Abstract

We observe pulse delays of up to twenty times the input pulse duration when 200ps laser pulses pass through a hot Rb 85 vapor cell. The pulse peak travels with a velocity equal to c20, and the energy transmission is 5%. For pulses with a linewidth greater than typical features in the atomic dispersion, pulse delay is predicted and observed for all center frequencies near resonance. Pulse advance is never observed. The measurements are in good agreement with a three-level linear-dispersion calculation. We are able to control the amount of delay by using a steady-state laser beam for optical pumping of the ground states prior to sending in the test pulse.

© 2007 Optical Society of America

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  1. L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960), pp. 1-137.
  2. A. Icsevgi and W. E. J. Lamb, "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
    [CrossRef]
  3. H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
    [CrossRef]
  4. R. Loudon, "The propagation of electromagnetic energy through an absorbing dielectric," J. Phys. A 3, 223-244 (1970).
    [CrossRef]
  5. S. Chu and S. Wong, "Linear pulse propagation in an absorbing medium," Phys. Rev. Lett. 48, 738-741 (1982).
    [CrossRef]
  6. B. Segard and B. Macke, "Observation of negative velocity pulse propagation," Phys. Lett. A 109, 213-216 (1985).
    [CrossRef]
  7. E. E. Mikhailov, A. V. Sautenkov, I. Novikova, and R. G. Welch, "Large negative and positive delay of optical pulses in coherently prepared dense Rb vapor with buffer gas," J. Opt. Soc. Am. B 21, 425-428 (2004).
    [CrossRef]
  8. D. Grischkowsky, "Adiabatic following and slow optical pulse propagation in rubidium vapor," Phys. Rev. A 7, 2096-2102 (1973).
    [CrossRef]
  9. S. Sarkar, Y. Guo and H. Wang, "Tunable optical delay via carrier induced exciton dephasing in semiconductor quantum well," Opt. Express 14, 2845-2850 (2006).
    [CrossRef] [PubMed]
  10. L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 46, 277-279 (2000).
    [CrossRef]
  11. L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987) Sec. 4-5, pp. 78-129.
  12. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, "Light speed reduction to 17 meters per second in an ultracold atomic gas," Nature 397, 594-598 (1999).
    [CrossRef]
  13. M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, "Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms," Phys. Rev. Lett. 74, 666-669 (1995).
    [CrossRef] [PubMed]
  14. D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation," Phys. Rev. Lett. 83, 1767-1770 (1999).
    [CrossRef]
  15. N. P. Butcher and D. Cotter, The Elements of Nonlinear Optics, (Cambridge U. Press, 1990), p. 71.
  16. G. P. Barwood, P. Gill, and W. R. C. Rowley, "Frequency measurements on optically narrowed Rb-stabilized laser diodes at 780 nm and 795 nm," Appl. Phys. B 53, 142-147 (1991).
    [CrossRef]
  17. D. Steck, "Rb 87 D Line Data," available online at: http://george.ph.utexas.edu/~dsteck/alkalidata/rubidium87numbers.pdf (accessed 5 Jul. 2006).
  18. J. R. Gardner, "Collisions of doubly spin-polarized ultracold Rb85 atoms," Phys. Rev. Lett. 74, 3764-3767 (1995).
    [CrossRef] [PubMed]
  19. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovstev, E. S. Fry, and M. O. Scully, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atoms," Phys. Rev. Lett. 82, 5229-5232 (1999).
    [CrossRef]
  20. O. M. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997), p. 228.
  21. B. E. A. Saleh and C. M. Teich, Fundamentals of Photonics (Wiley-Intersicence, 1991) Chap. 5.5-5.6, pp. 174-191.
  22. W. R. Boyd, J. D. Gauthier, L. A. Gaeta, and E. A. Willner, "Maximum time delay achievable on propagation through a slow-light medium," Phys. Rev. A 71, 23801 (2005).
    [CrossRef]
  23. P. W. Milonni, "Controlling the speed of light pulses," 2002, J. Phys. B 35, R31-R56.
    [CrossRef]
  24. C. G. B. Garrett and D. E. McCumber, "Propagation of a Gaussian light pulse through an anomalous dispersion medium," Phys. Rev. A 1, 305-313 (1970).
    [CrossRef]
  25. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
    [CrossRef] [PubMed]
  26. W. R. Boyd and J. D. Gauthier, "'Slow' and 'fast' light," Prog. Opt. 43, 497-530 (2002).
    [CrossRef]

