Abstract

The optical properties of a four-level atomic system via coherent and incoherent pumping fields are investigated. The giant Kerr nonlinearity with reduced linear and nonlinear absorption, which has a major role in decreasing the threshold of optical bistability (OB), can be obtained with subluminal light propagation via adjusting the intensities of coupling fields. An incoherent pumping field is noticed to be an extra parameter to reduce the threshold of OB and multistability, and it can be used as an effective parameter in producing lasing with or without population inversion. In this model, optical multistability is achieved simply by tuning the intensity of coupling laser fields. Furthermore, it is shown that the subluminal and the superluminal light propagation can be obtained by appropriate values of the incoherent pumping rate.

© 2013 Optical Society of America

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  2. A. Imamoglu, J. E. Field, and S. E. Harris, “Lasers without inversion: a closed lifetime broadened system,” Phys. Rev. Lett. 66, 1154–1157 (1991).
    [CrossRef]
  3. S. E. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Phys. Rev. Lett. 81, 3611–3614 (1998).
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  4. Y. P. Niu, S. Q. Gong, R. X. Li, Z. Z. Xu, and X. Y. Liang, “Giant Kerr nonlinearity induced by interacting dark resonance,” Opt. Lett. 30, 3371–3373 (2005).
    [CrossRef]
  5. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74, 2447–2450 (1995).
    [CrossRef]
  6. M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
    [CrossRef]
  7. M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
    [CrossRef]
  8. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
    [CrossRef]
  9. A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 68, 015806 (2004).
    [CrossRef]
  10. J. H. Li, “Controllable optical bistability in a four-subband semiconductor quantum well system,” Phys. Rev. B 75, 155329 (2007).
    [CrossRef]
  11. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–40 (1997).
    [CrossRef]
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  14. H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
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  15. H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
    [CrossRef]
  16. J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
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  18. A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67, 041801(R) (2003).
    [CrossRef]
  19. A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57, 1196–1220 (2010).
    [CrossRef]
  20. J.-H. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
    [CrossRef]
  21. H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77, 031801(R) (2008).
    [CrossRef]
  22. R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 497–502 (2002).
    [CrossRef]
  23. M. Fleischhauer, C. H. Kietel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
    [CrossRef]
  24. B. K. Dutta and P. K. Mahapatra, “Role of incoherent pumping scheme on gain without population inversion in four-level systems,” Phys. Scr. 77, 025403 (2008).
    [CrossRef]
  25. X. Bai, H. Guo, D. Han, and H. Sun, “Effects of incoherent pumping on the phase control of amplification without inversion in a Λ system with spontaneously generated coherence,” J. Opt. B Quantum Semiclass. Opt. 7, 35–40 (2005).
    [CrossRef]
  26. J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
    [CrossRef]
  27. J. Li, R. Yu, J. Liu, P. Huang, and X. Yang, “Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule,” J. Phys. E 41, 70–73 (2008).
    [CrossRef]
  28. J. M. Villas-Boas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
    [CrossRef]
  29. G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
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  32. K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68, 013810 (2003).
  33. X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quantum Semiclass. Opt. 3, 35–41 (2001).
    [CrossRef]
  34. W. Harshawerdhan and G. S. Agarwal, “Controlling optical bistability using electromagnetic-field-induced transparency and quantum interferences,” Phys. Rev. A 53, 1812–1817 (1996).
    [CrossRef]
  35. J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
    [CrossRef]
  36. H. Kang, L. Wen, and Y. Zhu, “Normal and anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
    [CrossRef]
  37. H. Kang, G. Hernandez, and Y. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(2004).
    [CrossRef]
  38. D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
    [CrossRef]
  39. W. H. Xu, J. H. Wu, and J. Y. Gao, “Effects of spontaneously generated coherence on transient process in a Λ system,” Phys. Rev. A 66, 063812 (2002).
    [CrossRef]

2011 (1)

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[CrossRef]

2010 (1)

A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57, 1196–1220 (2010).
[CrossRef]

2008 (3)

H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77, 031801(R) (2008).
[CrossRef]

B. K. Dutta and P. K. Mahapatra, “Role of incoherent pumping scheme on gain without population inversion in four-level systems,” Phys. Scr. 77, 025403 (2008).
[CrossRef]

J. Li, R. Yu, J. Liu, P. Huang, and X. Yang, “Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule,” J. Phys. E 41, 70–73 (2008).
[CrossRef]

2007 (2)

J.-H. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[CrossRef]

