Abstract

Coherent two-field spectroscopy calculations with different choices of the quantization (z) axis are compared. In a system driven by a strong coupling field and a weak probe field, alignment of the z axis along either the polarization direction of a linearly polarized coupling field or the propagation direction of a circularly polarized coupling field is shown to simplify the calculations and facilitate interpretation of the results. The advantages of a suitable choice of the z axis are highlighted with an example of a degenerate three-level system of electromagnetically induced transparency.

© 2002 Optical Society of America

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  1. A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
    [CrossRef] [PubMed]
  2. K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
    [CrossRef] [PubMed]
  3. For a recent review, see J. P. Marangos, “Electromagnetically induced transparency,” J. Mod. Opt. 45, 471–503 (1998).
    [CrossRef]
  4. H. M. Gray, R. M. Whitley, and C. R. Stroud, Jr., “Coherent trapping of atomic populations,” Opt. Lett. 3, 218–220 (1978).
    [CrossRef] [PubMed]
  5. For a recent review, see E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
    [CrossRef]
  6. A. V. Taĭchenachev, A. M. Tumaĭkin, and V. I. Yudin, “On the spontaneous-coherence-transfer-induced sign change of a sub-natural-width nonlinear resonance,” JETP Lett. 69, 819–824 (1999).
    [CrossRef]
  7. A. M. Akulshin, S. Barreiro, and A. Lezama, “Steep anomalous dispersion in coherently prepared Rb vapor,” Phys. Rev. Lett. 83, 4277–4280 (1999).
    [CrossRef]
  8. M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
    [CrossRef]
  9. Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
    [CrossRef]
  10. O. A. Kocharovskaya and Ya. I. Khanin, “Coherent amplification of an ultrashort pulse in a three-level medium without a population inversion,” JETP Lett. 48, 630–634 (1988).
  11. G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
    [CrossRef] [PubMed]
  12. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
    [CrossRef] [PubMed]
  13. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
    [CrossRef] [PubMed]
  14. A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
    [CrossRef] [PubMed]
  15. 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]
  16. S. Wang, D. G. Ducreay, R. Pina, M. Yan, and Y. Zhu, “Coherent population trapping and four-wave mixing via dark states in a Doppler-broadened open Rb system,” Phys. Rev. A 61, 033805 (2000).
    [CrossRef]
  17. Y. C. Chen, C. W. Lin, and I. A. Yu, “Role of degenerate Zeeman levels in electromagnetically induced transparency,” Phys. Rev. A 61, 053805 (2000).
    [CrossRef]
  18. D. McGloin, M. H. Dunn, and D. J. Fulton, “Polarization effects in electromagnetically induced transparency,” Phys. Rev. A 62, 053802 (2000).
    [CrossRef]
  19. Y. Li and M. Xiao, “Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms,” Phys. Rev. A 51, R2703–R2706 (1995).
    [CrossRef]
  20. Y. C. Chen, Y. W. Chen, J. J. Su, J. Y. Huang, and I. A. Yu, “Pump–probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
    [CrossRef]
  21. J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, “Recoil-induced resonances in cesium: an atomic analog to the free-electron laser,” Phys. Rev. Lett. 72, 3017–3020 (1994).
    [CrossRef] [PubMed]
  22. D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, “Raman spectroscopy of cesium atoms in a laser trap,” Europhys. Lett. 15, 149–154 (1991).
    [CrossRef]

2001

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[CrossRef]

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Y. C. Chen, Y. W. Chen, J. J. Su, J. Y. Huang, and I. A. Yu, “Pump–probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[CrossRef]

2000

S. Wang, D. G. Ducreay, R. Pina, M. Yan, and Y. Zhu, “Coherent population trapping and four-wave mixing via dark states in a Doppler-broadened open Rb system,” Phys. Rev. A 61, 033805 (2000).
[CrossRef]

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

D. McGloin, M. H. Dunn, and D. J. Fulton, “Polarization effects in electromagnetically induced transparency,” Phys. Rev. A 62, 053802 (2000).
[CrossRef]

