. Lu, “Phase effects on group velocity propagation in a V-type system with spontaneously generated coherence,” J. Mod. Opt. 54, 493–500 (2007).
[CrossRef]

Chiao, R. Y.

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).
[CrossRef]

Dasgupta, S.

G. S. Agarwal and S. Dasgupta, “Superluminal propagation via coherent manipulation of the Raman gain process,” Phys. Rev. A 70, 023802 (2004).
[CrossRef]

Deng, L.

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
[CrossRef]

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, “Optical-wave group-velocity reduction without electromagnetically induced transparency,” Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

Dey, T. N.

G. S. Agarwal and T. N. Dey, “Knob for changing light propagation from subluminal to superluminal,” Phys. Rev. A 64, 053809 (2001).
[CrossRef]

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[CrossRef]

Dutton, Z.

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]

Field, J. E.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Fleischhauer, A.

D. F. Philips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

Friedmann, H.

A. D. Wilson-Gordon and H. Friedmann, “Positive and negative dispersion in a three-level Λ system driven by a single pump,” J. Mod. Opt. 49, 125–139 (2002).
[CrossRef]

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

Ghosh, S.

S. Ghosh and S. Mandal, “Double-control coherent absorption and transparency in a six-level optical gain medium,” Phys. Scr. 84, 045405 (2011).
[CrossRef]

S. Ghosh and S. Mandal, “Analytical studies on pump-induced optical resonances in an M-type six-level system,” J. Phys. B 43, 245505 (2010).
[CrossRef]

Hagley, E. W.

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, “Optical-wave group-velocity reduction without electromagnetically induced transparency,” Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

Han, D.

D. Han, Y. Zeng, Y. Bai, W. Chen, and H. Lu, “Phase effects on group velocity propagation in a V-type system with spontaneously generated coherence,” J. Mod. Opt. 54, 493–500 (2007).
[CrossRef]

Hansen, N.

D. Hughes and N. Hansen, “Graded nanostructures produced by sliding and exhibiting universal behavior,” Phys. Rev. Lett. 87, 135503 (2001).
[CrossRef]

Harris, S. E.

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, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Hau, L. V.

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]

Hughes, D.

D. Hughes and N. Hansen, “Graded nanostructures produced by sliding and exhibiting universal behavior,” Phys. Rev. Lett. 87, 135503 (2001).
[CrossRef]

Imamoglu, A.

M. D. Lukin and A. Imamoglu, “Controlling photons with electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Kang, H.

H. Kang, L. Wen, and Y. Zhu, “Normal or anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

Kapale, K. T.

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Tunable phase control for subluminal to superluminal light propagation,” Phys. Rev. A 70, 023813 (2004).
[CrossRef]

Kim, J. B.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transit line,” Phys. Rev. A 68, 013810 (2003).
[CrossRef]

Kim, K.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transit line,” Phys. Rev. A 68, 013810 (2003).
[CrossRef]

Kim, S. K.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transit line,” Phys. Rev. A 68, 013810 (2003).
[CrossRef]

Kocharovskaya, O.

O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
[CrossRef]

Kozuma, M.

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, “Optical-wave group-velocity reduction without electromagnetically induced transparency,” Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[CrossRef]

Lange, W.

J. Miynek and W. Lange, “A simple method of observing coherent ground state transients,” Opt. Commun. 30, 337–340 (1979).
[CrossRef]

Lee, C.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transit line,” Phys. Rev. A 68, 013810 (2003).
[CrossRef]

Lu, H.

D. Han, Y. Zeng, Y. Bai, W. Chen, and H. Lu, “Phase effects on group velocity propagation in a V-type system with spontaneously generated coherence,” J. Mod. Opt. 54, 493–500 (2007).
[CrossRef]

Lukin, M. D.

D. F. Philips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

M. D. Lukin and A. Imamoglu, “Controlling photons with electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

M. Fleischhauer and M. D. Lukin, “Dark-state polaritons in electromagnetically induced transparency,” Phys. Rev. Lett. 84, 5094–5097 (2000).
[CrossRef]

Mair, A.

