Abstract

We report experimental studies of electromagnetically induced transparency in Λ-type and ladder-type atomic systems realized in  87Rb atoms cooled and confined in a magneto-optical trap. Complete transparency is observed in the Λ-type system with a moderate coupling field. Comparison between the two systems reveals that at the line center of a weak probe transition, destructive interference occurs for the Λ-type system, whereas constructive interference occurs for the ladder-type system. We discuss conditions of complete transparency in the Λ-type system that contains hyperfine magnetic sublevels. Our experimental measurements for the two systems agree with theoretical calculations based on simple three-level Λ-type and ladder-type models.

© 2001 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  4. J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened medium: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
    [CrossRef] [PubMed]
  5. D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically in-duced transparency: a comparison of V, Λ, and cascade systems,” Phys. Rev. A 52, 2302–2311 (1995).
    [CrossRef] [PubMed]
  6. O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
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  7. O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro, “Observation of transient electromagnetically induced transparency in a rubidium lambda system,” Phys. Rev. A 58, 1545–1548 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
  22. J. Kitching and L. Hollberg, “Interference-induced optical gain without inversion in cold, trapped atoms,” Phys. Rev. A 59, 4685–4689 (1999).
    [CrossRef]
  23. K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
    [CrossRef] [PubMed]
  24. W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous force,” Phys. Rev. Lett. 70, 2253–2254 (1993).
    [CrossRef] [PubMed]
  25. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
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  26. M. Yan, E. Rickey, and Y. Zhu, “Nonlinear absorption by quantum interference in cold atoms,” Opt. Lett. 26, 548–550 (2001).
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    [CrossRef] [PubMed]

2001 (1)

2000 (1)

Y. Chen, C. Lin, and I. A. Yu, “Role of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
[CrossRef]

1999 (2)

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

J. Kitching and L. Hollberg, “Interference-induced optical gain without inversion in cold, trapped atoms,” Phys. Rev. A 59, 4685–4689 (1999).
[CrossRef]

1998 (3)

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

A. V. Durrant, H. X. Chen, S. A. Hopkins, and J. A. Vaccaro, “Zeeman-coherence-induced transparency and gain without inversion in laser-cooled rubidium,” Opt. Commun. 151, 136–146 (1998).
[CrossRef]

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro, “Observation of transient electromagnetically induced transparency in a rubidium lambda system,” Phys. Rev. A 58, 1545–1548 (1998).
[CrossRef]

1997 (5)

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 (London) 397, 594–598 (1997).
[CrossRef]

T. Van Der Veldt, J. F. Roch, and Ph. Grangier, “Nonlinear absorption and dispersion in cold 87Rb atoms,” Opt. Commun. 137, 420–426 (1997).
[CrossRef]

S. A. Hopkins, E. Usadi, H. X. Chen, and A. V. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level lambda-type systems,” Opt. Commun. 138, 185–192 (1997).
[CrossRef]

F. S. Cataliotti, C. Fort, T. W. Hansch, M. Inguscio, and M. Prevedelli, “Electromagnetically induced transparency in cold free atoms: test of a sum rule for nonlinear optics,” Phys. Rev. A 56, 2221–2224 (1997).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997), and references therein.
[CrossRef]

1996 (3)

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef] [PubMed]

1995 (2)

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened medium: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef] [PubMed]

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically in-duced transparency: a comparison of V, Λ, and cascade systems,” Phys. Rev. A 52, 2302–2311 (1995).
[CrossRef] [PubMed]

1994 (1)

M. O. Scully and M. Fleischhauer, “Lasers without inversion,” Science 263, 337–338 (1994).
[CrossRef] [PubMed]

1993 (1)

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous force,” Phys. Rev. Lett. 70, 2253–2254 (1993).
[CrossRef] [PubMed]

1992 (3)

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef] [PubMed]

O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
[CrossRef]

M. O. Scully, “From lasers and masers to phaseonium and phasers,” Phys. Rep. 219, 191–201 (1992).
[CrossRef]

1991 (1)

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

1969 (1)

T. Hansch, R. Keil, A. Schabert, C. Schemelzer, and P. Toscheck, “Interaction of laser light waves by dynamic Stark splitting,” Z. Phys. 226, 293–296 (1969).
[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 (London) 397, 594–598 (1997).
[CrossRef]

Boller, K. J.