1999

A. V. Taĭchenachev, A. M. Tumaĭkin, and V. I. Yudin, “On the spontaneous-coherence-transfer-induced sign change of a sub-natural-width nonlinear resonance,” JETP Lett. 69, 819–824 (1999).
[CrossRef]

A. M. Akulshin, S. Barreiro, and A. Lezama, “Steep anomalous dispersion in coherently prepared Rb vapor,” Phys. Rev. Lett. 83, 4277–4280 (1999).
[CrossRef]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

1998

For a recent review, see J. P. Marangos, “Electromagnetically induced transparency,” J. Mod. Opt. 45, 471–503 (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]

1996

For a recent review, see E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[CrossRef]

G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
[CrossRef] [PubMed]

1995

Y. Li and M. Xiao, “Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms,” Phys. Rev. A 51, R2703–R2706 (1995).
[CrossRef]

1994

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, “Recoil-induced resonances in cesium: an atomic analog to the free-electron laser,” Phys. Rev. Lett. 72, 3017–3020 (1994).
[CrossRef] [PubMed]

1991

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, “Raman spectroscopy of cesium atoms in a laser trap,” Europhys. Lett. 15, 149–154 (1991).
[CrossRef]

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

1989

1988

O. A. Kocharovskaya and Ya. I. Khanin, “Coherent amplification of an ultrashort pulse in a three-level medium without a population inversion,” JETP Lett. 48, 630–634 (1988).

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

1978

Akulshin, A. M.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Steep anomalous dispersion in coherently prepared Rb vapor,” Phys. Rev. Lett. 83, 4277–4280 (1999).
[CrossRef]

Arimondo, E.

For a recent review, see E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Aspect, A.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Barreiro, S.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Steep anomalous dispersion in coherently prepared Rb vapor,” Phys. Rev. Lett. 83, 4277–4280 (1999).
[CrossRef]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Boller, K. J.

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

Chen, H. X.

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]

Chen, Y. C.

Y. C. Chen, Y. W. Chen, J. J. Su, J. Y. Huang, and I. A. Yu, “Pump–probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[CrossRef]

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[CrossRef]

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

Chen, Y. W.

Y. C. Chen, Y. W. Chen, J. J. Su, J. Y. Huang, and I. A. Yu, “Pump–probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[CrossRef]

Chiu, H. Y.

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[CrossRef]

Cohen-Tannoudji, C.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Courtois, J. Y.

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, “Raman spectroscopy of cesium atoms in a laser trap,” Europhys. Lett. 15, 149–154 (1991).
[CrossRef]

Courtois, J.-Y.

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, “Recoil-induced resonances in cesium: an atomic analog to the free-electron laser,” Phys. Rev. Lett. 72, 3017–3020 (1994).
[CrossRef] [PubMed]

Ducreay, D. G.

S. Wang, D. G. Ducreay, R. Pina, M. Yan, and Y. Zhu, “Coherent population trapping and four-wave mixing via dark states in a Doppler-broadened open Rb system,” Phys. Rev. A 61, 033805 (2000).
[CrossRef]

Dunn, M. H.

D. McGloin, M. H. Dunn, and D. J. Fulton, “Polarization effects in electromagnetically induced transparency,” Phys. Rev. A 62, 053802 (2000).
[CrossRef]

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]

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Fleischhauer, M.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

Fry, E. S.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
[CrossRef] [PubMed]

Fulton, D. J.

D. McGloin, M. H. Dunn, and D. J. Fulton, “Polarization effects in electromagnetically induced transparency,” Phys. Rev. A 62, 053802 (2000).
[CrossRef]

Gray, H. M.

Grison, D.

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, “Raman spectroscopy of cesium atoms in a laser trap,” Europhys. Lett. 15, 149–154 (1991).
[CrossRef]

Grynberg, G.

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, “Recoil-induced resonances in cesium: an atomic analog to the free-electron laser,” Phys. Rev. Lett. 72, 3017–3020 (1994).
[CrossRef] [PubMed]

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, “Raman spectroscopy of cesium atoms in a laser trap,” Europhys. Lett. 15, 149–154 (1991).
[CrossRef]

Harris, S. E.

