Abstract

We analyze the propagation of fast-light pulses through a finite-length resonant gain medium both analytically and numerically. We find that intrinsic instabilities can be avoided in attaining a substantial peak advance with an ultrashort rather than a long or adiabatic probe.

© 2006 Optical Society of America

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  1. S. E. Harris, Phys. Today 50(7), 36 (1997).
    [Crossref]
  2. R. Grobe, F. T. Hioe, and J. H. Eberly, Phys. Rev. Lett. 73, 3183 (1994).
    [Crossref] [PubMed]
  3. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
    [Crossref] [PubMed]
  4. L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
    [Crossref] [PubMed]
  5. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
    [Crossref] [PubMed]
  6. M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
    [Crossref] [PubMed]
  7. P. G. Kryukov and V. S. Letokhov, Sov. Phys. Usp. 12, 641 (1970).
    [Crossref]
  8. P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, 2005).
  9. N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, Sov. Phys. JETP 23, 16 (1966).
  10. A. Icsevgi and W. E. Lamb, Jr., Phys. Rev. 185, 517 (1969).
    [Crossref]
  11. I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, Theor. Math. Phys. 63, 328 (1985).
    [Crossref]
  12. J. C. MacGillivray and M. S. Feld, Phys. Rev. A 14, 1169 (1976).
    [Crossref]
  13. Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1992).
    [Crossref]
  14. A. V. Andreev, Sov. Phys. Usp. 33, 997 (1990).
    [Crossref]
  15. A. Rahman and J. H. Eberly, Phys. Rev. A 58, R805 (1998).
    [Crossref]
  16. P. W. Milonni, J. Phys. B 35, R31 (2002).
    [Crossref]
  17. S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
    [Crossref]
  18. G. L. Lamb, Jr., Phys. Rev. A 12, 2052 (1975).
    [Crossref]
  19. I. R. Gabitov and S. V. Manakov, Phys. Rev. Lett. 50, 495 (1983).
    [Crossref]
  20. D. C. Burnham and R. Y. Chiao, Phys. Rev. 188, 667 (1969).
    [Crossref]

2003 (2)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[Crossref] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[Crossref] [PubMed]

2002 (1)

P. W. Milonni, J. Phys. B 35, R31 (2002).
[Crossref]

2000 (1)

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[Crossref] [PubMed]

1998 (1)

A. Rahman and J. H. Eberly, Phys. Rev. A 58, R805 (1998).
[Crossref]

1997 (1)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[Crossref]

1995 (1)

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

1994 (1)

R. Grobe, F. T. Hioe, and J. H. Eberly, Phys. Rev. Lett. 73, 3183 (1994).
[Crossref] [PubMed]

1992 (1)

Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1992).
[Crossref]

1990 (1)

A. V. Andreev, Sov. Phys. Usp. 33, 997 (1990).
[Crossref]

1985 (1)

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, Theor. Math. Phys. 63, 328 (1985).
[Crossref]

1983 (1)

I. R. Gabitov and S. V. Manakov, Phys. Rev. Lett. 50, 495 (1983).
[Crossref]

1976 (1)

J. C. MacGillivray and M. S. Feld, Phys. Rev. A 14, 1169 (1976).
[Crossref]

1975 (1)

G. L. Lamb, Jr., Phys. Rev. A 12, 2052 (1975).
[Crossref]

1970 (1)

P. G. Kryukov and V. S. Letokhov, Sov. Phys. Usp. 12, 641 (1970).
[Crossref]

1969 (3)

A. Icsevgi and W. E. Lamb, Jr., Phys. Rev. 185, 517 (1969).
[Crossref]

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
[Crossref]

D. C. Burnham and R. Y. Chiao, Phys. Rev. 188, 667 (1969).
[Crossref]

1966 (1)

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, Sov. Phys. JETP 23, 16 (1966).

Ambartsumyan, R. V.

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, Sov. Phys. JETP 23, 16 (1966).

Andreev, A. V.

A. V. Andreev, Sov. Phys. Usp. 33, 997 (1990).
[Crossref]

Basov, N. G.