D. F. Philips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Mandal, S.

S. Ghosh and S. Mandal, “Double-control coherent absorption and transparency in a six-level optical gain medium,” Phys. Scr. 84, 045405 (2011).
[CrossRef]

S. Ghosh and S. Mandal, “Analytical studies on pump-induced optical resonances in an M-type six-level system,” J. Phys. B 43, 245505 (2010).
[CrossRef]

Miynek, J.

J. Miynek and W. Lange, “A simple method of observing coherent ground state transients,” Opt. Commun. 30, 337–340 (1979).
[CrossRef]

Moon, H. S.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transit line,” Phys. Rev. A 68, 013810 (2003).
[CrossRef]

Payne, M. G.

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, “Optical-wave group-velocity reduction without electromagnetically induced transparency,” Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

Philips, D. F.

D. F. Philips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Rostovtsev, Y.

O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
[CrossRef]

Sahrai, M.

H. Tajalli and M. Sahrai, “Switching from normal to anomalous dispersion via coherent field,” J. Opt. B 7, 168–173 (2005).
[CrossRef]

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Tunable phase control for subluminal to superluminal light propagation,” Phys. Rev. A 70, 023813 (2004).
[CrossRef]

Scully, M. O.

O. Kocharovskaya, Y. Rostovtsev, and M. O. Scully, “Stopping light via hot atoms,” Phys. Rev. Lett. 86, 628–631 (2001).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Steinberg, A. M.

A. M. Steinberg and R. Y. Chiao, “Dispersionless, highly superluminal propagation in a medium with a gain doublet,” Phys. Rev. A 49, 2071–2075 (1994).
[CrossRef]

Stenholm, S.

S. Stenholm, Foundations of Laser Spectroscopy (Wiley, 1983).

Tajalli, H.

H. Tajalli and M. Sahrai, “Switching from normal to anomalous dispersion via coherent field,” J. Opt. B 7, 168–173 (2005).
[CrossRef]

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Tunable phase control for subluminal to superluminal light propagation,” Phys. Rev. A 70, 023813 (2004).
[CrossRef]

Walsworth, R. L.

D. F. Philips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef]

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[CrossRef]

Wen, L.

H. Kang, L. Wen, and Y. Zhu, “Normal or anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

Wilson-Gordon, A. D.

A. D. Wilson-Gordon and H. Friedmann, “Positive and negative dispersion in a three-level Λ system driven by a single pump,” J. Mod. Opt. 49, 125–139 (2002).
[CrossRef]

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

Wu, Y.

X. Yang and Y. Wu, “Achieving an ultra-slowly propagating maximally entangled state of two light beams via four-wave mixing in a double-λ system,” J. Opt. B 7, 54–56 (2005).
[CrossRef]

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
[CrossRef]

Yang, X.

X. Yang and Y. Wu, “Achieving an ultra-slowly propagating maximally entangled state of two light beams via four-wave mixing in a double-λ system,” J. Opt. B 7, 54–56 (2005).
[CrossRef]

Zeng, Y.

D. Han, Y. Zeng, Y. Bai, W. Chen, and H. Lu, “Phase effects on group velocity propagation in a V-type system with spontaneously generated coherence,” J. Mod. Opt. 54, 493–500 (2007).
[CrossRef]

Zhu, Y.

H. Kang, L. Wen, and Y. Zhu, “Normal or anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

Zubairy, M. S.

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Tunable phase control for subluminal to superluminal light propagation,” Phys. Rev. A 70, 023813 (2004).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

J. Mod. Opt. (2)

D. Han, Y. Zeng, Y. Bai, W. Chen, and H. Lu, “Phase effects on group velocity propagation in a V-type system with spontaneously generated coherence,” J. Mod. Opt. 54, 493–500 (2007).
[CrossRef]

A. D. Wilson-Gordon and H. Friedmann, “Positive and negative dispersion in a three-level Λ system driven by a single pump,” J. Mod. Opt. 49, 125–139 (2002).
[CrossRef]