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

A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
[CrossRef] [PubMed]

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

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]

Huang, J. Y.

Y. C. Chen, Y. W. Chen, J. J. Su, J. Y. Huang, and I. A. Yu, “Pump–probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[CrossRef]

Imamoglu, A.

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

A. Imamoğlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
[CrossRef] [PubMed]

Kaiser, R.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Khanin, Ya. I.

O. A. Kocharovskaya and Ya. I. Khanin, “Coherent amplification of an ultrashort pulse in a three-level medium without a population inversion,” JETP Lett. 48, 630–634 (1988).

Kocharovskaya, O. A.

O. A. Kocharovskaya and Ya. I. Khanin, “Coherent amplification of an ultrashort pulse in a three-level medium without a population inversion,” JETP Lett. 48, 630–634 (1988).

Lezama, A.

A. M. Akulshin, S. Barreiro, and A. Lezama, “Steep anomalous dispersion in coherently prepared Rb vapor,” Phys. Rev. Lett. 83, 4277–4280 (1999).
[CrossRef]

Li, Y.

Y. Li and M. Xiao, “Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms,” Phys. Rev. A 51, R2703–R2706 (1995).
[CrossRef]

Liao, Y. A.

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[CrossRef]

Lin, C. W.

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

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409, 490–493 (2001).
[CrossRef] [PubMed]

Lounis, B.

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, “Recoil-induced resonances in cesium: an atomic analog to the free-electron laser,” Phys. Rev. Lett. 72, 3017–3020 (1994).
[CrossRef] [PubMed]

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, “Raman spectroscopy of cesium atoms in a laser trap,” Europhys. Lett. 15, 149–154 (1991).
[CrossRef]

Lukin, M. D.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
[CrossRef] [PubMed]

Mair, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Marangos, J. P.

For a recent review, see J. P. Marangos, “Electromagnetically induced transparency,” J. Mod. Opt. 45, 471–503 (1998).
[CrossRef]

McGloin, D.

D. McGloin, M. H. Dunn, and D. J. Fulton, “Polarization effects in electromagnetically induced transparency,” Phys. Rev. A 62, 053802 (2000).
[CrossRef]

Nikonov, D. E.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
[CrossRef] [PubMed]

Padmabandu, G. G.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
[CrossRef] [PubMed]

Phillips, D. F.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Pina, R.

S. Wang, D. G. Ducreay, R. Pina, M. Yan, and Y. Zhu, “Coherent population trapping and four-wave mixing via dark states in a Doppler-broadened open Rb system,” Phys. Rev. A 61, 033805 (2000).
[CrossRef]

Salomon, C.

D. Grison, B. Lounis, C. Salomon, J. Y. Courtois, and G. Grynberg, “Raman spectroscopy of cesium atoms in a laser trap,” Europhys. Lett. 15, 149–154 (1991).
[CrossRef]

Scully, M. O.

M. D. Lukin, S. F. Yelin, M. Fleischhauer, and M. O. Scully, “Quantum interference effects induced by interacting dark resonances,” Phys. Rev. A 60, 3225–3228 (1999).
[CrossRef]

G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
[CrossRef] [PubMed]

Shubin, I. N.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
[CrossRef] [PubMed]

Stroud Jr., C. R.

Su, J. J.

Y. C. Chen, Y. A. Liao, H. Y. Chiu, J. J. Su, and I. A. Yu, “Observation of the quantum interference phenomenon induced by interacting dark resonances,” Phys. Rev. A 64, 053806 (2001).
[CrossRef]

Y. C. Chen, Y. W. Chen, J. J. Su, J. Y. Huang, and I. A. Yu, “Pump–probe spectroscopy of cold 87Rb atoms in various polarization configurations,” Phys. Rev. A 63, 043808 (2001).
[CrossRef]

Tai?chenachev, A. V.

A. V. Taĭchenachev, A. M. Tumaĭkin, and V. I. Yudin, “On the spontaneous-coherence-transfer-induced sign change of a sub-natural-width nonlinear resonance,” JETP Lett. 69, 819–824 (1999).
[CrossRef]

Tumai?kin, A. M.

