Abstract

With one weak pulsed probe field, one strong pumping field, and one coupling field, superluminal optical solitons are formed in a lifetime-broadened Λ-type atomic medium with two-folded levels. The corresponding group velocity of the solitons can be larger than the vacuum light speed c; i.e., superluminal solitons can be presented.

© 2007 Optical Society of America

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References

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  1. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
  2. J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark,L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley,K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider, and W. Phillips, "Generating solitons by phase engineering of a Bose-Einstein condensate," Science 287, 97-101 (2000).
    [CrossRef]
  3. B. Wu, J. Liu, and Q. Niu, "Controlled generation of dark solitons with phase imprinting," Phys. Rev. Lett. 88, 034102 (2002).
    [CrossRef]
  4. H. A. Haus and W. S. Wong, "Solitons in optical communications," Rev. Mod. Phys. 68, 423-444 (1996), and references therein.
    [CrossRef]
  5. H. Kang and Y. Zhu, "Observation of large Kerr nonlinearity at low light intensities," Phys. Rev. Lett. 91, 093601 (2003).
    [CrossRef] [PubMed]
  6. T. Hong, "Spatial weak-light solitons in an electromagnetically induced nonlinear waveguide," Phys. Rev. Lett. 90, 183901 (2003).
    [CrossRef] [PubMed]
  7. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behrrozi, "Light speed reduction to 17 meterspersecond in an ultracold atomic gas," Nature 397, 594-598 (1999).
    [CrossRef]
  8. Y. Wu and L. Deng, "Ultraslow optical solitons in a cold four-state medium," Phys. Rev. Lett. 93, 143904 (2004).
    [CrossRef] [PubMed]
  9. Y. Wu and L. Deng, "Ultraslow bright and dark optical solitons in a cold three-state medium," Opt. Lett. 29, 2064-2066 (2004).
    [CrossRef] [PubMed]
  10. D. Han, Y. Zeng, Y. Bai, and C. Huang, "Superluminal optical solitons in a four-level tripod atomic system," J. Phys. B 39, 3029-3035 (2006).
    [CrossRef]
  11. D. Solli, R. Y. Chiao, and J. M. Hickmann, "Superluminal optical solitons in a four-level tripod atomic system," Phys. Rev. E 66, 056601 (2002).
    [CrossRef]
  12. R. Y. Chiao and A. M. Steinberg, Progress in Optics (Elsevier, 1997).
  13. L. J. Wang, A. Kuzmich, and P. Pogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
    [CrossRef] [PubMed]
  14. 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).
    [CrossRef]
  15. G. S. Agarwal, T. N. Dey, and S. Menon, "Knob for changing light propagation from subluminal to superluminal," Phys. Rev. A 64, 053809 (2001).
    [CrossRef]
  16. D. Han, H. Guo, Y. Bai, and H. Sun, "Subluminal and superluminal propagation of light in an N-type medium," Phys. Lett. A 334, 243-248 (2005).
    [CrossRef]
  17. D. Han, H. Guo, Y. BaiH. Sun, and Y. Zeng, "SGC switching between subluminal to superluminal propagation in V-type atom," Commun. Theor. Phys. 46, 731-734 (2006).
    [CrossRef]
  18. 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]
  19. C. Liu, S. Gong, D. Cheng, X. Fan, and Z. Xu, "Atom localization via interference of dark resonances," Phys. Rev. A 73, 025801 (2006).
    [CrossRef]
  20. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, "Electromagnetically induced transparency: propagation dynamics," Phys. Rev. Lett. 74, 2447-2450 (1995).
    [CrossRef] [PubMed]
  21. R. Buffa, S. Cavalieri, and M. V. Tognetti, "Coherent control of temporal pulse shaping by electromagnetically induced transparency," Phys. Rev. A 69, 033815 (2004).
    [CrossRef]
  22. J.-H. Li, W.-X. Yang, Z.-M. Zhan, and J.-C. Peng, "Ultraslow bright and dark solitons using only a pulsed laser in a cold three-state medium," Chin. Phys. Lett. 22, 357-360 (2005).
    [CrossRef]
  23. 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]

2006 (3)

D. Han, Y. Zeng, Y. Bai, and C. Huang, "Superluminal optical solitons in a four-level tripod atomic system," J. Phys. B 39, 3029-3035 (2006).
[CrossRef]

D. Han, H. Guo, Y. BaiH. Sun, and Y. Zeng, "SGC switching between subluminal to superluminal propagation in V-type atom," Commun. Theor. Phys. 46, 731-734 (2006).
[CrossRef]

C. Liu, S. Gong, D. Cheng, X. Fan, and Z. Xu, "Atom localization via interference of dark resonances," Phys. Rev. A 73, 025801 (2006).
[CrossRef]