J. Opt. B (2)

X. Yang and Y. Wu, “Achieving an ultra-slowly propagating maximally entangled state of two light beams via four-wave mixing in a double-λ system,” J. Opt. B 7, 54–56 (2005).
[CrossRef]

H. Tajalli and M. Sahrai, “Switching from normal to anomalous dispersion via coherent field,” J. Opt. B 7, 168–173 (2005).
[CrossRef]

J. Phys. B (1)

S. Ghosh and S. Mandal, “Analytical studies on pump-induced optical resonances in an M-type six-level system,” J. Phys. B 43, 245505 (2010).
[CrossRef]

Nature (3)

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]

M. D. Lukin and A. Imamoglu, “Controlling photons with electromagnetically induced transparency,” Nature 413, 273–276 (2001).
[CrossRef]

L. J. Wang, A. Kuzmich, and A. Dogariu, “Gain-assisted superluminal light propagation,” Nature 406, 277–279 (2000).
[CrossRef]

Opt. Commun. (1)

J. Miynek and W. Lange, “A simple method of observing coherent ground state transients,” Opt. Commun. 30, 337–340 (1979).
[CrossRef]

Phys. Rev. A (8)

G. S. Agarwal and T. N. Dey, “Knob for changing light propagation from subluminal to superluminal,” Phys. Rev. A 64, 053809 (2001).
[CrossRef]

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedmann, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

M. Sahrai, H. Tajalli, K. T. Kapale, and M. S. Zubairy, “Tunable phase control for subluminal to superluminal light propagation,” Phys. Rev. A 70, 023813 (2004).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Energy scheme of the five-level M-type atomic system (Rb87). The coupling field with Rabi frequency Ω1 and driving frequency ω1 couples the lower level |1 to the upper levels |4 while the dipole allowed transition for lower level |3 to the upper level |5 is driven by another coupling field with Rabi frequency Ω2 and driving frequency ω2. The transitions |2|4 and |2|5 are probed by a weak probe field with Rabi frequency Ωp and driving frequency ωp. The detuning and effective linewidth for probe transitions are (δp=ωp(ω24+ω25/2)) and Γi, respectively.

Fig. 2.
Fig. 2.

Diagrammatic representation of linear and nonlinear transitions. The coupling field induced transitions |1|4 and |1|5 depend on Ω12, while the transition |3|5 depends upon Ω22. The probe field induced transitions |2|4 and |2|5 depend on Ωp/2 and Ωp//2, respectively. The paths for forbidden lower levels |1|2, |1|3, and |2|3 depend on Ω12Ωp/Ωp//, Ω12Ω22 and Ω22Ωp//2, respectively.

Fig. 3.
Fig. 3.

Real and imaginary parts of susceptibility are plotted against probe detuning (δp) when both the coupling fields are switched off.

Fig. 4.
Fig. 4.

(a) Group index and (b) corresponding real and imaginary parts of susceptibility are plotted against probe detuning for different values of coupling Rabi frequencies Ωi and atomic coherence ϕij as indicated at the bottom of the curves. Arrows in (b) indicate the ultrahigh refractive index.

Fig. 5.
Fig. 5.

Group index is plotted against probe detuning (δp) for different values of coupling Rabi frequencies Ωi and atomic coherence ϕij as indicated at the bottom of the curves.

Fig. 6.
Fig. 6.

Group index at |2|4 probe transition (i.e., at δp=0.15GHz) is plotted against Rabi frequency of the coupling field Ω1 for different values of atomic coherence ϕ12, while the coupling field with Rabi frequency Ω2 is switched off.

Fig. 7.
Fig. 7.

Group index corresponding to both probe transitions |2|4 (i.e., at δp=0.15GHz) and |2|5 (i.e., at δp=0.15GHz) is plotted against atomic coherence ϕ12(ϕ23), for different values of Rabi frequencies of the coupling fields (as indicated in the graph).