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Cataliotti, F. S.

F. S. Cataliotti, C. Fort, T. W. Hansch, M. Inguscio, and M. Prevedelli, “Electromagnetically induced transparency in cold free atoms: test of a sum rule for nonlinear optics,” Phys. Rev. A 56, 2221–2224 (1997).
[CrossRef]

Chen, H. X.

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro, “Observation of transient electromagnetically induced transparency in a rubidium lambda system,” Phys. Rev. A 58, 1545–1548 (1998).
[CrossRef]

A. V. Durrant, H. X. Chen, S. A. Hopkins, and J. A. Vaccaro, “Zeeman-coherence-induced transparency and gain without inversion in laser-cooled rubidium,” Opt. Commun. 151, 136–146 (1998).
[CrossRef]

S. A. Hopkins, E. Usadi, H. X. Chen, and A. V. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level lambda-type systems,” Opt. Commun. 138, 185–192 (1997).
[CrossRef]

Chen, Y.

Y. Chen, C. Lin, and I. A. Yu, “Role of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
[CrossRef]

Davis, K. B.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous force,” Phys. Rev. Lett. 70, 2253–2254 (1993).
[CrossRef] [PubMed]

Dunn, M. H.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically in-duced transparency: a comparison of V, Λ, and cascade systems,” Phys. Rev. A 52, 2302–2311 (1995).
[CrossRef] [PubMed]

Durrant, A. V.

A. V. Durrant, H. X. Chen, S. A. Hopkins, and J. A. Vaccaro, “Zeeman-coherence-induced transparency and gain without inversion in laser-cooled rubidium,” Opt. Commun. 151, 136–146 (1998).
[CrossRef]

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro, “Observation of transient electromagnetically induced transparency in a rubidium lambda system,” Phys. Rev. A 58, 1545–1548 (1998).
[CrossRef]

S. A. Hopkins, E. Usadi, H. X. Chen, and A. V. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level lambda-type systems,” Opt. Commun. 138, 185–192 (1997).
[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 (London) 397, 594–598 (1997).
[CrossRef]

Fleischhauer, M.

M. O. Scully and M. Fleischhauer, “Lasers without inversion,” Science 263, 337–338 (1994).
[CrossRef] [PubMed]

Fort, C.

F. S. Cataliotti, C. Fort, T. W. Hansch, M. Inguscio, and M. Prevedelli, “Electromagnetically induced transparency in cold free atoms: test of a sum rule for nonlinear optics,” Phys. Rev. A 56, 2221–2224 (1997).
[CrossRef]

Fry, E. S.

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

Fulton, D. J.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically in-duced transparency: a comparison of V, Λ, and cascade systems,” Phys. Rev. A 52, 2302–2311 (1995).
[CrossRef] [PubMed]

Gea-Banacloche, J.

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened medium: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef] [PubMed]

Grangier, Ph.

T. Van Der Veldt, J. F. Roch, and Ph. Grangier, “Nonlinear absorption and dispersion in cold 87Rb atoms,” Opt. Commun. 137, 420–426 (1997).
[CrossRef]

Hansch, T.

T. Hansch, R. Keil, A. Schabert, C. Schemelzer, and P. Toscheck, “Interaction of laser light waves by dynamic Stark splitting,” Z. Phys. 226, 293–296 (1969).
[CrossRef]

Hansch, T. W.