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, Sov. Phys. JETP 23, 16 (1966).

Bigelow, M. S.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[Crossref] [PubMed]

Boyd, R. W.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[Crossref] [PubMed]

Burnham, D. C.

D. C. Burnham and R. Y. Chiao, Phys. Rev. 188, 667 (1969).
[Crossref]

Chiao, R. Y.

D. C. Burnham and R. Y. Chiao, Phys. Rev. 188, 667 (1969).
[Crossref]

Dogariu, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[Crossref] [PubMed]

Eberly, J. H.

A. Rahman and J. H. Eberly, Phys. Rev. A 58, R805 (1998).
[Crossref]

R. Grobe, F. T. Hioe, and J. H. Eberly, Phys. Rev. Lett. 73, 3183 (1994).
[Crossref] [PubMed]

Feld, M. S.

J. C. MacGillivray and M. S. Feld, Phys. Rev. A 14, 1169 (1976).
[Crossref]

Gabitov, I. R.

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, Theor. Math. Phys. 63, 328 (1985).
[Crossref]

I. R. Gabitov and S. V. Manakov, Phys. Rev. Lett. 50, 495 (1983).
[Crossref]

Gauthier, D. J.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[Crossref] [PubMed]

Grobe, R.

R. Grobe, F. T. Hioe, and J. H. Eberly, Phys. Rev. Lett. 73, 3183 (1994).
[Crossref] [PubMed]

Hahn, E. L.

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
[Crossref]

Harris, S. E.

S. E. Harris, Phys. Today 50(7), 36 (1997).
[Crossref]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

Hioe, F. T.

R. Grobe, F. T. Hioe, and J. H. Eberly, Phys. Rev. Lett. 73, 3183 (1994).
[Crossref] [PubMed]

Icsevgi, A.

A. Icsevgi and W. E. Lamb, Jr., Phys. Rev. 185, 517 (1969).
[Crossref]

Jain, M.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

Kasapi, A.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

Kryukov, P. G.

P. G. Kryukov and V. S. Letokhov, Sov. Phys. Usp. 12, 641 (1970).
[Crossref]

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, Sov. Phys. JETP 23, 16 (1966).

Kuzmich, A.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[Crossref] [PubMed]

Lamb, G. L.

G. L. Lamb, Jr., Phys. Rev. A 12, 2052 (1975).
[Crossref]

Lamb, W. E.

A. Icsevgi and W. E. Lamb, Jr., Phys. Rev. 185, 517 (1969).
[Crossref]

Lepeshkin, N. N.

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[Crossref] [PubMed]

Letokhov, V. S.

P. G. Kryukov and V. S. Letokhov, Sov. Phys. Usp. 12, 641 (1970).
[Crossref]

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, Sov. Phys. JETP 23, 16 (1966).

MacGillivray, J. C.

J. C. MacGillivray and M. S. Feld, Phys. Rev. A 14, 1169 (1976).
[Crossref]

Manakov, S. V.

I. R. Gabitov and S. V. Manakov, Phys. Rev. Lett. 50, 495 (1983).
[Crossref]

McCall, S. L.

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
[Crossref]

Mikhailov, A. V.

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, Theor. Math. Phys. 63, 328 (1985).
[Crossref]

Milonni, P. W.

P. W. Milonni, J. Phys. B 35, R31 (2002).
[Crossref]

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, 2005).

Neifeld, M. A.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[Crossref] [PubMed]

Park, Q-Han

Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1992).
[Crossref]

Rahman, A.

A. Rahman and J. H. Eberly, Phys. Rev. A 58, R805 (1998).
[Crossref]

Shin, H. J.

Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1992).
[Crossref]

Stenner, M. D.

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[Crossref] [PubMed]

Wang, L. J.

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[Crossref] [PubMed]

Yin, G. Y.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

Zakharov, V. E.

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, Theor. Math. Phys. 63, 328 (1985).
[Crossref]

Zuev, V. S.

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, Sov. Phys. JETP 23, 16 (1966).