J. H. Li, “Controllable optical bistability in a four-subband semiconductor quantum well system,” Phys. Rev. B 75, 155329 (2007).
[CrossRef]

2006 (2)

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
[CrossRef]

2005 (2)

X. Bai, H. Guo, D. Han, and H. Sun, “Effects of incoherent pumping on the phase control of amplification without inversion in a Λ system with spontaneously generated coherence,” J. Opt. B Quantum Semiclass. Opt. 7, 35–40 (2005).
[CrossRef]

Y. P. Niu, S. Q. Gong, R. X. Li, Z. Z. Xu, and X. Y. Liang, “Giant Kerr nonlinearity induced by interacting dark resonance,” Opt. Lett. 30, 3371–3373 (2005).
[CrossRef]

2004 (4)

J. M. Villas-Boas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
[CrossRef]

H. Kang, G. Hernandez, and Y. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(2004).
[CrossRef]

D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 68, 015806 (2004).
[CrossRef]

2003 (4)

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

H. Kang, L. Wen, and Y. Zhu, “Normal and anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67, 041801(R) (2003).
[CrossRef]

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68, 013810 (2003).

2002 (3)

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

W. H. Xu, J. H. Wu, and J. Y. Gao, “Effects of spontaneously generated coherence on transient process in a Λ system,” Phys. Rev. A 66, 063812 (2002).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 497–502 (2002).
[CrossRef]

2001 (3)

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quantum Semiclass. Opt. 3, 35–41 (2001).
[CrossRef]

1999 (2)

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

1998 (1)

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

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–40 (1997).
[CrossRef]

1996 (1)

W. Harshawerdhan and G. S. Agarwal, “Controlling optical bistability using electromagnetic-field-induced transparency and quantum interferences,” Phys. Rev. A 53, 1812–1817 (1996).
[CrossRef]

1995 (2)

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74, 2447–2450 (1995).
[CrossRef]

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef]

1992 (1)

M. Fleischhauer, C. H. Kietel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

1991 (1)

A. Imamoglu, J. E. Field, and S. E. Harris, “Lasers without inversion: a closed lifetime broadened system,” Phys. Rev. Lett. 66, 1154–1157 (1991).
[CrossRef]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

1989 (1)

M. O. Scully, S. Y. Zhu, and A. Gavrielides, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[CrossRef]

1984 (1)

L. A. Lugiato and E. Wolf, ed., “Theory of optical bistability,” Prog. Opt. 21, 69–216 (1984).
[CrossRef]

Agarwal, G. S.

W. Harshawerdhan and G. S. Agarwal, “Controlling optical bistability using electromagnetic-field-induced transparency and quantum interferences,” Phys. Rev. A 53, 1812–1817 (1996).
[CrossRef]

Bai, X.

X. Bai, H. Guo, D. Han, and H. Sun, “Effects of incoherent pumping on the phase control of amplification without inversion in a Λ system with spontaneously generated coherence,” J. Opt. B Quantum Semiclass. Opt. 7, 35–40 (2005).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Bimberg, D.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Bortman-Arbiv, D.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 497–502 (2002).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Brown, A.

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67, 041801(R) (2003).
[CrossRef]

Dutta, B. K.

B. K. Dutta and P. K. Mahapatra, “Role of incoherent pumping scheme on gain without population inversion in four-level systems,” Phys. Scr. 77, 025403 (2008).
[CrossRef]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Field, J. E.

A. Imamoglu, J. E. Field, and S. E. Harris, “Lasers without inversion: a closed lifetime broadened system,” Phys. Rev. Lett. 66, 1154–1157 (1991).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, C. H. Kietel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

Friedman, H.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

Fry, E. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Gao, J. Y.

W. H. Xu, J. H. Wu, and J. Y. Gao, “Effects of spontaneously generated coherence on transient process in a Λ system,” Phys. Rev. A 66, 063812 (2002).
[CrossRef]

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 497–502 (2002).
[CrossRef]

Gavrielides, A.

M. O. Scully, S. Y. Zhu, and A. Gavrielides, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[CrossRef]

Gea-Banacloche, J.

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef]

Gong, S. Q.

Goorskey, D.

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

Govorov, A. O.

J. M. Villas-Boas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
[CrossRef]

Guo, H.

X. Bai, H. Guo, D. Han, and H. Sun, “Effects of incoherent pumping on the phase control of amplification without inversion in a Λ system with spontaneously generated coherence,” J. Opt. B Quantum Semiclass. Opt. 7, 35–40 (2005).
[CrossRef]

Han, D.

