Abstract

New spectral features in an inhomogeneously broadened N-type four-level atomic system are analyzed and discussed. The atomic-level scheme uses an incoherent pumping rate in place of the incoherent recycling pump. We show that the gain profile includes an extra dip that appears only in the Doppler-broadened case. The dependence of this feature on various parameters, as well as consequences for the dispersion, are explored theoretically. For certain combinations of temperature and incoherent pump rate, this gain is shown to be independent of temperature fluctuations.

© 2000 Optical Society of America

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  1. K. J. Boller, A. Imamoǧlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
    [CrossRef] [PubMed]
  2. J. Gea-Banacloche, Y. Li, S. Jin, and M. Xiao, “Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: theory and experiment,” Phys. Rev. A 51, 576–584 (1995).
    [CrossRef] [PubMed]
  3. Y. Li and M. Xiao, “Electromagnetically induced transparency in a three-level Λ-type system of rubidium atoms,” Phys. Rev. A 51, R2703–R2706 (1995).
    [CrossRef]
  4. S. E. Harris, “Lasers without inversion: interference of lifetime-broadened resonances,” Phys. Rev. Lett. 62, 1033–1036 (1989).
    [CrossRef] [PubMed]
  5. A. Immamoǧlu and S. E. Harris, “Lasers without inversion: interference of dressed lifetime-broadened states,” Opt. Lett. 14, 1344–1346 (1989).
    [CrossRef]
  6. Y. Zhu, M. Xiao, and Y. Zhao, “Intensity characteristics of inversionless lasers from induced atomic coherence,” Phys. Rev. A 49, 4016–4023 (1994).
    [CrossRef] [PubMed]
  7. E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
    [CrossRef] [PubMed]
  8. G. G. Padmabandu, G. R. Welch, I. N. Shubin, E. S. Fry, D. E. Nikonov, M. D. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
    [CrossRef] [PubMed]
  9. A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
    [CrossRef] [PubMed]
  10. M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1855–1858 (1991).
    [CrossRef] [PubMed]
  11. O. Kocharovskaya, “Amplification and lasing without inversion,” Phys. Rep. 219, 175–190 (1992).
    [CrossRef]
  12. E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
    [CrossRef]
  13. W. J. Brown, J. R. Gardner, D. J. Gauthier, and R. Vilaseca, “Amplification of laser beams counterpropagating through a potassium vapor: the effects of atomic coherence,” Phys. Rev. A 56, 3255–3261 (1997).
    [CrossRef]
  14. A. Karawajczyk and J. Zakrzewski, “Lasers without inversion in a Doppler-broadened medium,” Phys. Rev. A 51, 830–834 (1995).
    [CrossRef] [PubMed]
  15. D. Z. Wang and J. Y. Gao, “Effect of Doppler broadening on optical gain without inversion in a four-level model,” Phys. Rev. A 52, 3201–3208 (1995).
    [CrossRef] [PubMed]
  16. G. Vemuri and G. S. Agarwal, “Role of inhomogeneous broadening in lasing without inversion in ladder systems,” Phys. Rev. A 53, 1060–1064 (1996).
    [CrossRef] [PubMed]
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  18. L. M. Narducci, M. O. Scully, C. H. Keitel, S. Y. Zhu, and M. H. Doss, “Physical origin of the gain in a four-level model of a Raman driven laser without inversion,” Opt. Commun. 86, 324–332 (1991).
    [CrossRef]
  19. H. M. Doss, L. M. Narducci, M. O. Scully, and J. Gao, “Theoretical analysis of a four-level laser without inversion driven by a pulsed Raman field,” Opt. Commun. 95, 57–63 (1992).
    [CrossRef]

1997

W. J. Brown, J. R. Gardner, D. J. Gauthier, and R. Vilaseca, “Amplification of laser beams counterpropagating through a potassium vapor: the effects of atomic coherence,” Phys. Rev. A 56, 3255–3261 (1997).
[CrossRef]

1996

G. Vemuri and G. S. Agarwal, “Role of inhomogeneous broadening in lasing without inversion in ladder systems,” Phys. Rev. A 53, 1060–1064 (1996).
[CrossRef] [PubMed]

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. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
[CrossRef] [PubMed]

1995

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

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

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

A. Karawajczyk and J. Zakrzewski, “Lasers without inversion in a Doppler-broadened medium,” Phys. Rev. A 51, 830–834 (1995).
[CrossRef] [PubMed]