F. S. Cataliotti, C. Fort, T. W. Hansch, M. Inguscio, and M. Prevedelli, “Electromagnetically induced transparency in cold free atoms: test of a sum rule for nonlinear optics,” Phys. Rev. A 56, 2221–2224 (1997).
[CrossRef]

Harris, S. E.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

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 (London) 397, 594–598 (1997).
[CrossRef]

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36–42 (1997), and references therein.
[CrossRef]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Hau, L. V.

S. E. Harris and L. V. Hau, “Nonlinear optics at low light levels,” Phys. Rev. Lett. 82, 4611–4614 (1999).
[CrossRef]

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 (London) 397, 594–598 (1997).
[CrossRef]

Hollberg, L.

J. Kitching and L. Hollberg, “Interference-induced optical gain without inversion in cold, trapped atoms,” Phys. Rev. A 59, 4685–4689 (1999).
[CrossRef]

Hopkins, S. A.

A. V. Durrant, H. X. Chen, S. A. Hopkins, and J. A. Vaccaro, “Zeeman-coherence-induced transparency and gain without inversion in laser-cooled rubidium,” Opt. Commun. 151, 136–146 (1998).
[CrossRef]

S. A. Hopkins, E. Usadi, H. X. Chen, and A. V. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level lambda-type systems,” Opt. Commun. 138, 185–192 (1997).
[CrossRef]

Hussein, Z.

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

Imamoglu, A.

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef] [PubMed]

K. J. Boller, A. Imamoglu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Inguscio, M.

F. S. Cataliotti, C. Fort, T. W. Hansch, M. Inguscio, and M. Prevedelli, “Electromagnetically induced transparency in cold free atoms: test of a sum rule for nonlinear optics,” Phys. Rev. A 56, 2221–2224 (1997).
[CrossRef]

Jin, S.

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened medium: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef] [PubMed]

Joffe, M. A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous force,” Phys. Rev. Lett. 70, 2253–2254 (1993).
[CrossRef] [PubMed]

Keil, R.

T. Hansch, R. Keil, A. Schabert, C. Schemelzer, and P. Toscheck, “Interaction of laser light waves by dynamic Stark splitting,” Z. Phys. 226, 293–296 (1969).
[CrossRef]

Ketterle, W.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous force,” Phys. Rev. Lett. 70, 2253–2254 (1993).
[CrossRef] [PubMed]

Kitching, J.

J. Kitching and L. Hollberg, “Interference-induced optical gain without inversion in cold, trapped atoms,” Phys. Rev. A 59, 4685–4689 (1999).
[CrossRef]

Kocharovskaya, O.

O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
[CrossRef]

Li, Y.

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened medium: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef] [PubMed]

Lin, C.

Y. Chen, C. Lin, and I. A. Yu, “Role of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
[CrossRef]

Lindquist, K.

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef] [PubMed]

Lukin, M. D.

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

Marangos, J. P.

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro, “Observation of transient electromagnetically induced transparency in a rubidium lambda system,” Phys. Rev. A 58, 1545–1548 (1998).
[CrossRef]

Martin, A.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous force,” Phys. Rev. Lett. 70, 2253–2254 (1993).
[CrossRef] [PubMed]

Meschede, D.

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

Moseley, R. R.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically in-duced transparency: a comparison of V, Λ, and cascade systems,” Phys. Rev. A 52, 2302–2311 (1995).
[CrossRef] [PubMed]

Nikonov, D. E.

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

Padmabandu, G. G.

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

Prevedelli, M.

F. S. Cataliotti, C. Fort, T. W. Hansch, M. Inguscio, and M. Prevedelli, “Electromagnetically induced transparency in cold free atoms: test of a sum rule for nonlinear optics,” Phys. Rev. A 56, 2221–2224 (1997).
[CrossRef]

Pritchard, D. E.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous force,” Phys. Rev. Lett. 70, 2253–2254 (1993).
[CrossRef] [PubMed]

Rickey, E.

Roch, J. F.

T. Van Der Veldt, J. F. Roch, and Ph. Grangier, “Nonlinear absorption and dispersion in cold 87Rb atoms,” Opt. Commun. 137, 420–426 (1997).
[CrossRef]

Schabert, A.