X. Bai, H. Guo, D. Han, and H. Sun, “Effects of incoherent pumping on the phase control of amplification without inversion in a Λ system with spontaneously generated coherence,” J. Opt. B Quantum Semiclass. Opt. 7, 35–40 (2005).
[CrossRef]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

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

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–40 (1997).
[CrossRef]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74, 2447–2450 (1995).
[CrossRef]

A. Imamoglu, J. E. Field, and S. E. Harris, “Lasers without inversion: a closed lifetime broadened system,” Phys. Rev. Lett. 66, 1154–1157 (1991).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Harshawerdhan, W.

W. Harshawerdhan and G. S. Agarwal, “Controlling optical bistability using electromagnetic-field-induced transparency and quantum interferences,” Phys. Rev. A 53, 1812–1817 (1996).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Hernandez, G.

H. Kang, G. Hernandez, and Y. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(2004).
[CrossRef]

Hollberg, L.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Hu, X. M.

X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quantum Semiclass. Opt. 3, 35–41 (2001).
[CrossRef]

Huang, P.

J. Li, R. Yu, J. Liu, P. Huang, and X. Yang, “Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule,” J. Phys. E 41, 70–73 (2008).
[CrossRef]

Huang, Q.-J.

J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
[CrossRef]

Imamoglu, A.

A. Imamoglu, J. E. Field, and S. E. Harris, “Lasers without inversion: a closed lifetime broadened system,” Phys. Rev. Lett. 66, 1154–1157 (1991).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

Jain, M.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74, 2447–2450 (1995).
[CrossRef]

Jin, S. Z.

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef]

Joshi, A.

A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57, 1196–1220 (2010).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 68, 015806 (2004).
[CrossRef]

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67, 041801(R) (2003).
[CrossRef]

Kang, H.

H. Kang, G. Hernandez, and Y. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(2004).
[CrossRef]

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

H. Kang, L. Wen, and Y. Zhu, “Normal and anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

Kasapi, A.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74, 2447–2450 (1995).
[CrossRef]

Kash, M. M.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Kietel, C. H.

M. Fleischhauer, C. H. Kietel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

Kim, J. B.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68, 013810 (2003).

Kim, K.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68, 013810 (2003).

Kim, S. K.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68, 013810 (2003).

Kissel, H.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Lee, C.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68, 013810 (2003).

Li, J.

J. Li, R. Yu, J. Liu, P. Huang, and X. Yang, “Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule,” J. Phys. E 41, 70–73 (2008).
[CrossRef]

Li, J. H.

J. H. Li, “Controllable optical bistability in a four-subband semiconductor quantum well system,” Phys. Rev. B 75, 155329 (2007).
[CrossRef]

Li, J.-H.

J.-H. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[CrossRef]

J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
[CrossRef]

Li, R. X.

Li, Y. Q.

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef]

Liang, X. Y.

Lisitsa, M. P.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Liu, J.

J. Li, R. Yu, J. Liu, P. Huang, and X. Yang, “Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule,” J. Phys. E 41, 70–73 (2008).
[CrossRef]

Lü, X.-Y.

J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
[CrossRef]

Lukin, M. D.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Luo, J.-M.

J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
[CrossRef]

Mahapatra, P. K.

B. K. Dutta and P. K. Mahapatra, “Role of incoherent pumping scheme on gain without population inversion in four-level systems,” Phys. Scr. 77, 025403 (2008).
[CrossRef]

Malakyan, Y. P.

D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
[CrossRef]

Mazur, Y. I.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Moon, H. S.

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68, 013810 (2003).

Niu, Y. P.

Petrosyan, D.

D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
[CrossRef]

Rostovtsev, Y.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Salamo, G. J.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Sautenkov, V. A.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Scully, M. O.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

M. Fleischhauer, C. H. Kietel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

M. O. Scully, S. Y. Zhu, and A. Gavrielides, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[CrossRef]

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

Sheng, J.

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[CrossRef]

Su, C.

M. Fleischhauer, C. H. Kietel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

Sun, H.

X. Bai, H. Guo, D. Han, and H. Sun, “Effects of incoherent pumping on the phase control of amplification without inversion in a Λ system with spontaneously generated coherence,” J. Opt. B Quantum Semiclass. Opt. 7, 35–40 (2005).
[CrossRef]

Tarasov, G. G.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Ulloa, S. E.