J. Phys. B (1)

P. W. Milonni, J. Phys. B 35, R31 (2002).
[Crossref]

Nature (2)

L. J. Wang, A. Kuzmich, and A. Dogariu, Nature 406, 277 (2000).
[Crossref] [PubMed]

M. D. Stenner, D. J. Gauthier, and M. A. Neifeld, Nature 425, 695 (2003).
[Crossref] [PubMed]

Phys. Rev. (3)

S. L. McCall and E. L. Hahn, Phys. Rev. 183, 457 (1969).
[Crossref]

A. Icsevgi and W. E. Lamb, Jr., Phys. Rev. 185, 517 (1969).
[Crossref]

D. C. Burnham and R. Y. Chiao, Phys. Rev. 188, 667 (1969).
[Crossref]

Phys. Rev. A (4)

A. Rahman and J. H. Eberly, Phys. Rev. A 58, R805 (1998).
[Crossref]

J. C. MacGillivray and M. S. Feld, Phys. Rev. A 14, 1169 (1976).
[Crossref]

Q-Han Park and H. J. Shin, Phys. Rev. A 57, 4643 (1992).
[Crossref]

G. L. Lamb, Jr., Phys. Rev. A 12, 2052 (1975).
[Crossref]

Phys. Rev. Lett. (3)

I. R. Gabitov and S. V. Manakov, Phys. Rev. Lett. 50, 495 (1983).
[Crossref]

R. Grobe, F. T. Hioe, and J. H. Eberly, Phys. Rev. Lett. 73, 3183 (1994).
[Crossref] [PubMed]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, Phys. Rev. Lett. 74, 2447 (1995).
[Crossref] [PubMed]

Phys. Today (1)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[Crossref]

Science (1)

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, Science 301, 200 (2003).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

N. G. Basov, R. V. Ambartsumyan, V. S. Zuev, P. G. Kryukov, and V. S. Letokhov, Sov. Phys. JETP 23, 16 (1966).

Sov. Phys. Usp. (2)

P. G. Kryukov and V. S. Letokhov, Sov. Phys. Usp. 12, 641 (1970).
[Crossref]

A. V. Andreev, Sov. Phys. Usp. 33, 997 (1990).
[Crossref]

Theor. Math. Phys. (1)

I. R. Gabitov, V. E. Zakharov, and A. V. Mikhailov, Theor. Math. Phys. 63, 328 (1985).
[Crossref]

Other (1)

P. W. Milonni, Fast Light, Slow Light and Left-Handed Light (Institute of Physics, 2005).

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Figures (3)

Fig. 1
Fig. 1

Two-level atom with level 1 connected to level 2 via the Rabi frequency Ω of a laser field detuned from resonance by an amount Δ, and a sketch of a significant pulse advance in an inverted two-level gain medium.

Fig. 2
Fig. 2

Snapshots of the analytic solutions given in Eq. (4). The horizontal axis is x in units of c τ . The shaded region indicates the location of the medium, whose features are described in the text. For an EIT comparison, see Fig. 15 in Ref. [16].

Fig. 3
Fig. 3

Snapshots during evolution of the numerical pulse solution to Eqs. (2, 3) with the same parameters as for Fig. 2, but for a pulse initially entirely outside the medium with abrupt edges at ± 25 units from the peak. The pulse advance is 10 units forward, thus still well behind the front edge of the pulse.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

H = Ω 2 1 2 Ω 2 2 1 + Δ 2 2 ,
c 1 t = i Ω 2 c 2 ,
c 2 t = i Ω 2 c 1 i Δ c 2 .
( c x + t ) Ω = i g c 1 c 2 * = i g d Δ F ( Δ ) c 1 c 2 * ,
Ω ( x , t ) = { 2 τ sech 1 τ ( t x c ) x < x 0 2 τ sech 1 τ ( t x v g + ϕ 0 ) x 0 x x 1 , 2 τ sech 1 τ ( t x c + ϕ 1 ) x > x 1 , )
1 c v g = g 2 F ( Δ ) d Δ Δ 2 + ( 1 τ ) 2 g τ 2 2 ,

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