Abstract

In order to identify special information from a light pulse sequence, we propose a few viable schemes for marking a desired slow light signal with a fast optical precursor in a Λ-type and N-type atomic system. The fast optical precursor is characterized by transient beating patterns originating from the temporal discontinuity of the marking pulse at the sharp rising or falling edge. Compared with the schemes in the Λ system, the one in the N system has the advantage of flexibility in situations in which we are not the sender of the original probe signals. Besides, there is no disturbance to the probe signals nor an undesired main pulse coming from the marking field.

© 2013 Optical Society of America

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  1. T. Sauter, “Gaussian pulses and superluminality,” J. Phys. A 35, 6743–6754 (2002).
    [CrossRef]
  2. A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 349, 177–202 (1914).
  3. L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 349, 203–240 (1914).
  4. J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353–R5356 (1991).
    [CrossRef]
  5. É. Falcon, C. Laroche, and S. Fauve, “Observation of sommerfeld precursors on a fluid surface,” Phys. Rev. Lett. 91, 064502 (2003).
    [CrossRef]
  6. H. Jeong, A. M. C. Dawes, and D. J. Gauthier, “Direct observation of optical precursors in a region of anomalous dispersion,” Phys. Rev. Lett. 96, 143901 (2006).
    [CrossRef]
  7. F. J. Lynch, R. E. Holland, and M. Hamermesh, “Time dependence of resonantly filtered gamma rays from Fe57,” Phys. Rev. 120, 513 (1960).
    [CrossRef]
  8. P. Pleshko and I. Palocz, “Experimental observation of Sommerfeld and Brillouin precursors in the microwave domain,” Phys. Rev. Lett. 22, 1201–1204 (1969).
    [CrossRef]
  9. E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: application to sound waves in superfluid B3,” Phys. Rev. B 34, 7617–7640 (1986).
  10. S.-H. Choi and U. L. Österberg, “Observation of optical precursors in water,” Phys. Rev. Lett. 92, 193903 (2004).
    [CrossRef]
  11. D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursors with electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 103, 093602 (2009).
    [CrossRef]
  12. J. F. Chen, H. Jeong, L. Feng, M. M. T. Loy, G. K. L. Wong, and S. Du, “Stacked optical precursors from amplitude and phase modulations,” Phys. Rev. Lett. 104, 223602 (2010).
    [CrossRef]
  13. P. Kolchin, C. Belthangady, S. Du, G. Y. Yin, and S. E. Harris, “Electro-optic modulation of single photons,” Phys. Rev. Lett. 101, 103601 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  17. H. Jeong and S. Du, “Two-way transparency in the light-matter interaction: optical precursors with electromagnetically induced transparency,” Phys. Rev. A 79, 011802 (2009).
    [CrossRef]
  18. J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: From free-induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010).
    [CrossRef]
  19. B. Macke and B. Segard, “Optical precursors in transparent media,” Phys. Rev. A 80, 011803 (2009).
    [CrossRef]
  20. S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
    [CrossRef]
  21. S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149 (2008).
    [CrossRef]
  22. S. C. Zhang, J. F. Chen, C. Liu, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursor of a single photon,” Phys. Rev. Lett. 106, 243602 (2011).
    [CrossRef]
  23. B. Macke and B. Ségard, “Optical precursors with self-induced transparency,” Phys. Rev. A 81, 015803 (2010).
    [CrossRef]
  24. Y. D. Peng, Y. P. Niu, Y. H. Qi, H. F. Yao, and S. Q. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
    [CrossRef]
  25. H. Jeong and S. Du, “Slow-light-induced interference with stacked optical precursors for square input pulses,” Opt. Lett. 35, 124–126 (2010).
    [CrossRef]
  26. Y. D. Peng, Y. P. Niu, L. D. Zhang, A. H. Yang, L. Jiang, and S. Q. Gong, “Enhanced optical precursors by Doppler effect via active Raman gain process,” Opt. Lett. 37, 3333–3335 (2012).
    [CrossRef]

2012

2011

S. C. Zhang, J. F. Chen, C. Liu, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursor of a single photon,” Phys. Rev. Lett. 106, 243602 (2011).
[CrossRef]

Y. D. Peng, Y. P. Niu, Y. H. Qi, H. F. Yao, and S. Q. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
[CrossRef]

2010

B. Macke and B. Ségard, “Optical precursors with self-induced transparency,” Phys. Rev. A 81, 015803 (2010).
[CrossRef]

H. Jeong and S. Du, “Slow-light-induced interference with stacked optical precursors for square input pulses,” Opt. Lett. 35, 124–126 (2010).
[CrossRef]