J. M. Villas-Boas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
[CrossRef]

Villas-Boas, J. M.

J. M. Villas-Boas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
[CrossRef]

Wang, H.

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67, 041801(R) (2003).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

Wang, Z. M.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Warming, T.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Welch, G. R.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Wen, L.

H. Kang, L. Wen, and Y. Zhu, “Normal and anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

Wilson-Gordon, A. D.

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

Wu, H.

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[CrossRef]

H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77, 031801(R) (2008).
[CrossRef]

Wu, J. H.

W. H. Xu, J. H. Wu, and J. Y. Gao, “Effects of spontaneously generated coherence on transient process in a Λ system,” Phys. Rev. A 66, 063812 (2002).
[CrossRef]

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

Xiao, M.

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[CrossRef]

A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57, 1196–1220 (2010).
[CrossRef]

H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77, 031801(R) (2008).
[CrossRef]

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 68, 015806 (2004).
[CrossRef]

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67, 041801(R) (2003).
[CrossRef]

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef]

Xu, W. H.

W. H. Xu, J. H. Wu, and J. Y. Gao, “Effects of spontaneously generated coherence on transient process in a Λ system,” Phys. Rev. A 66, 063812 (2002).
[CrossRef]

Xu, Z. Z.

Y. P. Niu, S. Q. Gong, R. X. Li, Z. Z. Xu, and X. Y. Liang, “Giant Kerr nonlinearity induced by interacting dark resonance,” Opt. Lett. 30, 3371–3373 (2005).
[CrossRef]

X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quantum Semiclass. Opt. 3, 35–41 (2001).
[CrossRef]

Yamamoto, Y.

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

Yang, W.

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 68, 015806 (2004).
[CrossRef]

Yang, X.

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[CrossRef]

J. Li, R. Yu, J. Liu, P. Huang, and X. Yang, “Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule,” J. Phys. E 41, 70–73 (2008).
[CrossRef]

Yin, G. Y.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74, 2447–2450 (1995).
[CrossRef]

Yu, R.

J. Li, R. Yu, J. Liu, P. Huang, and X. Yang, “Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule,” J. Phys. E 41, 70–73 (2008).
[CrossRef]

Zhu, S. Y.

M. O. Scully, S. Y. Zhu, and A. Gavrielides, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[CrossRef]

Zhu, Y.

H. Kang, G. Hernandez, and Y. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(2004).
[CrossRef]

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

H. Kang, L. Wen, and Y. Zhu, “Normal and anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

Zhuchenko, Z. Y.

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Zibrov, A. S.

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

Zubairy, M. S.

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

J. Mod. Opt. (1)

A. Joshi and M. Xiao, “Atomic optical bistability in two- and three-level systems: perspectives and prospects,” J. Mod. Opt. 57, 1196–1220 (2010).
[CrossRef]

J. Opt. B Quantum Semiclass. Opt. (2)

X. Bai, H. Guo, D. Han, and H. Sun, “Effects of incoherent pumping on the phase control of amplification without inversion in a Λ system with spontaneously generated coherence,” J. Opt. B Quantum Semiclass. Opt. 7, 35–40 (2005).
[CrossRef]

X. M. Hu and Z. Z. Xu, “Phase control of amplitude-fluctuation-induced bistability,” J. Opt. B Quantum Semiclass. Opt. 3, 35–41 (2001).
[CrossRef]

J. Phys. E (1)

J. Li, R. Yu, J. Liu, P. Huang, and X. Yang, “Voltage-controlled optical bistability of a tunable three-level system in a quantum-dot molecule,” J. Phys. E 41, 70–73 (2008).
[CrossRef]

Nature (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 meters per second in an ultracold atomic gas,” Nature 397, 594–598 (1999).
[CrossRef]

Opt. Commun. (2)

J.-H. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[CrossRef]

M. Fleischhauer, C. H. Kietel, M. O. Scully, and C. Su, “Lasing without inversion and enhancement of the index of refraction via interference of incoherent pump processes,” Opt. Commun. 87, 109–114 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

A. Joshi, W. Yang, and M. Xiao, “Effect of spontaneously generated coherence on the dynamics of multi-level atomic systems,” Phys. Lett. A 68, 015806 (2004).
[CrossRef]

Phys. Rev. A (12)

D. Petrosyan and Y. P. Malakyan, “Magneto-optical rotation and cross-phase modulation via coherently driven four-level atoms in a tripod configuration,” Phys. Rev. A 70, 023822 (2004).
[CrossRef]