2005 (2)

D. Han, H. Guo, Y. Bai, and H. Sun, "Subluminal and superluminal propagation of light in an N-type medium," Phys. Lett. A 334, 243-248 (2005).
[CrossRef]

J.-H. Li, W.-X. Yang, Z.-M. Zhan, and J.-C. Peng, "Ultraslow bright and dark solitons using only a pulsed laser in a cold three-state medium," Chin. Phys. Lett. 22, 357-360 (2005).
[CrossRef]

2004 (3)

Y. Wu and L. Deng, "Ultraslow bright and dark optical solitons in a cold three-state medium," Opt. Lett. 29, 2064-2066 (2004).
[CrossRef] [PubMed]

R. Buffa, S. Cavalieri, and M. V. Tognetti, "Coherent control of temporal pulse shaping by electromagnetically induced transparency," Phys. Rev. A 69, 033815 (2004).
[CrossRef]

Y. Wu and L. Deng, "Ultraslow optical solitons in a cold four-state medium," Phys. Rev. Lett. 93, 143904 (2004).
[CrossRef] [PubMed]

2003 (3)

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

T. Hong, "Spatial weak-light solitons in an electromagnetically induced nonlinear waveguide," Phys. Rev. Lett. 90, 183901 (2003).
[CrossRef] [PubMed]

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).
[CrossRef]

2002 (2)

B. Wu, J. Liu, and Q. Niu, "Controlled generation of dark solitons with phase imprinting," Phys. Rev. Lett. 88, 034102 (2002).
[CrossRef]

D. Solli, R. Y. Chiao, and J. M. Hickmann, "Superluminal optical solitons in a four-level tripod atomic system," Phys. Rev. E 66, 056601 (2002).
[CrossRef]

2001 (2)

G. S. Agarwal, T. N. Dey, and S. Menon, "Knob for changing light propagation from subluminal to superluminal," Phys. Rev. A 64, 053809 (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]

2000 (2)

L. J. Wang, A. Kuzmich, and P. Pogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark,L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley,K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider, and W. Phillips, "Generating solitons by phase engineering of a Bose-Einstein condensate," Science 287, 97-101 (2000).
[CrossRef]

1999 (2)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behrrozi, "Light speed reduction to 17 meterspersecond in an ultracold atomic gas," Nature 397, 594-598 (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]

1996 (1)

H. A. Haus and W. S. Wong, "Solitons in optical communications," Rev. Mod. Phys. 68, 423-444 (1996), and references therein.
[CrossRef]

1995 (1)

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

Chin. Phys. Lett. (1)

J.-H. Li, W.-X. Yang, Z.-M. Zhan, and J.-C. Peng, "Ultraslow bright and dark solitons using only a pulsed laser in a cold three-state medium," Chin. Phys. Lett. 22, 357-360 (2005).
[CrossRef]

Commun. Theor. Phys. (1)

D. Han, H. Guo, Y. BaiH. Sun, and Y. Zeng, "SGC switching between subluminal to superluminal propagation in V-type atom," Commun. Theor. Phys. 46, 731-734 (2006).
[CrossRef]

J. Phys. B (1)

D. Han, Y. Zeng, Y. Bai, and C. Huang, "Superluminal optical solitons in a four-level tripod atomic system," J. Phys. B 39, 3029-3035 (2006).
[CrossRef]

Nature (2)

L. J. Wang, A. Kuzmich, and P. Pogariu, "Gain-assisted superluminal light propagation," Nature 406, 277-279 (2000).
[CrossRef] [PubMed]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behrrozi, "Light speed reduction to 17 meterspersecond in an ultracold atomic gas," Nature 397, 594-598 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

D. Han, H. Guo, Y. Bai, and H. Sun, "Subluminal and superluminal propagation of light in an N-type medium," Phys. Lett. A 334, 243-248 (2005).
[CrossRef]

Phys. Rev. A (6)

R. Buffa, S. Cavalieri, and M. V. Tognetti, "Coherent control of temporal pulse shaping by electromagnetically induced transparency," Phys. Rev. A 69, 033815 (2004).
[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]

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).
[CrossRef]

G. S. Agarwal, T. N. Dey, and S. Menon, "Knob for changing light propagation from subluminal to superluminal," Phys. Rev. A 64, 053809 (2001).
[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]

C. Liu, S. Gong, D. Cheng, X. Fan, and Z. Xu, "Atom localization via interference of dark resonances," Phys. Rev. A 73, 025801 (2006).
[CrossRef]

Phys. Rev. E (1)