A. V. Taĭchenachev, A. M. Tumaĭkin, and V. I. Yudin, “On the spontaneous-coherence-transfer-induced sign change of a sub-natural-width nonlinear resonance,” JETP Lett. 69, 819–824 (1999).
[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]

Vansteenkiste, N.

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Verkerk, P.

J.-Y. Courtois, G. Grynberg, B. Lounis, and P. Verkerk, “Recoil-induced resonances in cesium: an atomic analog to the free-electron laser,” Phys. Rev. Lett. 72, 3017–3020 (1994).
[CrossRef] [PubMed]

Walsworth, R. L.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[CrossRef] [PubMed]

Wang, S.

S. Wang, D. G. Ducreay, R. Pina, M. Yan, and Y. Zhu, “Coherent population trapping and four-wave mixing via dark states in a Doppler-broadened open Rb system,” Phys. Rev. A 61, 033805 (2000).
[CrossRef]

Welch, G. R.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, 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, 2053–2056 (1996).
[CrossRef] [PubMed]

Whitley, R. M.

Xiao, M.

Y. Li and M. Xiao, “Electromagnetically induced transparency in a three-level Λ-type system in rubidium atoms,” Phys. Rev. A 51, R2703–R2706 (1995).
[CrossRef]

Yan, M.

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Figures (5)

Fig. 1
Fig. 1

Probe-absorption spectrum for the system in which the coupling and probe fields drive the |F=1|F=2 and |F=2|F=2 transitions, respectively. The two fields are linearly polarized, and their polarization directions are orthogonal. In the calculation, the coupling frequency ωc is on the resonance, Ωc=3Γ, and the collision rate is γ=0.001Γ.

Fig. 2
Fig. 2

Excitation diagrams for (a) the z axis along the polarization direction of the coupling field, (b) the z axis along the polarization direction of the probe field, and (c) the z axis normal to the polarization directions of both fields. In all diagrams, solid and dashed arrows indicate coupling and probe transitions, respectively.

Fig. 3
Fig. 3

Imaginary parts of the weighted coherences versus probe detuning for the z axis along the polarization direction of the coupling field. All vertical scales are the same, as are all horizontal scales: (a) ρ˜9,5 or ρ˜13,7; (b) ρ˜10,4 or ρ˜12,8; (c) ρ˜10,6 or ρ˜12,6; (d) ρ˜11,5 or ρ˜11,7.

Fig. 4
Fig. 4

Imaginary parts of the weighted coherences versus probe detuning for the z axis along the polarization direction of the probe field. All vertical scales are the same, as are all horizontal scales: (a) ρ˜9,4 or ρ˜13,8; (b) ρ˜10,5 or ρ˜12,7.

Fig. 5
Fig. 5

Imaginary parts of the weighted coherences versus probe detuning for the z axis normal to the polarization directions of both the coupling and probe fields. All vertical scales are the same, as are all horizontal scales: (a) ρ˜9,5 or ρ˜13,7; (b) ρ˜10,4 or ρ˜12,8; (c) ρ˜10,6 or ρ˜12,6; (d) ρ˜11,5 or ρ˜11,7.

Equations (11)

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

dρdt=1i[Hatom+Hcoupling+Hprobe, ρ]+dρdt,
Hatom=(ω1-ω2)i=48|ii|+ω1j=913|jj|,
Hcoupling=-Ωc2 i=139j13[(ˆc*·dˆij)Cij|ij|×exp(iωct)+h.c.],
Hprobe=-Ωp2 i=489j13[(ˆp*·dˆij)Cij|ij|×exp(iωpt)+h.c.],
dρiidt1i3=Γ9j13Cij2ρjj-γρii-12 ki,k=13ρkk,
dρiidt4i8=Γ9j13Cij2ρjj-γρii-14 ki,k=48ρkk,
dρjjdt9j13=-Γρjj,
dρiidtii,1i,i8=-γρii,
dρijdt1i8,9j13=-Γ+γ2ρij,
dρjjdtjj,9j,j13=-Γρjj.
Im3λ22π ΓΩp i=489j13(ˆp*·dˆij)Cijρ˜ji,

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