J. F. Chen, H. Jeong, L. Feng, M. M. T. Loy, G. K. L. Wong, and S. Du, “Stacked optical precursors from amplitude and phase modulations,” Phys. Rev. Lett. 104, 223602 (2010).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: From free-induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010).
[CrossRef]

2009

B. Macke and B. Segard, “Optical precursors in transparent media,” Phys. Rev. A 80, 011803 (2009).
[CrossRef]

H. Jeong and S. Du, “Two-way transparency in the light-matter interaction: optical precursors with electromagnetically induced transparency,” Phys. Rev. A 79, 011802 (2009).
[CrossRef]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursors with electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

2008

P. Kolchin, C. Belthangady, S. Du, G. Y. Yin, and S. E. Harris, “Electro-optic modulation of single photons,” Phys. Rev. Lett. 101, 103601 (2008).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149 (2008).
[CrossRef]

2006

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, “Direct observation of optical precursors in a region of anomalous dispersion,” Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

2005

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

2004

S.-H. Choi and U. L. Österberg, “Observation of optical precursors in water,” Phys. Rev. Lett. 92, 193903 (2004).
[CrossRef]

2003

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

É. Falcon, C. Laroche, and S. Fauve, “Observation of sommerfeld precursors on a fluid surface,” Phys. Rev. Lett. 91, 064502 (2003).
[CrossRef]

2002

T. Sauter, “Gaussian pulses and superluminality,” J. Phys. A 35, 6743–6754 (2002).
[CrossRef]

1991

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353–R5356 (1991).
[CrossRef]

1989

1986

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: application to sound waves in superfluid B3,” Phys. Rev. B 34, 7617–7640 (1986).

1969

P. Pleshko and I. Palocz, “Experimental observation of Sommerfeld and Brillouin precursors in the microwave domain,” Phys. Rev. Lett. 22, 1201–1204 (1969).
[CrossRef]

1960

F. J. Lynch, R. E. Holland, and M. Hamermesh, “Time dependence of resonantly filtered gamma rays from Fe57,” Phys. Rev. 120, 513 (1960).
[CrossRef]

1914

A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 349, 177–202 (1914).

L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 349, 203–240 (1914).

Aaviksoo, J.

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353–R5356 (1991).
[CrossRef]

Albanese, R.

Avenel, O.

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: application to sound waves in superfluid B3,” Phys. Rev. B 34, 7617–7640 (1986).

Belthangady, C.

P. Kolchin, C. Belthangady, S. Du, G. Y. Yin, and S. E. Harris, “Electro-optic modulation of single photons,” Phys. Rev. Lett. 101, 103601 (2008).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149 (2008).
[CrossRef]

Brillouin, L.

L. Brillouin, “Über die fortpflanzung des licht in disperdierenden medien,” Ann. Phys. (Leipzig) 349, 203–240 (1914).

Chen, J. F.

S. C. Zhang, J. F. Chen, C. Liu, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursor of a single photon,” Phys. Rev. Lett. 106, 243602 (2011).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: From free-induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010).
[CrossRef]

J. F. Chen, H. Jeong, L. Feng, M. M. T. Loy, G. K. L. Wong, and S. Du, “Stacked optical precursors from amplitude and phase modulations,” Phys. Rev. Lett. 104, 223602 (2010).
[CrossRef]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursors with electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

Choi, S.-H.

S.-H. Choi and U. L. Österberg, “Observation of optical precursors in water,” Phys. Rev. Lett. 92, 193903 (2004).
[CrossRef]

Dawes, A. M. C.

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, “Direct observation of optical precursors in a region of anomalous dispersion,” Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

Du, S.

S. C. Zhang, J. F. Chen, C. Liu, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursor of a single photon,” Phys. Rev. Lett. 106, 243602 (2011).
[CrossRef]

J. F. Chen, H. Jeong, L. Feng, M. M. T. Loy, G. K. L. Wong, and S. Du, “Stacked optical precursors from amplitude and phase modulations,” Phys. Rev. Lett. 104, 223602 (2010).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: From free-induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010).
[CrossRef]

H. Jeong and S. Du, “Slow-light-induced interference with stacked optical precursors for square input pulses,” Opt. Lett. 35, 124–126 (2010).
[CrossRef]

H. Jeong and S. Du, “Two-way transparency in the light-matter interaction: optical precursors with electromagnetically induced transparency,” Phys. Rev. A 79, 011802 (2009).
[CrossRef]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursors with electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

P. Kolchin, C. Belthangady, S. Du, G. Y. Yin, and S. E. Harris, “Electro-optic modulation of single photons,” Phys. Rev. Lett. 101, 103601 (2008).
[CrossRef]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149 (2008).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef]

Falcon, É.