2006

2005

W. R. Boyd, J. D. Gauthier, L. A. Gaeta, and E. A. Willner, "Maximum time delay achievable on propagation through a slow-light medium," Phys. Rev. A 71, 23801 (2005).
[CrossRef]

2004

2003

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

2002

P. W. Milonni, "Controlling the speed of light pulses," 2002, J. Phys. B 35, R31-R56.
[CrossRef]

W. R. Boyd and J. D. Gauthier, "'Slow' and 'fast' light," Prog. Opt. 43, 497-530 (2002).
[CrossRef]

2000

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 46, 277-279 (2000).
[CrossRef]

1999

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

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation," Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

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

1995

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

J. R. Gardner, "Collisions of doubly spin-polarized ultracold Rb85 atoms," Phys. Rev. Lett. 74, 3764-3767 (1995).
[CrossRef] [PubMed]

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, "Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms," Phys. Rev. Lett. 74, 666-669 (1995).
[CrossRef] [PubMed]

1991

G. P. Barwood, P. Gill, and W. R. C. Rowley, "Frequency measurements on optically narrowed Rb-stabilized laser diodes at 780 nm and 795 nm," Appl. Phys. B 53, 142-147 (1991).
[CrossRef]

1985

B. Segard and B. Macke, "Observation of negative velocity pulse propagation," Phys. Lett. A 109, 213-216 (1985).
[CrossRef]

1982

S. Chu and S. Wong, "Linear pulse propagation in an absorbing medium," Phys. Rev. Lett. 48, 738-741 (1982).
[CrossRef]

1973

D. Grischkowsky, "Adiabatic following and slow optical pulse propagation in rubidium vapor," Phys. Rev. A 7, 2096-2102 (1973).
[CrossRef]

1970

C. G. B. Garrett and D. E. McCumber, "Propagation of a Gaussian light pulse through an anomalous dispersion medium," Phys. Rev. A 1, 305-313 (1970).
[CrossRef]

R. Loudon, "The propagation of electromagnetic energy through an absorbing dielectric," J. Phys. A 3, 223-244 (1970).
[CrossRef]

1969

A. Icsevgi and W. E. J. Lamb, "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
[CrossRef]

Allen, L.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987) Sec. 4-5, pp. 78-129.

Barwood, G. P.

G. P. Barwood, P. Gill, and W. R. C. Rowley, "Frequency measurements on optically narrowed Rb-stabilized laser diodes at 780 nm and 795 nm," Appl. Phys. B 53, 142-147 (1991).
[CrossRef]

Behroozi, C. H.

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

Boyd, W. R.

W. R. Boyd, J. D. Gauthier, L. A. Gaeta, and E. A. Willner, "Maximum time delay achievable on propagation through a slow-light medium," Phys. Rev. A 71, 23801 (2005).
[CrossRef]

W. R. Boyd and J. D. Gauthier, "'Slow' and 'fast' light," Prog. Opt. 43, 497-530 (2002).
[CrossRef]

Brillouin, L.

L. Brillouin, Wave Propagation and Group Velocity (Academic, 1960), pp. 1-137.

Budker, D.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation," Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

Butcher, N. P.

N. P. Butcher and D. Cotter, The Elements of Nonlinear Optics, (Cambridge U. Press, 1990), p. 71.

Chu, S.

S. Chu and S. Wong, "Linear pulse propagation in an absorbing medium," Phys. Rev. Lett. 48, 738-741 (1982).
[CrossRef]

Cotter, D.