H. Wu and M. Xiao, “White-light cavity with competing linear and nonlinear dispersions,” Phys. Rev. A 77, 031801(R) (2008).
[CrossRef]

J. Sheng, X. Yang, H. Wu, and M. Xiao, “Modified self-Kerr-nonlinearity in a four-level N-type atomic system,” Phys. Rev. A 84, 053820 (2011).
[CrossRef]

A. Joshi, A. Brown, H. Wang, and M. Xiao, “Controlling optical bistability in a three-level atomic system,” Phys. Rev. A 67, 041801(R) (2003).
[CrossRef]

J. H. Wu and J. Y. Gao, “Phase control of light amplification without inversion in a Λ system with spontaneously generated coherence,” Phys. Rev. A 65, 063807 (2002).
[CrossRef]

W. Harshawerdhan and G. S. Agarwal, “Controlling optical bistability using electromagnetic-field-induced transparency and quantum interferences,” Phys. Rev. A 53, 1812–1817 (1996).
[CrossRef]

J.-H. Li, X.-Y. Lü, J.-M. Luo, and Q.-J. Huang, “Optical bistability and multistability via atomic coherence in an N-type atomic medium,” Phys. Rev. A 74, 035801 (2006).
[CrossRef]

H. Kang, L. Wen, and Y. Zhu, “Normal and anomalous dispersion and gain in a resonant coherent medium,” Phys. Rev. A 68, 063806 (2003).
[CrossRef]

H. Kang, G. Hernandez, and Y. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(2004).
[CrossRef]

D. Bortman-Arbiv, A. D. Wilson-Gordon, and H. Friedman, “Phase control of group velocity: from subluminal to superluminal light propagation,” Phys. Rev. A 63, 043818 (2001).
[CrossRef]

W. H. Xu, J. H. Wu, and J. Y. Gao, “Effects of spontaneously generated coherence on transient process in a Λ system,” Phys. Rev. A 66, 063812 (2002).
[CrossRef]

K. Kim, H. S. Moon, C. Lee, S. K. Kim, and J. B. Kim, “Observation of arbitrary group velocities of light from superluminal to subluminal on a single atomic transition line,” Phys. Rev. A 68, 013810 (2003).

Phys. Rev. B (2)

J. M. Villas-Boas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
[CrossRef]

J. H. Li, “Controllable optical bistability in a four-subband semiconductor quantum well system,” Phys. Rev. B 75, 155329 (2007).
[CrossRef]

Phys. Rev. Lett. (9)

H. Wang, D. Goorskey, and M. Xiao, “Enhanced Kerr nonlinearity via atomic coherence in a three-level atomic system,” Phys. Rev. Lett. 87, 073601 (2001).
[CrossRef]

H. Kang and Y. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
[CrossRef]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74, 2447–2450 (1995).
[CrossRef]

M. Xiao, Y. Q. Li, S. Z. Jin, and J. Gea-Banacloche, “Measurement of dispersive properties of electromagnetically induced transparency in rubidium atoms,” Phys. Rev. Lett. 74, 666–669 (1995).
[CrossRef]

M. M. Kash, V. A. Sautenkov, A. S. Zibrov, L. Hollberg, G. R. Welch, M. D. Lukin, Y. Rostovtsev, E. S. Fry, and M. O. Scully, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229–5232 (1999).
[CrossRef]

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[CrossRef]

M. O. Scully, S. Y. Zhu, and A. Gavrielides, “Degenerate quantum-beat laser: lasing without inversion and inversion without lasing,” Phys. Rev. Lett. 62, 2813–2816 (1989).
[CrossRef]

A. Imamoglu, J. E. Field, and S. E. Harris, “Lasers without inversion: a closed lifetime broadened system,” Phys. Rev. Lett. 66, 1154–1157 (1991).
[CrossRef]

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

Phys. Scr. (1)

B. K. Dutta and P. K. Mahapatra, “Role of incoherent pumping scheme on gain without population inversion in four-level systems,” Phys. Scr. 77, 025403 (2008).
[CrossRef]

Phys. Today (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–40 (1997).
[CrossRef]

Prog. Opt. (2)

L. A. Lugiato and E. Wolf, ed., “Theory of optical bistability,” Prog. Opt. 21, 69–216 (1984).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Slow and fast light,” Prog. Opt. 43, 497–502 (2002).
[CrossRef]

Semiconductors (1)

G. G. Tarasov, Z. Y. Zhuchenko, M. P. Lisitsa, Y. I. Mazur, Z. M. Wang, G. J. Salamo, T. Warming, D. Bimberg, and H. Kissel, “Optical detection of asymmetric quantum-dot molecules in double-layer InAs/GaAs structures,” Semiconductors 40, 79–83 (2006).
[CrossRef]

Other (2)

M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University, 1997).