É. Falcon, C. Laroche, and S. Fauve, “Observation of sommerfeld precursors on a fluid surface,” Phys. Rev. Lett. 91, 064502 (2003).
[CrossRef]

Fauve, S.

É. Falcon, C. Laroche, and S. Fauve, “Observation of sommerfeld precursors on a fluid surface,” Phys. Rev. Lett. 91, 064502 (2003).
[CrossRef]

Feng, L.

J. F. Chen, H. Jeong, L. Feng, M. M. T. Loy, G. K. L. Wong, and S. Du, “Stacked optical precursors from amplitude and phase modulations,” Phys. Rev. Lett. 104, 223602 (2010).
[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]

Gauthier, D. J.

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, “Direct observation of optical precursors in a region of anomalous dispersion,” Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

Gong, S. Q.

Y. D. Peng, Y. P. Niu, L. D. Zhang, A. H. Yang, L. Jiang, and S. Q. Gong, “Enhanced optical precursors by Doppler effect via active Raman gain process,” Opt. Lett. 37, 3333–3335 (2012).
[CrossRef]

Y. D. Peng, Y. P. Niu, Y. H. Qi, H. F. Yao, and S. Q. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
[CrossRef]

Hamermesh, M.

F. J. Lynch, R. E. Holland, and M. Hamermesh, “Time dependence of resonantly filtered gamma rays from Fe57,” Phys. Rev. 120, 513 (1960).
[CrossRef]

Harris, S. E.

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149 (2008).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef]

P. Kolchin, C. Belthangady, S. Du, G. Y. Yin, and S. E. Harris, “Electro-optic modulation of single photons,” Phys. Rev. Lett. 101, 103601 (2008).
[CrossRef]

Holland, R. E.

F. J. Lynch, R. E. Holland, and M. Hamermesh, “Time dependence of resonantly filtered gamma rays from Fe57,” Phys. Rev. 120, 513 (1960).
[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]

Jeong, H.

J. F. Chen, H. Jeong, L. Feng, M. M. T. Loy, G. K. L. Wong, and S. Du, “Stacked optical precursors from amplitude and phase modulations,” Phys. Rev. Lett. 104, 223602 (2010).
[CrossRef]

H. Jeong and S. Du, “Slow-light-induced interference with stacked optical precursors for square input pulses,” Opt. Lett. 35, 124–126 (2010).
[CrossRef]

H. Jeong and S. Du, “Two-way transparency in the light-matter interaction: optical precursors with electromagnetically induced transparency,” Phys. Rev. A 79, 011802 (2009).
[CrossRef]

H. Jeong, A. M. C. Dawes, and D. J. Gauthier, “Direct observation of optical precursors in a region of anomalous dispersion,” Phys. Rev. Lett. 96, 143901 (2006).
[CrossRef]

Jiang, L.

Kolchin, P.

P. Kolchin, C. Belthangady, S. Du, G. Y. Yin, and S. E. Harris, “Electro-optic modulation of single photons,” Phys. Rev. Lett. 101, 103601 (2008).
[CrossRef]

S. Du, C. Belthangady, P. Kolchin, G. Y. Yin, and S. E. Harris, “Observation of optical precursors at the biphoton level,” Opt. Lett. 33, 2149 (2008).
[CrossRef]

S. Du, P. Kolchin, C. Belthangady, G. Y. Yin, and S. E. Harris, “Subnatural linewidth biphotons with controllable temporal length,” Phys. Rev. Lett. 100, 183603 (2008).
[CrossRef]

Kuhl, J.

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353–R5356 (1991).
[CrossRef]

Laroche, C.

É. Falcon, C. Laroche, and S. Fauve, “Observation of sommerfeld precursors on a fluid surface,” Phys. Rev. Lett. 91, 064502 (2003).
[CrossRef]

Liu, C.

S. C. Zhang, J. F. Chen, C. Liu, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursor of a single photon,” Phys. Rev. Lett. 106, 243602 (2011).
[CrossRef]

Loy, M. M. T.