D. Z. Wang and J. Y. Gao, “Effect of Doppler broadening on optical gain without inversion in a four-level model,” Phys. Rev. A 52, 3201–3208 (1995).
[CrossRef] [PubMed]

1994

Y. Zhu, M. Xiao, and Y. Zhao, “Intensity characteristics of inversionless lasers from induced atomic coherence,” Phys. Rev. A 49, 4016–4023 (1994).
[CrossRef] [PubMed]

1993

E. S. Fry, X. Li, D. Nikonov, G. G. Padmabandu, M. O. Scully, A. V. Smith, F. K. Tittel, C. Wang, S. R. Wilkinson, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

1992

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

H. M. Doss, L. M. Narducci, M. O. Scully, and J. Gao, “Theoretical analysis of a four-level laser without inversion driven by a pulsed Raman field,” Opt. Commun. 95, 57–63 (1992).
[CrossRef]

1991

L. M. Narducci, M. O. Scully, C. H. Keitel, S. Y. Zhu, and M. H. Doss, “Physical origin of the gain in a four-level model of a Raman driven laser without inversion,” Opt. Commun. 86, 324–332 (1991).
[CrossRef]

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

M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1855–1858 (1991).
[CrossRef] [PubMed]

1989

S. E. Harris, “Lasers without inversion: interference of lifetime-broadened resonances,” Phys. Rev. Lett. 62, 1033–1036 (1989).
[CrossRef] [PubMed]

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

Agarwal, G. S.

G. Vemuri and G. S. Agarwal, “Role of inhomogeneous broadening in lasing without inversion in ladder systems,” Phys. Rev. A 53, 1060–1064 (1996).
[CrossRef] [PubMed]

Arimondo, E.

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

Boller, K. J.

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

Brown, W. J.

W. J. Brown, J. R. Gardner, D. J. Gauthier, and R. Vilaseca, “Amplification of laser beams counterpropagating through a potassium vapor: the effects of atomic coherence,” Phys. Rev. A 56, 3255–3261 (1997).
[CrossRef]

Doss, H. M.

H. M. Doss, L. M. Narducci, M. O. Scully, and J. Gao, “Theoretical analysis of a four-level laser without inversion driven by a pulsed Raman field,” Opt. Commun. 95, 57–63 (1992).
[CrossRef]

Doss, M. H.

L. M. Narducci, M. O. Scully, C. H. Keitel, S. Y. Zhu, and M. H. Doss, “Physical origin of the gain in a four-level model of a Raman driven laser without inversion,” Opt. Commun. 86, 324–332 (1991).
[CrossRef]

Fry, E. S.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, E. S. Fry, D. E. Nikonov, M. D. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
[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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

Gao, J.

H. M. Doss, L. M. Narducci, M. O. Scully, and J. Gao, “Theoretical analysis of a four-level laser without inversion driven by a pulsed Raman field,” Opt. Commun. 95, 57–63 (1992).
[CrossRef]

Gao, J. Y.

D. Z. Wang and J. Y. Gao, “Effect of Doppler broadening on optical gain without inversion in a four-level model,” Phys. Rev. A 52, 3201–3208 (1995).
[CrossRef] [PubMed]

Gardner, J. R.

W. J. Brown, J. R. Gardner, D. J. Gauthier, and R. Vilaseca, “Amplification of laser beams counterpropagating through a potassium vapor: the effects of atomic coherence,” Phys. Rev. A 56, 3255–3261 (1997).
[CrossRef]

Gauthier, D. J.

W. J. Brown, J. R. Gardner, D. J. Gauthier, and R. Vilaseca, “Amplification of laser beams counterpropagating through a potassium vapor: the effects of atomic coherence,” Phys. Rev. A 56, 3255–3261 (1997).
[CrossRef]

Gea-Banacloche, J.

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

Harris, S. E.

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

S. E. Harris, “Lasers without inversion: interference of lifetime-broadened resonances,” Phys. Rev. Lett. 62, 1033–1036 (1989).
[CrossRef] [PubMed]

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

Hollberg, L.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Imamog?lu, A.

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

Immamog?lu, A.

Jin, S.

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

Jukin, M. D.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, E. S. Fry, D. E. Nikonov, M. D. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
[CrossRef] [PubMed]

Karawajczyk, A.

