Abstract

We describe the transient behavior of an electromagnetically induced transparency in three-level atomic systems. When the coupling field is switched on, the absorption for the probe field is oscillatorily damped to its new steady-state (transparent) value. Transient gain without population inversion and enhancement of dispersion are discussed. A realistic system for experimental testing of these effects is presented.

© 1995 Optical Society of America

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References

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  1. K. J. Boller, A. Imamoglu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
    [CrossRef] [PubMed]
  2. K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
    [CrossRef] [PubMed]
  3. Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R1754 (1995); Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R2703 (1995)J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, 576 (1995).
    [CrossRef] [PubMed]
  4. M. Xiao, Y. Q. Li, S. Z. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74, 666 (1995).
    [CrossRef] [PubMed]
  5. S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989); A. Imamoglu, S. E. Harris, Opt. Lett. 14, 1344 (1989).
    [CrossRef] [PubMed]
  6. E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
    [CrossRef] [PubMed]
  7. K. M. Gheri, D. F. Walls, Phys. Rev. A 49, 4134 (1994).
    [CrossRef] [PubMed]
  8. M. Fleischhauer, Phys. Rev. Lett. 72, 989 (1994); G. S. Agarwal, Phys. Rev. Lett. 71, 1351 (1993).
    [CrossRef] [PubMed]
  9. S. E. Harris, Phys. Rev. Lett. 70, 552 (1993); J. H. Eberly, M. L. Pons, H. R. Haq, Phys. Rev. Lett. 72, 56 (1994).
    [CrossRef] [PubMed]
  10. Y. Zhao, D. H. Huang, C. K. Wu, Quantum Opt. 6, 327 (1994).
    [CrossRef]
  11. S. E. Harris, J. E. Field, A. Kasapi, Phys. Rev. A 46, R29 (1992).
    [CrossRef] [PubMed]
  12. S. E. Harris, J. J. Macklin, Phys. Rev. A 40, R4135 (1989); M. Scully, Quantum Opt. 6, 203 (1994); V. R. Blok, G. M. Krochik, Phys. Rev. A 44, 2036 (1991).
    [CrossRef]
  13. R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
    [CrossRef]

1995 (2)

Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R1754 (1995); Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R2703 (1995)J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

M. Xiao, Y. Q. Li, S. Z. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74, 666 (1995).
[CrossRef] [PubMed]

1994 (3)

Y. Zhao, D. H. Huang, C. K. Wu, Quantum Opt. 6, 327 (1994).
[CrossRef]

K. M. Gheri, D. F. Walls, Phys. Rev. A 49, 4134 (1994).
[CrossRef] [PubMed]

M. Fleischhauer, Phys. Rev. Lett. 72, 989 (1994); G. S. Agarwal, Phys. Rev. Lett. 71, 1351 (1993).
[CrossRef] [PubMed]

1993 (2)

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993); J. H. Eberly, M. L. Pons, H. R. Haq, Phys. Rev. Lett. 72, 56 (1994).
[CrossRef] [PubMed]

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

1992 (1)

S. E. Harris, J. E. Field, A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

1991 (2)

K. J. Boller, A. Imamoglu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

1989 (2)

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989); A. Imamoglu, S. E. Harris, Opt. Lett. 14, 1344 (1989).
[CrossRef] [PubMed]

S. E. Harris, J. J. Macklin, Phys. Rev. A 40, R4135 (1989); M. Scully, Quantum Opt. 6, 203 (1994); V. R. Blok, G. M. Krochik, Phys. Rev. A 44, 2036 (1991).
[CrossRef]

1976 (1)

R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
[CrossRef]

Boller, K. J.

K. J. Boller, A. Imamoglu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

Brewer, R. G.

R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
[CrossRef]

Field, J. E.

S. E. Harris, J. E. Field, A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

Fleischhauer, M.

M. Fleischhauer, Phys. Rev. Lett. 72, 989 (1994); G. S. Agarwal, Phys. Rev. Lett. 71, 1351 (1993).
[CrossRef] [PubMed]

Fry, E. S.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Gea-Banacloche, J.

M. Xiao, Y. Q. Li, S. Z. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74, 666 (1995).
[CrossRef] [PubMed]

Genack, A. Z.