S. C. Zhang, J. F. Chen, C. Liu, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursor of a single photon,” Phys. Rev. Lett. 106, 243602 (2011).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: From free-induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010).
[CrossRef]

J. F. Chen, H. Jeong, L. Feng, M. M. T. Loy, G. K. L. Wong, and S. Du, “Stacked optical precursors from amplitude and phase modulations,” Phys. Rev. Lett. 104, 223602 (2010).
[CrossRef]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursors with electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

Lukin, M. D.

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

Lynch, F. J.

F. J. Lynch, R. E. Holland, and M. Hamermesh, “Time dependence of resonantly filtered gamma rays from Fe57,” Phys. Rev. 120, 513 (1960).
[CrossRef]

Macke, B.

B. Macke and B. Ségard, “Optical precursors with self-induced transparency,” Phys. Rev. A 81, 015803 (2010).
[CrossRef]

B. Macke and B. Segard, “Optical precursors in transparent media,” Phys. Rev. A 80, 011803 (2009).
[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]

Medina, R.

Niu, Y. P.

Y. D. Peng, Y. P. Niu, L. D. Zhang, A. H. Yang, L. Jiang, and S. Q. Gong, “Enhanced optical precursors by Doppler effect via active Raman gain process,” Opt. Lett. 37, 3333–3335 (2012).
[CrossRef]

Y. D. Peng, Y. P. Niu, Y. H. Qi, H. F. Yao, and S. Q. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
[CrossRef]

Österberg, U. L.

S.-H. Choi and U. L. Österberg, “Observation of optical precursors in water,” Phys. Rev. Lett. 92, 193903 (2004).
[CrossRef]

Palocz, I.

P. Pleshko and I. Palocz, “Experimental observation of Sommerfeld and Brillouin precursors in the microwave domain,” Phys. Rev. Lett. 22, 1201–1204 (1969).
[CrossRef]

Peng, Y. D.

Y. D. Peng, Y. P. Niu, L. D. Zhang, A. H. Yang, L. Jiang, and S. Q. Gong, “Enhanced optical precursors by Doppler effect via active Raman gain process,” Opt. Lett. 37, 3333–3335 (2012).
[CrossRef]

Y. D. Peng, Y. P. Niu, Y. H. Qi, H. F. Yao, and S. Q. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
[CrossRef]

Penn, J.

Pleshko, P.

P. Pleshko and I. Palocz, “Experimental observation of Sommerfeld and Brillouin precursors in the microwave domain,” Phys. Rev. Lett. 22, 1201–1204 (1969).
[CrossRef]

Ploog, K.

J. Aaviksoo, J. Kuhl, and K. Ploog, “Observation of optical precursors at pulse propagation in GaAs,” Phys. Rev. A 44, R5353–R5356 (1991).
[CrossRef]

Qi, Y. H.

Y. D. Peng, Y. P. Niu, Y. H. Qi, H. F. Yao, and S. Q. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
[CrossRef]

Sauter, T.

T. Sauter, “Gaussian pulses and superluminality,” J. Phys. A 35, 6743–6754 (2002).
[CrossRef]

Segard, B.

B. Macke and B. Segard, “Optical precursors in transparent media,” Phys. Rev. A 80, 011803 (2009).
[CrossRef]

Ségard, B.

B. Macke and B. Ségard, “Optical precursors with self-induced transparency,” Phys. Rev. A 81, 015803 (2010).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, “Über die fortpflanzung des lichtes in disperdierenden medien,” Ann. Phys. (Leipzig) 349, 177–202 (1914).

Varoquaux, E.

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: application to sound waves in superfluid B3,” Phys. Rev. B 34, 7617–7640 (1986).

Wang, S.

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: From free-induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010).
[CrossRef]

Wei, D.

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: From free-induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010).
[CrossRef]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursors with electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

Williams, G. A.

E. Varoquaux, G. A. Williams, and O. Avenel, “Pulse propagation in a resonant medium: application to sound waves in superfluid B3,” Phys. Rev. B 34, 7617–7640 (1986).

Wong, G. K. L.

S. C. Zhang, J. F. Chen, C. Liu, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursor of a single photon,” Phys. Rev. Lett. 106, 243602 (2011).
[CrossRef]

J. F. Chen, S. Wang, D. Wei, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical coherent transients in cold atoms: From free-induction decay to optical precursors,” Phys. Rev. A 81, 033844 (2010).
[CrossRef]

J. F. Chen, H. Jeong, L. Feng, M. M. T. Loy, G. K. L. Wong, and S. Du, “Stacked optical precursors from amplitude and phase modulations,” Phys. Rev. Lett. 104, 223602 (2010).
[CrossRef]

D. Wei, J. F. Chen, M. M. T. Loy, G. K. L. Wong, and S. Du, “Optical precursors with electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 103, 093602 (2009).
[CrossRef]

Yang, A. H.