A. Karawajczyk and J. Zakrzewski, “Lasers without inversion in a Doppler-broadened medium,” Phys. Rev. A 51, 830–834 (1995).
[CrossRef] [PubMed]

Keitel, C. H.

L. M. Narducci, M. O. Scully, C. H. Keitel, S. Y. Zhu, and M. H. Doss, “Physical origin of the gain in a four-level model of a Raman driven laser without inversion,” Opt. Commun. 86, 324–332 (1991).
[CrossRef]

Kocharovskaya, O.

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

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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

Li, Y.

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

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

Lukin, M. D.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Narducci, L. M.

H. M. Doss, L. M. Narducci, M. O. Scully, and J. Gao, “Theoretical analysis of a four-level laser without inversion driven by a pulsed Raman field,” Opt. Commun. 95, 57–63 (1992).
[CrossRef]

L. M. Narducci, M. O. Scully, C. H. Keitel, S. Y. Zhu, and M. H. Doss, “Physical origin of the gain in a four-level model of a Raman driven laser without inversion,” Opt. Commun. 86, 324–332 (1991).
[CrossRef]

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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

Nikonov, D. E.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, E. S. Fry, D. E. Nikonov, M. D. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
[CrossRef] [PubMed]

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Padmabandu, G. G.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, E. S. Fry, D. E. Nikonov, M. D. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
[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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

Robinson, H. G.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Scully, M. O.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, E. S. Fry, D. E. Nikonov, M. D. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
[CrossRef] [PubMed]

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

H. M. Doss, L. M. Narducci, M. O. Scully, and J. Gao, “Theoretical analysis of a four-level laser without inversion driven by a pulsed Raman field,” Opt. Commun. 95, 57–63 (1992).
[CrossRef]

M. O. Scully, “Enhancement of the index of refraction via quantum coherence,” Phys. Rev. Lett. 67, 1855–1858 (1991).
[CrossRef] [PubMed]

L. M. Narducci, M. O. Scully, C. H. Keitel, S. Y. Zhu, and M. H. Doss, “Physical origin of the gain in a four-level model of a Raman driven laser without inversion,” Opt. Commun. 86, 324–332 (1991).
[CrossRef]

Shubin, I. N.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, E. S. Fry, D. E. Nikonov, M. D. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
[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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

Velichansky, V. L.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Vemuri, G.

G. Vemuri and G. S. Agarwal, “Role of inhomogeneous broadening in lasing without inversion in ladder systems,” Phys. Rev. A 53, 1060–1064 (1996).
[CrossRef] [PubMed]

Vilaseca, R.

W. J. Brown, J. R. Gardner, D. J. Gauthier, and R. Vilaseca, “Amplification of laser beams counterpropagating through a potassium vapor: the effects of atomic coherence,” Phys. Rev. A 56, 3255–3261 (1997).
[CrossRef]

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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

Wang, D. Z.

D. Z. Wang and J. Y. Gao, “Effect of Doppler broadening on optical gain without inversion in a four-level model,” Phys. Rev. A 52, 3201–3208 (1995).
[CrossRef] [PubMed]

Welch, G. R.

G. G. Padmabandu, G. R. Welch, I. N. Shubin, E. S. Fry, D. E. Nikonov, M. D. Jukin, and M. O. Scully, “Laser oscillation without population inversion in a sodium atomic beam,” Phys. Rev. Lett. 76, 2053–2056 (1996).
[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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

Xiao, M.

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

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

Y. Zhu, M. Xiao, and Y. Zhao, “Intensity characteristics of inversionless lasers from induced atomic coherence,” Phys. Rev. A 49, 4016–4023 (1994).
[CrossRef] [PubMed]

Zakrzewski, J.

A. Karawajczyk and J. Zakrzewski, “Lasers without inversion in a Doppler-broadened medium,” Phys. Rev. A 51, 830–834 (1995).
[CrossRef] [PubMed]

Zhao, Y.

Y. Zhu, M. Xiao, and Y. Zhao, “Intensity characteristics of inversionless lasers from induced atomic coherence,” Phys. Rev. A 49, 4016–4023 (1994).
[CrossRef] [PubMed]

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, and S. Y. Zhu, “Atomic coherence effects within the sodium D1 line: lasing without inversion via population trapping,” Phys. Rev. Lett. 70, 3235–3238 (1993).
[CrossRef] [PubMed]

L. M. Narducci, M. O. Scully, C. H. Keitel, S. Y. Zhu, and M. H. Doss, “Physical origin of the gain in a four-level model of a Raman driven laser without inversion,” Opt. Commun. 86, 324–332 (1991).
[CrossRef]

Zhu, Y.