N. P. Butcher and D. Cotter, The Elements of Nonlinear Optics, (Cambridge U. Press, 1990), p. 71.

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 46, 277-279 (2000).
[CrossRef]

Dutton, Z.

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

Eberly, J. H.

L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, 1987) Sec. 4-5, pp. 78-129.

Fry, E. S.

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

Fukuda, Y.

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

Furue, S.

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

Gaeta, L. A.

W. R. Boyd, J. D. Gauthier, L. A. Gaeta, and E. A. Willner, "Maximum time delay achievable on propagation through a slow-light medium," Phys. Rev. A 71, 23801 (2005).
[CrossRef]

Gardner, J. R.

J. R. Gardner, "Collisions of doubly spin-polarized ultracold Rb85 atoms," Phys. Rev. Lett. 74, 3764-3767 (1995).
[CrossRef] [PubMed]

Garrett, C. G. B.

C. G. B. Garrett and D. E. McCumber, "Propagation of a Gaussian light pulse through an anomalous dispersion medium," Phys. Rev. A 1, 305-313 (1970).
[CrossRef]

Gauthier, J. D.

W. R. Boyd, J. D. Gauthier, L. A. Gaeta, and E. A. Willner, "Maximum time delay achievable on propagation through a slow-light medium," Phys. Rev. A 71, 23801 (2005).
[CrossRef]

W. R. Boyd and J. D. Gauthier, "'Slow' and 'fast' light," Prog. Opt. 43, 497-530 (2002).
[CrossRef]

Gea-Banacloche, J.

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, "Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms," Phys. Rev. Lett. 74, 666-669 (1995).
[CrossRef] [PubMed]

Gill, P.

G. P. Barwood, P. Gill, and W. R. C. Rowley, "Frequency measurements on optically narrowed Rb-stabilized laser diodes at 780 nm and 795 nm," Appl. Phys. B 53, 142-147 (1991).
[CrossRef]

Grischkowsky, D.

D. Grischkowsky, "Adiabatic following and slow optical pulse propagation in rubidium vapor," Phys. Rev. A 7, 2096-2102 (1973).
[CrossRef]

Guo, Y.

Harris, S. E.

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

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Hau, L. V.

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

Hayami, K.

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

Hollberg, L.

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

Icsevgi, A.

A. Icsevgi and W. E. J. Lamb, "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
[CrossRef]

Jain, M.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Jin, S. Z.

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, "Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms," Phys. Rev. Lett. 74, 666-669 (1995).
[CrossRef] [PubMed]

Kasapi, A.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Kash, M. M.

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

Kimball, D. F.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation," Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

Kohmoto, T.

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

Kunitomo, M.

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 46, 277-279 (2000).
[CrossRef]

Lamb, W. E. J.

A. Icsevgi and W. E. J. Lamb, "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
[CrossRef]

Li, Y. Q.

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, "Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms," Phys. Rev. Lett. 74, 666-669 (1995).
[CrossRef] [PubMed]

Loudon, R.

R. Loudon, "The propagation of electromagnetic energy through an absorbing dielectric," J. Phys. A 3, 223-244 (1970).
[CrossRef]

Lukin, M. D.

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

Macke, B.

B. Segard and B. Macke, "Observation of negative velocity pulse propagation," Phys. Lett. A 109, 213-216 (1985).
[CrossRef]

McCumber, D. E.

C. G. B. Garrett and D. E. McCumber, "Propagation of a Gaussian light pulse through an anomalous dispersion medium," Phys. Rev. A 1, 305-313 (1970).
[CrossRef]

Mikhailov, E. E.

Milonni, P. W.

P. W. Milonni, "Controlling the speed of light pulses," 2002, J. Phys. B 35, R31-R56.
[CrossRef]

Nakayama, K.

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

Niwa, H.

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

Novikova, I.