Equations (19)

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H=H02μεpcos(ωpt)2με1cos(ω1t)2με2cos(ω2t),
ρ˙11=γ1ρ112iΩ1cosω1t(ρ41ρ14+ρ51ρ15),ρ˙22=γ2ρ222iΩp/cosωpt(ρ42ρ24)2iΩp//cosωpt(ρ52ρ25),ρ˙33=γ3ρ332iΩ2cosω2t(ρ53ρ35),ρ˙44=γ4ρ44+2iΩ1cosω1t(ρ41ρ14)+2iΩp/cosωpt(ρ42ρ24),ρ˙55=γ5ρ55+2iΩ1cosω1t(ρ51ρ15)+2iΩp//cosωpt(ρ52ρ25)+2iΩ2cosω2t(ρ53ρ35),ρ˙12=ρ˙21*=(γ12+iω12)ρ122iΩ1cosω1tρ422iΩ1cosω1tρ52+2iΩp/cosωptρ14+2iΩp//cosωptρ15,ρ˙13=ρ˙31*=(γ13+iω13)ρ132iΩ1cosω1t(ρ43+ρ53)+2iΩ2cosω2tρ15,ρ˙23=ρ˙32*=(γ23+iω23)ρ23+2iΩ2cosω2tρ252iΩp/cosωptρ43+2iΩp//cosωptρ53,ρ˙45=ρ˙54*=(γ45+iω45)ρ452iΩ1cosω1t(ρ15ρ41)2iΩp/cosωptρ25+2iΩp//cosωptρ42+2iΩ2cosω2tρ43,ρ˙14=ρ˙41*=(γ14+iω14)ρ14+2iΩ1cosω1t(ρ11ρ44)2iΩ1cosω1tρ54+2iΩp/cosωptρ12,ρ˙15=ρ˙51*=(γ15+iω15)ρ15+2iΩ1cosω1t(ρ11ρ55)2iΩ1cosω1tρ45+2iΩp//cosωptρ12+2iΩ2cosω2tρ13,ρ˙24=ρ˙42*=(γ24+iω24)ρ24+2iΩp/cosωpt(ρ22ρ44)2iΩp//cosωptρ54+2iΩ1cosω1tρ21,ρ˙25=ρ˙52*=(γ25+iω25)ρ25+2iΩp//cosωpt(ρ22ρ55)2iΩp/cosωptρ45+2iΩ1cosω1tρ21+2iΩ2cosω2tρ23,ρ˙35=ρ˙53*=(γ35+iω35)ρ35+2iΩ2cosω2t(ρ33ρ55)+2iΩp//cosωptρ32+2iΩ1cosω1tρ31.
ρ35=ρ˜35exp(iω2t)ρ1j=ρ˜1jexp(iω1t)ρ2j=ρ˜2jexp(iωpt)(j=4,5),
2cos(ωkt)exp(iωkt)=exp(2iωkt)+11.
ρ11(t)=ρ11(0)eγ1tiΩ1γ1(ρ˜41ρ˜14+ρ˜51ρ˜15)(1eγ1t),ρ22(t)=ρ22(0)eγ2tiΩpγ2(ρ˜42ρ˜24+ρ˜52ρ˜25)(1eγ2t),ρ33(t)=ρ33(0)eγ3tiΩ2γ3(ρ˜53ρ˜35)(1eγ3t),ρ44(t)=ρ44(0)eγ4t+[iΩ1γ4(ρ˜41ρ˜14)+iΩpγ4(ρ˜42ρ˜24)](1eγ4t),ρ55(t)=ρ55(0)eγ5t+[iΩ2γ5(ρ˜53ρ˜35)+iΩpγ5(ρ˜52ρ˜25)](1eγ5t).
ρ12(t)=ρ12(0)e(γ12+iω12)t+i[Ωp(ρ˜14+ρ˜15)Ω1ρ˜42Ω2ρ˜52][eiΔ1te(γ12+iω12)tγ12+i(ω12Δ1)t],ρ23(t)=ρ23(0)e(γ23+iω23)t+i[Ω2ρ˜25Ωp(ρ˜43+ρ˜53)][eiΔ2te(γ23+iω23)tγ23+i(ω23Δ2)t],ρ13(t)=ρ13(0)e(γ13+iω13)t+i[Ω2ρ˜15Ω1(ρ˜43+ρ˜53)][eiΔte(γ13+iω13)tγ13+i(ω13Δ)t].