Y. Zhu, M. Xiao, and Y. Zhao, “Intensity characteristics of inversionless lasers from induced atomic coherence,” Phys. Rev. A 49, 4016–4023 (1994).
[CrossRef] [PubMed]

Zibrov, A. S.

A. S. Zibrov, M. D. Lukin, D. E. Nikonov, L. Hollberg, M. O. Scully, V. L. Velichansky, and H. G. Robinson, “Experimental demonstration of laser oscillation without population inversion via quantum interference in Rb,” Phys. Rev. Lett. 75, 1499–1502 (1995).
[CrossRef] [PubMed]

Opt. Commun.

L. M. Narducci, M. O. Scully, C. H. Keitel, S. Y. Zhu, and M. H. Doss, “Physical origin of the gain in a four-level model of a Raman driven laser without inversion,” Opt. Commun. 86, 324–332 (1991).
[CrossRef]

H. M. Doss, L. M. Narducci, M. O. Scully, and J. Gao, “Theoretical analysis of a four-level laser without inversion driven by a pulsed Raman field,” Opt. Commun. 95, 57–63 (1992).
[CrossRef]

Opt. Lett.

Phys. Rep.

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

Phys. Rev. A

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

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

Y. Zhu, M. Xiao, and Y. Zhao, “Intensity characteristics of inversionless lasers from induced atomic coherence,” Phys. Rev. A 49, 4016–4023 (1994).
[CrossRef] [PubMed]

W. J. Brown, J. R. Gardner, D. J. Gauthier, and R. Vilaseca, “Amplification of laser beams counterpropagating through a potassium vapor: the effects of atomic coherence,” Phys. Rev. A 56, 3255–3261 (1997).
[CrossRef]

A. Karawajczyk and J. Zakrzewski, “Lasers without inversion in a Doppler-broadened medium,” Phys. Rev. A 51, 830–834 (1995).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Equivalent physical models for our system: (a) Four-level model. A strong coupling laser drives |3〉–|2〉, a weak probe drives |1〉–|2〉, and an inhomogeneous recycling field places a small population in level |4〉. (b) Three-level model. We have replaced level |4〉 and the incoherent recycling field with a ΓI, a “decay” from |1〉 to |3〉.

Fig. 2
Fig. 2

Gain for different values of ΓI. The normalized gain is plotted versus the probe detuning for ΓI=0.4Γ21 (dashed curve), with a population inversion of 0.29, and for ΓI=0.3Γ21 (solid curve), with a population inversion of 0.17. The other parameters are given in Table 1.

Fig. 3
Fig. 3

Dispersion for different values of ΓI. The normalized gain is plotted versus the probe detuning for ΓI=0.4Γ21 (dashed curve), with a population inversion of 0.29, and for ΓI=0.3Γ21 (solid curve), with a population inversion of 0.17. The other parameters are given in Table 1.

Fig. 4
Fig. 4

Gain for different values of T. The normalized gain is plotted versus the probe detuning for T=100 K (dashed curve), with a population inversion of 0.10, and for T=300 K (solid curve), with a population inversion of 0.23. The other parameters are given in Table 1.

Fig. 5
Fig. 5

Gain for different values of T, one being very small. The normalized gain is plotted versus the probe detuning for T=20 K (dashed curve), with a population inversion of -0.08, and for T=300 K (solid curve), with a population inversion of 0.23. The other parameters are given in Table 1.

Fig. 6
Fig. 6

Gain versus ΓI for different temperatures: (a) T=300 K, (b) T=125 K, and (c) T=50 K. The probe detuning is Δp=10.2 MHz, and the other parameters are given in Table 1.

Fig. 7
Fig. 7

Closeup plot of the gain versus detuning for different temperatures: (a) T=300 K, (b) T=125 K, and (c) T=50 K. Notice that at detunings of ±10.2Γ21, the gain is the same, regardless of T. The value of ΓI is 0.1575Γ21, and the other parameters are given in Table 1.