Rochester, S. M.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation," Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

Rostovstev, Y.

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

Rowley, W. R. C.

G. P. Barwood, P. Gill, and W. R. C. Rowley, "Frequency measurements on optically narrowed Rb-stabilized laser diodes at 780 nm and 795 nm," Appl. Phys. B 53, 142-147 (1991).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and C. M. Teich, Fundamentals of Photonics (Wiley-Intersicence, 1991) Chap. 5.5-5.6, pp. 174-191.

Sarkar, S.

Sautenkov, A. V.

Sautenkov, V. A.

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

Scully, M. O.

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

Scully, O. M.

O. M. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997), p. 228.

Segard, B.

B. Segard and B. Macke, "Observation of negative velocity pulse propagation," Phys. Lett. A 109, 213-216 (1985).
[CrossRef]

Steck, D.

D. Steck, "Rb 87 D Line Data," available online at: http://george.ph.utexas.edu/~dsteck/alkalidata/rubidium87numbers.pdf (accessed 5 Jul. 2006).

Tanaka, H.

H. Tanaka, H. Niwa, K. Hayami, S. Furue, K. Nakayama, T. Kohmoto, M. Kunitomo, and Y. Fukuda, "Propagation of optical pulses in a resonantly absorbing medium: Observation of negative velocity in Rb vapor, " Phys. Rev. A 68, 53801 (2003).
[CrossRef]

Teich, C. M.

B. E. A. Saleh and C. M. Teich, Fundamentals of Photonics (Wiley-Intersicence, 1991) Chap. 5.5-5.6, pp. 174-191.

Wang, H.

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 46, 277-279 (2000).
[CrossRef]

Welch, G. R.

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

Welch, R. G.

Willner, E. A.

W. R. Boyd, J. D. Gauthier, L. A. Gaeta, and E. A. Willner, "Maximum time delay achievable on propagation through a slow-light medium," Phys. Rev. A 71, 23801 (2005).
[CrossRef]

Wong, S.

S. Chu and S. Wong, "Linear pulse propagation in an absorbing medium," Phys. Rev. Lett. 48, 738-741 (1982).
[CrossRef]

Xiao, M.

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, "Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms," Phys. Rev. Lett. 74, 666-669 (1995).
[CrossRef] [PubMed]

Yashchuk, V. V.

D. Budker, D. F. Kimball, S. M. Rochester, and V. V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation," Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

Yin, G. Y.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
[CrossRef] [PubMed]

Zibrov, A. S.

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

Zubairy, M. S.

O. M. Scully and M. S. Zubairy, Quantum Optics (Cambridge U. Press, 1997), p. 228.

Appl. Phys. B

G. P. Barwood, P. Gill, and W. R. C. Rowley, "Frequency measurements on optically narrowed Rb-stabilized laser diodes at 780 nm and 795 nm," Appl. Phys. B 53, 142-147 (1991).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. A

R. Loudon, "The propagation of electromagnetic energy through an absorbing dielectric," J. Phys. A 3, 223-244 (1970).
[CrossRef]

J. Phys. B

P. W. Milonni, "Controlling the speed of light pulses," 2002, J. Phys. B 35, R31-R56.
[CrossRef]

Nature

L. J. Wang, A. Kuzmich, and A. Dogariu, "Gain-assisted superluminal light propagation," Nature 46, 277-279 (2000).
[CrossRef]

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

Opt. Express

Phys. Lett. A

B. Segard and B. Macke, "Observation of negative velocity pulse propagation," Phys. Lett. A 109, 213-216 (1985).
[CrossRef]

Phys. Rev.

A. Icsevgi and W. E. J. Lamb, "Propagation of light pulses in a laser amplifier," Phys. Rev. 185, 517-545 (1969).
[CrossRef]

Phys. Rev. A

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Figures (8)

Fig. 1
Fig. 1

Experiment setup. Laser pulses from a Tsunami Ti:sapphire laser are sent to the regenerative cavity to be amplified. Their wavelength and pulse mode-locking stability are monitored by a wavemeter and fast photodiode, correspondingly. After the pulses reflect from a grating and pass through an attenuator and polarizer, they propagate through the hot Rb 85 vapor cell and reach the D1 detector.