T. Hansch, R. Keil, A. Schabert, C. Schemelzer, and P. Toscheck, “Interaction of laser light waves by dynamic Stark splitting,” Z. Phys. 226, 293–296 (1969).
[CrossRef]

Schemelzer, C.

T. Hansch, R. Keil, A. Schabert, C. Schemelzer, and P. Toscheck, “Interaction of laser light waves by dynamic Stark splitting,” Z. Phys. 226, 293–296 (1969).
[CrossRef]

Schmidt, H.

Schmidt, O.

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

Scully, M. O.

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

M. O. Scully and M. Fleischhauer, “Lasers without inversion,” Science 263, 337–338 (1994).
[CrossRef] [PubMed]

M. O. Scully, “From lasers and masers to phaseonium and phasers,” Phys. Rep. 219, 191–201 (1992).
[CrossRef]

Shepherd, S.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically in-duced transparency: a comparison of V, Λ, and cascade systems,” Phys. Rev. A 52, 2302–2311 (1995).
[CrossRef] [PubMed]

Sinclair, B. D.

D. J. Fulton, S. Shepherd, R. R. Moseley, B. D. Sinclair, and M. H. Dunn, “Continuous-wave electromagnetically in-duced transparency: a comparison of V, Λ, and cascade systems,” Phys. Rev. A 52, 2302–2311 (1995).
[CrossRef] [PubMed]

Smith, Z. N.

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

Stephens, M.

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef] [PubMed]

Toscheck, P.

T. Hansch, R. Keil, A. Schabert, C. Schemelzer, and P. Toscheck, “Interaction of laser light waves by dynamic Stark splitting,” Z. Phys. 226, 293–296 (1969).
[CrossRef]

Usadi, E.

S. A. Hopkins, E. Usadi, H. X. Chen, and A. V. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level lambda-type systems,” Opt. Commun. 138, 185–192 (1997).
[CrossRef]

Vaccaro, J. A.

A. V. Durrant, H. X. Chen, S. A. Hopkins, and J. A. Vaccaro, “Zeeman-coherence-induced transparency and gain without inversion in laser-cooled rubidium,” Opt. Commun. 151, 136–146 (1998).
[CrossRef]

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro, “Observation of transient electromagnetically induced transparency in a rubidium lambda system,” Phys. Rev. A 58, 1545–1548 (1998).
[CrossRef]

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T. Van Der Veldt, J. F. Roch, and Ph. Grangier, “Nonlinear absorption and dispersion in cold 87Rb atoms,” Opt. Commun. 137, 420–426 (1997).
[CrossRef]

Welch, G. R.

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

Wieman, C.

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef] [PubMed]

Wynands, R.

O. Schmidt, R. Wynands, Z. Hussein, and D. Meschede, “Steep dispersion and group velocity below c/3000 in coherent population trapping,” Phys. Rev. A 53, R27–R30 (1996).
[CrossRef] [PubMed]

Xiao, M.

J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened medium: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
[CrossRef] [PubMed]

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S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
[CrossRef]

Yan, M.

Yu, I. A.

Y. Chen, C. Lin, and I. A. Yu, “Role of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
[CrossRef]

Zhu, Y.

Nature (London) (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 (London) 397, 594–598 (1997).
[CrossRef]

Opt. Commun. (3)

T. Van Der Veldt, J. F. Roch, and Ph. Grangier, “Nonlinear absorption and dispersion in cold 87Rb atoms,” Opt. Commun. 137, 420–426 (1997).
[CrossRef]

S. A. Hopkins, E. Usadi, H. X. Chen, and A. V. Durrant, “Electromagnetically induced transparency of laser-cooled rubidium atoms in three-level lambda-type systems,” Opt. Commun. 138, 185–192 (1997).
[CrossRef]