Tables (1)

Tables Icon

Table 1 Default Atomic and Laser Parameters

Equations (34)

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ρˆ˙=-i[H, ρˆ]+L(ρˆ),
H=-Δp|22|-(Δp-Δc)|31|+Ωpc|21|+Ωc2|23|+c.c.,
L(ρˆ)=(Γ21ρ22+Γ31ρ33)|11|-12ΓI(|11|ρˆ+ρˆ|11|)-12(Γ21+Γ23)(|22|ρˆ+ρˆ|22|)+(Γ23ρ22+ΓIρ11)|33|-12Γ31(|33|ρˆ+ρˆ|33|).
ρ˙11=-i2Ωp*ρ21+i2Ωpρ21*+Γ21ρ22+Γ31ρ33-ΓIρ11,
ρ˙33=-i2Ωc*ρ23+i2Ωcρ23*+Γ23ρ22-Γ31ρ11+ΓIρ11,
ρ˙21=(iΔp-γ21)ρ21+i2Ωp(ρ22-ρ11)-i2Ωcρ31,
ρ˙23=(iΔc-γ23)ρ23+i2Ωc(ρ22-ρ33)-i2Ωpρ31*,
ρ˙31=[i(Δp-Δc)-γ31]ρ31-i2Ωc*ρ21+i2Ωpρ23*,
Δp(ωp+iγp)-ω21,
Δc-(ωc+iγc)+ω23,
γ21γ21+γp,
γ23γ23+γc,
γ31γ31+γp+γc.
ρ23*=i2Ωp*ρ31-Ωc*(ρ22-ρ33)iΔc+γ23,
ρ31=i2Ωc*ρ21-Ωpρ23*i(Δp-Δc)-γ31/2.
ρ31=(iΔc+γ23)ΩpΩc*(ρ22-ρ11)-(iΔp-γ21)ΩpΩc*(ρ22-ρ33)4[i(Δp-Δc)-γ31/2](iΔp-γ21)(iΔc+γ23)+(iΔc+γ23)|Ωc|2-(iΔp-γ21)|Ωp|2.
R(Δp)=γ232(2γ21γ31-4Δp2+|Ωc|2)2+4γ232Δp2(2γ21-γ31)2(Δp2+γ212)|Ωp|41.
ρ22(0)=-ρ33(0)+ΓIΓ21+ΓI,
ρ33(0)=WC+Γ23+Γ21WC(1+)+(Γ23-ΓI)+(Γ31+ΓI)ΓIΓ21+ΓI,
Wcγ23|Ωc|2/2Δc2+γ232,Γ31+ΓIΓ21+ΓI.
ρ21
=-Ωp2(ρ22(0)-ρ11(0))(Δp-iγ21)Δp2+γ212+Ωp2×(AD+BC)(iΔp+γ21)+(AC-BD)(Δp-iγ21)(C2+D2)(Δp2+γ212),
A=|Ωc|2[γ23(ρ22(0)-ρ11(0))+γ21(ρ22(0)-ρ33(0))],
B=|Ωc|2[Δc(ρ22(0)-ρ11(0))-Δp(ρ22(0)-ρ33(0))],
C=2γ31(ΔpΔc+γ21γ23)-4(Δp-Δc)(Δpγ23-Δcγ21)+γ23|Ωc|2,
D=2γ31(Δpγ23-Δcγ21)+4(Δp-Δc)(ΔpΔc+γ21γ23)-Δc|Ωc|2.
χ=-2Nμ212Ωpρ21
ΔpΔp+ωpvc,ΔcΔc+ωcvc,
N(v)dv=N0uπexp-v2u2dv,
αα0=-γ21(ρ22(0)-ρ11(0))(Δp+ωp v/c2)+γ212+(Δp+ωpv/c)(AD+BC)-γ21(AC-BD)[(Δp+ωpv/c)2+γ212](C2+D2)×exp-v2u2dv,
α0=- γ21(ΓI=0)[γ21(ΓI=0)]2+(ωpv/c)2exp-v2u2dv,
ββmax=-(Δp+ωpv/c)(ρ22(0)-ρ11(0))(Δp+ωpv/c)2+γ212+(Δp+ωpv/c)(AC-BD)+γ21(AD+BC)[(Δp+ωpv/c)2+γ212](C2+D2)×exp-v2u2dv,
ddΔp- Δp+ωpv/c(Δp+ωpv/c)2+[γ21(ΓI=0)]2
×exp-v2u2dv=0

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