Fig. 2
Fig. 2

The black curve with square points is the experimental observation of pulse delay versus pulse center frequency. The gray curve is the simulation of delay versus frequency, using no free parameters.

Fig. 3
Fig. 3

Rb 85 D1 line. The hyperfine splitting in 5 s 1 2 , 5 p 1 2 state is 3.04 GHz and 0.36 GHz , respectively. The transition frequency between F = 3 and F = 2 is 37 , 7105.9 GHz

Fig. 4
Fig. 4

Theoretical calculation of (a) real part (dashed curve, scale adjusted) and imaginary part (dash-dotted curve, scale adjusted) of linear susceptibility, group velocity (solid curve) versus laser frequency and (b) figure of merit versus laser frequency for monochromatic light. Here and in following figures, zero in the frequency axis corresponds to the middle frequency between the two resonant peaks 377,106 and 377,109 GHz, which is 377 , 107.5 GHz . Here and in following figures, experiment and simulation conditions are for pulse propagation in a 100°C, 75 mm long Rb 85 vapor cell, unless otherwise specified.

Fig. 5
Fig. 5

Simulation result of both input and output spectrum at (a) 377,106 and (b) 377,107.5 GHz. The imaginary part of χ is also given (black dotted curve, scale adjusted) to indicate the two resonant absorption regions. The dash-dotted curve and the solid curve are the corresponding input and output spectra.

Fig. 6
Fig. 6

Simulated and measured pulse shapes. (a) The wave shapes from simulation. The dashed curve is the 200 ps input pulse, and the dotted curve and the solid curve are output shapes for center frequencies at 377,106 and 377,107.5 GHz, respectively, with the assumption of a noiseless and infinitely fast detector. Their scales are adjusted (dashed/20, dash-dotted x3, and solid x1) to fit in one plot. (b) The wave shape recorded (scale adjusted) with a 1 ns rise-time detector and oscilloscope; the dotted curve and the solid curve are output wave shapes for center frequencies at 377,106 and 377,107.5 GHz, respectively.

Fig. 7
Fig. 7

Optical pumping effect on the delay. The delay is measured when pulse passes through the 75 mm long, 88°C Rb 85 vapor cell. The stars represent the delay versus frequency when there is no pump. The squares, circles, and triangles represent the delays versus frequency when Rb 85 is pumped by cw light with corresponding linewidths of 590 MHz (equal to Doppler linewidth), 1.1 GHz (greater than Doppler linewidth), 200 MHz (sub-Doppler linewidth).

Fig. 8
Fig. 8

Theoretical calculation of (a) the real part (dashed curve, scale adjusted) and the imaginary part (dash-dotted curve, scale adjusted) of linear susceptibility, the group velocity (solid curve) for near-monochromatic pulses, versus laser frequency. The sharp changes in the group velocity versus frequency near resonant regions are not observable in experiments using short pulses. (b) The energy delay/advance, defined in Eq. (5), for a 2.3 GHz linewidth pulse versus frequency, for gain (dashed curve) and absorbing situation (solid curve). The positive/negative signs on the vertical axis indicate pulse energy delay/advance.

Equations (5)

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χ ( ν ) = N ϵ 0 n , m ( ρ ¯ m m ρ ¯ n n ) μ m n μ n m ω n m ν i γ n m .
v g = c n + ν n ν = c n + 1 2 ν Re χ ν .
FoM = 1 v g c α .
H ( ν ) = exp { 1 2 α ( ν ) z i [ k ( ν ) k 0 ] z } = exp { 1 2 k 0 z Im χ ( ν ) i 1 2 k 0 z Re χ ( ν ) } .
τ D = I ( t ) t d t I ( t ) d t .

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