R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
[CrossRef]

Gheri, K. M.

K. M. Gheri, D. F. Walls, Phys. Rev. A 49, 4134 (1994).
[CrossRef] [PubMed]

Hakuta, K.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Harris, S. E.

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993); J. H. Eberly, M. L. Pons, H. R. Haq, Phys. Rev. Lett. 72, 56 (1994).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

K. J. Boller, A. Imamoglu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989); A. Imamoglu, S. E. Harris, Opt. Lett. 14, 1344 (1989).
[CrossRef] [PubMed]

S. E. Harris, J. J. Macklin, Phys. Rev. A 40, R4135 (1989); M. Scully, Quantum Opt. 6, 203 (1994); V. R. Blok, G. M. Krochik, Phys. Rev. A 44, 2036 (1991).
[CrossRef]

Huang, D. H.

Y. Zhao, D. H. Huang, C. K. Wu, Quantum Opt. 6, 327 (1994).
[CrossRef]

Imamoglu, A.

K. J. Boller, A. Imamoglu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

Jin, S. Z.

Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R1754 (1995); Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R2703 (1995)J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

M. Xiao, Y. Q. Li, S. Z. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74, 666 (1995).
[CrossRef] [PubMed]

Kasapi, A.

S. E. Harris, J. E. Field, A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

Li, X.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Li, Y. Q.

Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R1754 (1995); Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R2703 (1995)J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

M. Xiao, Y. Q. Li, S. Z. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74, 666 (1995).
[CrossRef] [PubMed]

Macklin, J. J.

S. E. Harris, J. J. Macklin, Phys. Rev. A 40, R4135 (1989); M. Scully, Quantum Opt. 6, 203 (1994); V. R. Blok, G. M. Krochik, Phys. Rev. A 44, 2036 (1991).
[CrossRef]

Marmet, L.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Nikonov, D.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Padmabandu, G. G.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Scully, M. O.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Smith, A. V.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Stoicheff, B. P.

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

Tittel, F. K.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Walls, D. F.

K. M. Gheri, D. F. Walls, Phys. Rev. A 49, 4134 (1994).
[CrossRef] [PubMed]

Wang, C.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Wilkinson, S. R.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Wu, C. K.

Y. Zhao, D. H. Huang, C. K. Wu, Quantum Opt. 6, 327 (1994).
[CrossRef]

Xiao, M.

Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R1754 (1995); Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R2703 (1995)J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

M. Xiao, Y. Q. Li, S. Z. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74, 666 (1995).
[CrossRef] [PubMed]

Zhao, Y.

Y. Zhao, D. H. Huang, C. K. Wu, Quantum Opt. 6, 327 (1994).
[CrossRef]

Zhu, S.-Y.

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Phys. Rev. A (4)

Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R1754 (1995); Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, R2703 (1995)J. Gea-Banacloche, Y. Q. Li, S. Z. Jin, M. Xiao, Phys. Rev. A 51, 576 (1995).
[CrossRef] [PubMed]

K. M. Gheri, D. F. Walls, Phys. Rev. A 49, 4134 (1994).
[CrossRef] [PubMed]

S. E. Harris, J. E. Field, A. Kasapi, Phys. Rev. A 46, R29 (1992).
[CrossRef] [PubMed]

S. E. Harris, J. J. Macklin, Phys. Rev. A 40, R4135 (1989); M. Scully, Quantum Opt. 6, 203 (1994); V. R. Blok, G. M. Krochik, Phys. Rev. A 44, 2036 (1991).
[CrossRef]

Phys. Rev. Lett. (8)

R. G. Brewer, A. Z. Genack, Phys. Rev. Lett. 36, 959 (1976).
[CrossRef]

K. J. Boller, A. Imamoglu, S. E. Harris, Phys. Rev. Lett. 66, 2593 (1991); J. E. Field, K. H. Hahn, S. E. Harris, Phys. Rev. Lett. 67, 3062 (1991).
[CrossRef] [PubMed]