Yao, H. F.

Y. D. Peng, Y. P. Niu, Y. H. Qi, H. F. Yao, and S. Q. Gong, “Optical precursors with tunneling-induced transparency in asymmetric quantum wells,” Phys. Rev. A 83, 013812 (2011).
[CrossRef]

Yin, G. Y.

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Figures (5)

Fig. 1.
Fig. 1.

Energy level of a N -type atomic system driven by a strong coupling field ω c , a weak probe field ω p , and a weak disturbing field ω d . Atomic population is assumed on level | 1 . The four-level N system will turn into a three-level Λ system in the case where the disturbing field ω d is not applied.

Fig. 2.
Fig. 2.

(a) and (b) Red thick lines represent the output probe pulse sequence [ f ( l , τ ) ] 2 at the sample exit as a function of time. Gray thin lines stand for the input probe pulse sequence [ f ( 0 , τ ) ] 2 . (c) Enlarged view of the output marked pulse at the marked period for both situations in (a) and (b). We have set the temporal width of the half-Gaussian marking pulse τ m = 1.2 μs in (a) and τ m = 0.3 μs in (b). Other parameters are Ω c = 3.5 MHz , l = 2.0 mm , Δ p = Δ c = 0 , γ 12 = 2.0 kHz , γ 13 = 6.0 MHz , and OD ( optical depth ) = 98 .

Fig. 3.
Fig. 3.

(a) Red thick lines represent the output probe pulse sequence [ f ( l , τ ) ] 2 at the sample exit as a function of time. Gray thin lines stand for the input probe pulse sequence [ f ( 0 , τ ) ] 2 . (b) Enlarged view of the output marked pulse at the marked period. We have set Ω c = 6.85 MHz and other relevant parameters given at Fig. 2.

Fig. 4.
Fig. 4.

Red thick lines represent the output probe pulse sequence [ f ( l , τ ) ] 2 at the sample exit as a function of time. Gray thin lines stand for the input probe pulse sequence [ f ( 0 , τ ) ] 2 . (a) The third input signal is modulated with a step rising edge at 22.0 μs, Ω c = 2.26 MHz . (b) The third input signal is modulated with a step falling edge at 24.0 μs, Ω c = 2.04 MHz . Other relevant parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

(a) Red thick solid lines represent the intensity composition of the output probe and disturbing field [ f ( l , τ ) ] 2 + [ g ( l , τ ) ] 2 at the sample exit as a function of time. Gray thin solid and blue dashed lines stand for the input probe pulse sequence [ f ( 0 , τ ) ] 2 and the input rectangular disturbing field [ g ( 0 , τ ) ] 2 , respectively. (b) Enlarged view of the intensity composition [ f ( l , τ ) ] 2 + [ g ( l , τ ) ] 2 at the first marked period. (c) Red solid (blue dashed) line represents the output probe (disturbing) field [ f ( l , τ ) ] 2 ( [ g ( l , τ ) ] 2 ) at the sample exit as a function of time. We have set the temporal width of the disturbing field τ d = 10 μs , Ω c = 3.0 MHz , and Δ p = Δ c = Δ d = 0 and other relevant parameters given at Fig. 2.

Equations (9)

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t ρ 12 = [ γ 12 + i ( Δ p Δ c ) ] ρ 12 i Ω c ρ 13 ,
t ρ 13 = ( γ 13 + i Δ p ) ρ 13 i Ω c * ρ 12 i Ω p * ,
t ρ 14 = ( γ 14 + i Δ d ) ρ 14 i Ω d * ,
Ω p ( z , t ) z + 1 c Ω p ( z , t ) t = i α γ 13 ρ 31 ( z , t ) ,
Ω d ( z , t ) z + 1 c Ω d ( z , t ) t = i β γ 14 ρ 41 ( z , t ) ,
f ( ξ , τ ) ξ = i α γ 13 Ω p 0 ρ 31 ( ξ , τ ) ,
g ( ξ , τ ) ξ = i β γ 14 Ω d 0 ρ 41 ( ξ , τ ) ,
υ g = 2 ε 0 c N d 13 2 ω p Ω c 2
T delay = l υ g .

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