D. Solli, R. Y. Chiao, and J. M. Hickmann, "Superluminal optical solitons in a four-level tripod atomic system," Phys. Rev. E 66, 056601 (2002).
[CrossRef]

Phys. Rev. Lett. (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] [PubMed]

Y. Wu and L. Deng, "Ultraslow optical solitons in a cold four-state medium," Phys. Rev. Lett. 93, 143904 (2004).
[CrossRef] [PubMed]

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

T. Hong, "Spatial weak-light solitons in an electromagnetically induced nonlinear waveguide," Phys. Rev. Lett. 90, 183901 (2003).
[CrossRef] [PubMed]

B. Wu, J. Liu, and Q. Niu, "Controlled generation of dark solitons with phase imprinting," Phys. Rev. Lett. 88, 034102 (2002).
[CrossRef]

Rev. Mod. Phys. (1)

H. A. Haus and W. S. Wong, "Solitons in optical communications," Rev. Mod. Phys. 68, 423-444 (1996), and references therein.
[CrossRef]

Science (1)

J. Denschlag, J. E. Simsarian, D. L. Feder, C. W. Clark,L. A. Collins, J. Cubizolles, L. Deng, E. W. Hagley,K. Helmerson, W. P. Reinhardt, S. L. Rolston, B. I. Schneider, and W. Phillips, "Generating solitons by phase engineering of a Bose-Einstein condensate," Science 287, 97-101 (2000).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

R. Y. Chiao and A. M. Steinberg, Progress in Optics (Elsevier, 1997).

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Figures (3)

Fig. 1
Fig. 1

Schematic of the four-level Λ-type system with two-folded levels. The lower states are coupled near-resonantly to the excited state by three laser fields. Each field couples only one transition.

Fig. 2
Fig. 2

(a) Ω 1 Ω 10 2 e β ξ , where Ω 1 2 is the numerical solution from Eq. (9). (b) Single soliton Ω 1 Ω 10 2 = sech 2 ( η τ ) given in Eq. (10). l = 1 cm and τ = 1 × 10 3 s . Other parameters are explained in the text.

Fig. 3
Fig. 3

(a) Relevant energy level of Rb 87 atoms and excitations of the laser and microwave fields in the experiment of [23]. (b) Four-level system in the experiment.

Equations (17)

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H = Δ 1 2 2 ( Δ 1 Δ 2 ) 3 3 ( Δ 1 Δ 2 Δ 3 ) 4 4 + ( Ω 1 e i k p r 2 1 + Ω 2 e i k c r 3 2 + Ω 3 e i k d r 4 3 + H.c. ) ,
A ̇ 2 = i Ω 1 A 1 + ( i Δ 1 γ 2 ) A 2 i Ω 2 * A 3 ,
A ̇ 3 = i Ω 2 A 2 + [ i ( Δ 1 Δ 2 ) γ 3 ] A 3 i Ω 3 * A 4 ,
A ̇ 4 = i Ω 3 A 3 + [ i ( Δ 1 Δ 2 Δ 3 ) γ 4 ] A 4 ,
Ω 1 z + 1 c Ω 1 t = i κ A 2 A 1 * ,
( Δ 1 + ω + i γ 2 ) α 2 ( 1 ) Ω 2 * α 3 ( 1 ) = Λ 1 ,
( Δ 1 Δ 2 + ω + i γ 3 ) α 3 ( 1 ) Ω 3 * α 4 ( 1 ) Ω 2 α 2 ( 1 ) = 0 ,
( Δ 1 Δ 2 Δ 3 + ω + i γ 4 ) α 4 ( 1 ) Ω 3 α 3 ( 1 ) = 0 ,
Λ 1 z i ω c Λ 1 = i κ α 2 ( 1 ) ,
Λ 1 ( z , ω ) = Λ 1 ( 0 , ω ) e i K z ,
K = ω c + κ A ( Δ 1 + ω ) A Ω 2 2 = K 0 + K 1 ω + K 2 ω 2 +
[ z + K 1 t ] Ω ̃ 1 + K 2 2 t 2 Ω ̃ 1 = NLT ,
NLT = W e β z Ω ̃ 1 ( z , t ) 2 Ω ̃ 1 ( z , t ) ,
i ξ Ω ̃ 1 1 2 K 2 2 η 2 Ω ̃ 1 = W exp ( β ξ ) Ω ̃ 1 2 Ω ̃ 1 .
i ξ Ω ̃ 1 1 2 K 2 r 2 η 2 Ω ̃ 1 = W r Ω ̃ 1 2 Ω ̃ 1 .
Ω ̃ 1 = Ω 10 sech ( η τ ) exp ( i ξ W r Ω 10 2 2 ) ,
γ 2 2 < Δ 2 .

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