K. Hakuta, L. Marmet, B. P. Stoicheff, Phys. Rev. Lett. 66, 596 (1991).
[CrossRef] [PubMed]

M. Fleischhauer, Phys. Rev. Lett. 72, 989 (1994); G. S. Agarwal, Phys. Rev. Lett. 71, 1351 (1993).
[CrossRef] [PubMed]

S. E. Harris, Phys. Rev. Lett. 70, 552 (1993); J. H. Eberly, M. L. Pons, H. R. Haq, Phys. Rev. Lett. 72, 56 (1994).
[CrossRef] [PubMed]

M. Xiao, Y. Q. Li, S. Z. Jin, J. Gea-Banacloche, Phys. Rev. Lett. 74, 666 (1995).
[CrossRef] [PubMed]

S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989); A. Imamoglu, S. E. Harris, Opt. Lett. 14, 1344 (1989).
[CrossRef] [PubMed]

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, S.-Y. Zhu, Phys. Rev. Lett. 70, 3235 (1993); W. E. Van der Veer, A. Donszelmann, H. B. Linden van den Heuvell, Phys. Rev. Lett. 70, 3243 (1993); A. Nottelmann, C. Peers, W. Lange, Phys. Rev. Lett. 70, 1783 (1993).
[CrossRef] [PubMed]

Quantum Opt. (1)

Y. Zhao, D. H. Huang, C. K. Wu, Quantum Opt. 6, 327 (1994).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Ladder-type three-level system; (b) Λ-type system. The coupling laser is denoted by the solid line and the probe laser by the dashed line. (c) Dressed-state pictures: left, atoms in level |1〉 will not absorb probe laser light; right, stimulated emission of the excited atoms by the probe laser.

Fig. 2
Fig. 2

Normalized linear susceptibility Im(χ21) versus normalized time γ21t in units of μ21 2Nγ21 = 1. The simulation parameters are Δ1 = Δ2 = 0 and γ31 = 10−3γ21 for Ω2 = 10γ21 (curve a), Ω2 = 5.0γ21 (curve b), Ω2 = 2.0 γ21 (curve c), and Ω2 = 1.0γ21 (curve d).

Fig. 3
Fig. 3

Time-dependent absorption (solid curves) and dispersion (dotted curves) versus probe detuning Δ1 in units of μ21 2N /ħγ21 = 1. The simulation parameters are Δ2 = 0, γ31 = 10−3γ21, and Ω2 = 5.0γ21 for (a) γ21 t = 0, (b) γ21 t = .25, and (c) γ21 t = 10. Gain without population inversion and enhancement of dispersion are found for γ21 t = 1.25.

Equations (10)

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

ρ ˙ 21 = ( i Δ 1 - γ 21 ) ρ 21 + i Ω 1 2 ( ρ 22 - ρ 11 ) - i Ω 2 * 2 ρ 31 ,
ρ ˙ 32 = ( i Δ 2 - γ 32 ) ρ 32 + i Ω 2 2 ( ρ 33 - ρ 22 ) + i Ω 1 * 2 ρ 31 ,
ρ ˙ 31 = [ i ( Δ 1 + Δ 2 ) - γ 31 ] ρ 31 - i Ω 2 2 ρ 21 + i Ω 1 2 ρ 32 ,
ρ ˙ 11 = - i Ω 1 * 2 ρ 21 + i Ω 1 2 ρ 21 * + Γ 2 ρ 22 ,
ρ ˙ 33 = i Ω 2 * 2 ρ 32 - i Ω 2 2 ρ 32 * - Γ 3 ρ 33 ,
ρ ˙ 21 = ( i Δ 1 - γ 21 ) ρ 21 - i Ω 1 2 - i Ω 2 * 2 ρ 31 ,
ρ ˙ 31 = [ i ( Δ 1 + Δ 2 ) - γ 31 ] ρ 31 - i Ω 2 2 ρ 21 .
ρ 21 ( t ) = ρ 21 ( 0 ) exp ( - γ 21 2 t ) ( cos Ω 2 t + γ 21 Ω sin Ω 2 t ) ,
ɛ 1 z + c - 1 ɛ 1 t = i g 1 ɛ 1 2 χ 21 ( t ) ,
ɛ 1 ( z , t ) = ɛ 0 exp [ i g 1 χ 21 ( t ) 2 z ] ,

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