A. V. Durrant, H. X. Chen, S. A. Hopkins, and J. A. Vaccaro, “Zeeman-coherence-induced transparency and gain without inversion in laser-cooled rubidium,” Opt. Commun. 151, 136–146 (1998).
[CrossRef]

Opt. Lett. (2)

Phys. Rep. (2)

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[CrossRef]

M. O. Scully, “From lasers and masers to phaseonium and phasers,” Phys. Rep. 219, 191–201 (1992).
[CrossRef]

Phys. Rev. A (8)

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[CrossRef] [PubMed]

H. X. Chen, A. V. Durrant, J. P. Marangos, and J. A. Vaccaro, “Observation of transient electromagnetically induced transparency in a rubidium lambda system,” Phys. Rev. A 58, 1545–1548 (1998).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

G. G. Padmabandu, G. R. Welch, Z. N. Smith, E. S. Fry, D. E. Nikonov, M. D. Lukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2054 (1996).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

(a) Three-level Λ-type atomic system and laser-coupling scheme. (b) Three-level ladder-type atomic system and laser-coupling scheme. (c) Dressed-state picture. Ω(Ωp) is the Rabi frequency of the coupling (probe) field.

Fig. 2
Fig. 2

(a) Λ-type system coupled by linearly polarized probe and coupling fields with Fc=F+1=2 and Fp=F, in which complete EIT is possible. Solid arrows show the probe transitions with its polarization parallel to the coupling polarization, and dashed arrows show the probe polarization perpendicular to the coupling polarization. (b) Λ-type system coupled by linearly polarized probe and coupling fields with Fc=F-1=1 and Fp=F=2, in which complete EIT is not possible. Solid arrows show the probe transitions with its polarization parallel to the coupling polarization, and dashed arrows show the probe polarization perpendicular to the coupling polarization.

Fig. 3
Fig. 3

(a) Level structure and the laser-coupling scheme for a Λ-type  87Rb atomic system. (b) Level structure and the laser-coupling scheme for a ladder-type  87Rb atomic system. The right figures in (a) and (b) show the detailed coupling among the magnetic sublevels with the laser polarization used in the experiments.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup: AOM, acousto-optic modulator; BK, beam blocker; M, mirror; PD, photodiode detector; P, polarizer; λ/2, half-wave plate; λ/4, quater-wave plate.

Fig. 5
Fig. 5

Probe-absorption spectra versus the probe-frequency detuning in the Λ-type Rb system. Solid curves are the experimental data, and dashed curves are the theoretical calculations. (a) Coupling Rabi frequency Ω6 MHz. The observed EIT depth is ∼92%. (b) Coupling Rabi frequency Ω12 MHz. The Rabi frequency of the weak probe field is estimated to be Ωp1 MHz. The two parameters are used in the theoretical calculations.

Fig. 6
Fig. 6

Transparency depth versus Ω in the Λ-type system. Dots are the experimental data, and the solid (dashed) curve is the calculation including (excluding) the dephasing effect of the finite laser linewidth.

Fig. 7
Fig. 7

Probe-absorption spectra versus the probe-frequency detuning in the ladder-type Rb system. Solid curves are the experimental data, and dashed curves are the theoretical calculations. (a) Coupling Rabi frequency Ω6 MHz. (b) Coupling Rabi frequency Ω13 MHz. The Rabi frequency of the weak probe field is estimated to be Ωp1.2 MHz.

Fig. 8
Fig. 8

Transparency depth versus Ω in the ladder-type type system. Dots are the experimental data and the solid (dashed) curve is the calculation including (excluding) the dephasing effect of the finite laser linewidth.

Equations (8)

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ρ12=0.
ρ12=-iΩpΓ+2ΩP2/Γ+Ω2/Γ.
|+=12(|2+|3),
|-=12(|2-|3),
|+=12(|3+|2),
|-=12(|3-|2).
P1|d·Ep|+Ω+1|d·Ep|--Ω2=0.
P1|d·Ep|+Ω+1|d·Ep|--Ω2=ΩP2Ω2.

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