R. W. Boyd, Nonlinear Optics (Academic, 2003).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic diagram of proposed four-level atomic system.

Fig. 2.
Fig. 2.

Linear (a) and nonlinear (b) absorption and Kerr nonlinearity (c) versus probe field detuning (d) Kerr nonlinearity comparison between our model and the model in [39]. The common parameters are γ1=γ2=2γ, γ3=0.1γ, γ4=0.1γ, Ω2=5γ, and Ω1=5γ (solid curve), Ω1=10γ (dotted curve).

Fig. 3.
Fig. 3.

Real part of susceptibility (a) and group velocity (b) versus probe field detuning. Solid curve corresponds to Ω1=5γ and dotted curve corresponds to Ω1=10γ. Other parameters are the same as those in Fig. 2.

Fig. 4.
Fig. 4.

Unidirectional ring cavity with sample of length L.

Fig. 5.
Fig. 5.

Plots of the input–output field curves for different values of Ω1. Other parameters values are chosen as γ1=γ2=2γ, γ3=0.1γ, γ4=0.1γ, Δp=Δ1=Δ2=0, C=200, and Ω2=1γ.

Fig. 6.
Fig. 6.

Plot of the input–output field curves for different values of Ω1. The dashed curve corresponds to Ω1=5γ, and the solid curve corresponds to Ω1=10γ. The other parameters are the same as in Fig. 2.

Fig. 7.
Fig. 7.

Plot of the input–output field curves for different values of the incoherent pumping rate. The solid curve corresponds to r=0.5γ, and the dotted curve corresponds to r=3γ. The other parameters are the same as in Fig. 2.

Fig. 8.
Fig. 8.

Absorption spectrum (a) and population inversion (b) as function of probe field detuning. r=0.0 (solid curve), r=1γ (dashed curve), and r=2γ (dotted curve). The other parameters are same as in Fig. 2.

Fig. 9.
Fig. 9.

Real (a) and imaginary (b) part of susceptibility and the group index (c) versus the probe field detuning for Ω1=5γ and Ω2=10γ·r=0.0 (solid curve), r=1γ (dashed curve), and r=2γ (dotted curve). The other parameters are the same as in Fig. 2.

Equations (11)

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ρ41=(iΔp+12(γ1+γ2))ρ41+i2Ωp(ρ11ρ44)i2Ω1ρ42+i2Ω2ρ31,ρ42=(i(ΔpΔ1)+12(γ1+γ2+γ4+r))ρ42i2Ω1ρ41+i2Ω2ρ32+i2Ωpρ12,ρ43=(iΔ2+12(γ1+γ2+γ3+r))ρ43+i2Ωpρ13+i2Ω2(ρ33ρ44),ρ31=(i(ΔpΔ2)+12(γ3+r))ρ31+i2Ω2ρ41i2Ω1ρ32i2Ωpρ34,ρ32=(i(Δp(Δ1+Δ2)+r)+12(γ3+γ4))ρ32i2Ω1ρ31+i2Ω2ρ42,ρ21=(iΔ1+12(γ4+r))ρ21+i2Ω1(ρ11ρ22)i2Ωpρ24,ρ33=i2Ω2(ρ43ρ34)+rρ22+γ2ρ44γ3ρ33,ρ11=γ1ρ44+γ4ρ22+i2Ω1(ρ21ρ12)+i2Ωp(ρ41ρ14),ρ22=γ3ρ33γ4ρ22+i2Ω1(ρ12ρ21)rρ22,
χ(1)=2N|P14|2ε0Ωpρ41(1),
χ(3)=2N|P14|43ε03Ωp3ρ41(3),
vg=c1+2πRe(χ(νp))+2πνpνpRe(χ(νp)).
E=Epeiνpt+E1eiν1t+E2eiν2t+C.C,
Ept+cEpz=iωp2ε0P(ωp).
P(ωp)=NP14ρ41.
Epz=iNωpP142cε0ρ41.
Ep(L)=EpTT,
Ep(0)=TEPI+REp(L),
y=2xicγ1ρ41.

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