ρ45(t)=ρ45(0)e(γ45+iω45)t+iγ45+iω45[Ω1(ρ˜41ρ˜15)+Ωp(ρ˜42ρ˜25)+Ω2ρ˜43][1e(γ45+iω45)t].
ρ˜42=iΩp[ρ22(0)eγ2tρ44(0)eγ4tρ45(0)e(γ45+iω45)t]iΩ1ρ12(0)e[γ12+i(δp+ω452)]tγ24+i(δp+ω452)+Ωp2γ45+iω45+Ω12γ12+i(δp+ω452),
ρ˜52=iΩp[ρ22(0)eγ2tρ55(0)eγ5tρ45(0)e(γ45iω45)t]iΩ1ρ12(0)e[γ12+i(δp+ω452)]tiΩ2ρ32(0)e[γ32i(δpω452)]tγ25+i(δpω452)+Ωp2γ45iω45+Ω12γ12+i(δp+ω452)+Ω22γ23i(δpω452).
χ=rε0εp0T(μ24ρ42(t)+μ25ρ52(t))dt,
ρ12(0)γ12+i(δp+ω452)=|ρ12(0)|γ122+(δp+ω452)2exp(iϕ12).
ρ32(0)γ23i(δpω452)=|ρ32(0)|γ232+(δpω452)2exp(iϕ23).
Re(χ˜)=K[Γ1{(Ω1Ωp)|ρ12(0)|sinϕ12γ122+(δp+ω452)2}+Δω1{ρ22(0)γ2ρ44(0)γ4|ρ45(0)|γ452+ω452+(Ω1Ωp)|ρ12(0)|cosϕ12γ122+(δp+ω452)2}Γ12+Δω12+Γ2{(Ω1Ωp)|ρ12(0)|sinϕ12γ122+(δp+ω452)2+(Ω2Ωp)|ρ32(0)|sinϕ23γ232+(δpω452)2}+Δω2{ρ22(0)γ2ρ55(0)γ5|ρ45(0)|γ452+ω452+(Ω1Ωp)|ρ12(0)|cosϕ12γ122+(δp+ω452)2+(Ω2Ωp)|ρ32(0)|cosϕ23γ232+(δpω452)2}Γ22+Δω22]
Im(χ˜)=K[Γ1{ρ22(0)γ2ρ44(0)γ4|ρ45(0)|γ452+ω452+(Ω1Ωp)|ρ12(0)|cosϕ12γ122+(δp+ω452)2}+Δω1{(Ω1Ωp)|ρ12(0)|sinϕ12γ122+(δp+ω452)2}Γ12+Δω12+Γ2{ρ22(0)γ2ρ55(0)γ5|ρ45(0)|γ452+ω452+(Ω1Ωp)|ρ12(0)|cosϕ12γ122+(δp+ω452)2+(Ω2Ωp)|ρ32(0)|cosϕ23γ232+(δpω452)2}+Δω2{(Ω1Ωp)|ρ12(0)|sinϕ12γ122+(δp+ω452)2(Ω2Ωp)|ρ32(0)|sinϕ23γ232+(δpω452)2}Γ22+Δω22]
vg=c[1+2πRe(χ˜)+2πωpRe((χ˜)ωp)],
Γ1=γ24+Ωp2γ45γ452+ω452+Ω12γ12γ122+(δp+ω452)2,
Γ2=γ25+Ωp2γ45γ452+ω452+Ω12γ12γ122+(δp+ω452)2+Ω22γ23γ232+(δpω452)2,
Δω1=(δp+ω452)Ωp2ω45γ452+ω452Ω12(δp+ω452)γ122+(δp+ω452)2,
Δω2=(δpω452)+Ωp2ω45γ452+ω452Ω12(δp+ω452)γ122+(δp+ω452)2+Ω22(δpω452)γ232+(δpω452)2.

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