Abstract

We show the formation of ultraslow bright and dark optical solitons in a lifetime-broadened three-state atomic system under Raman excitation. We also discuss why such ultraslow optical solitons may not exist under the conditions of the usual electromagnetically induced transparency configuration where zero one- and two-photon detunings are required.

© 2004 Optical Society of America

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References

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  1. H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996) and references therein.
    [CrossRef]
  2. Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998) and references therein.
    [CrossRef]
  3. See, e.g., G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001), Chap. 5.
  4. J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
    [CrossRef]
  5. S. E. Harris, Phys. Today 50(7), 36 (1997).
    [CrossRef]
  6. S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
    [CrossRef]
  7. H. Schmidt and A. Imamoğlu, Opt. Lett. 21, 1936 (1996).
    [CrossRef] [PubMed]
  8. M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
    [CrossRef] [PubMed]
  9. L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
    [CrossRef]
  10. L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, Phys. Rev. A 65, 051805(R) (2002).
    [CrossRef]
  11. M. Kozuma, D. Akamatsu, L. Deng, E. W. Hagley, and M. G. Payne, Phys. Rev. A 66, 031801(R) (2002).
    [CrossRef]
  12. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
    [CrossRef]
  13. 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, Phys. Rev. Lett. 82, 5229 (1999).
    [CrossRef]
  14. X. J. Liu, H. Jing, and M. Ge, (2004), http://xxx.lanl.gov .

2002 (3)

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

M. Kozuma, D. Akamatsu, L. Deng, E. W. Hagley, and M. G. Payne, Phys. Rev. A 66, 031801(R) (2002).
[CrossRef]

2000 (1)

M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

1999 (3)

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

1998 (1)

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998) and references therein.
[CrossRef]

1997 (1)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

1996 (2)

H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996) and references therein.
[CrossRef]

H. Schmidt and A. Imamoğlu, Opt. Lett. 21, 1936 (1996).
[CrossRef] [PubMed]

1974 (1)

J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Agrawal, G. P.

See, e.g., G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001), Chap. 5.

Akamatsu, D.

M. Kozuma, D. Akamatsu, L. Deng, E. W. Hagley, and M. G. Payne, Phys. Rev. A 66, 031801(R) (2002).
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Deng, L.

M. Kozuma, D. Akamatsu, L. Deng, E. W. Hagley, and M. G. Payne, Phys. Rev. A 66, 031801(R) (2002).
[CrossRef]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Ge, M.

X. J. Liu, H. Jing, and M. Ge, (2004), http://xxx.lanl.gov .

Hagley, E. W.

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

M. Kozuma, D. Akamatsu, L. Deng, E. W. Hagley, and M. G. Payne, Phys. Rev. A 66, 031801(R) (2002).
[CrossRef]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

Hau, L. V.

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Haus, H. A.

H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996) and references therein.
[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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Imamoglu, A.

M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

H. Schmidt and A. Imamoğlu, Opt. Lett. 21, 1936 (1996).
[CrossRef] [PubMed]

Jing, H.

X. J. Liu, H. Jing, and M. Ge, (2004), http://xxx.lanl.gov .

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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998) and references therein.
[CrossRef]

Kozuma, M.

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

M. Kozuma, D. Akamatsu, L. Deng, E. W. Hagley, and M. G. Payne, Phys. Rev. A 66, 031801(R) (2002).
[CrossRef]

Liu, X. J.

X. J. Liu, H. Jing, and M. Ge, (2004), http://xxx.lanl.gov .

Lukin, M. D.

M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998) and references therein.
[CrossRef]

Payne, M. G.

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

M. Kozuma, D. Akamatsu, L. Deng, E. W. Hagley, and M. G. Payne, Phys. Rev. A 66, 031801(R) (2002).
[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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Satsuma, J.

J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Schmidt, H.

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, Phys. Rev. Lett. 82, 5229 (1999).
[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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Wong, W. S.

H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996) and references therein.
[CrossRef]

Yajima, N.

J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

Nature (1)

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, Nature 397, 594 (1999).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (1)

Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998) and references therein.
[CrossRef]

Phys. Rev. A (2)

L. Deng, E. W. Hagley, M. Kozuma, and M. G. Payne, Phys. Rev. A 65, 051805(R) (2002).
[CrossRef]

M. Kozuma, D. Akamatsu, L. Deng, E. W. Hagley, and M. G. Payne, Phys. Rev. A 66, 031801(R) (2002).
[CrossRef]

Phys. Rev. Lett. (4)

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, Phys. Rev. Lett. 82, 5229 (1999).
[CrossRef]

M. D. Lukin and A. Imamoğlu, Phys. Rev. Lett. 84, 1419 (2000).
[CrossRef] [PubMed]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

S. E. Harris and L. V. Hau, Phys. Rev. Lett. 82, 4611 (1999).
[CrossRef]

Phys. Today (1)

S. E. Harris, Phys. Today 50(7), 36 (1997).
[CrossRef]

Prog. Theor. Phys. Suppl. (1)

J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Rev. Mod. Phys. (1)

H. A. Haus and W. S. Wong, Rev. Mod. Phys. 68, 423 (1996) and references therein.
[CrossRef]

Other (2)

See, e.g., G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, New York, 2001), Chap. 5.

X. J. Liu, H. Jing, and M. Ge, (2004), http://xxx.lanl.gov .

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Figures (2)

Fig. 1
Fig. 1

Lifetime-broadened three-state atomic system interacts with a cw strong control laser (frequency ωC and Rabi frequency 2ΩC) and a pulsed probe field (frequency ωp and Rabi frequency 2Ωp).

Fig. 2
Fig. 2

Surface plots of the relative probe intensity versus dimensionless time η/τ and distance ξ/l. Left, ΩP/ΩP02 exp-αξ, where ΩP2 is the numerical solution to Eq. (7); right, single bright soliton of Eq. (9) as given by ΩP/ΩP02=sech2η/τ in Eq. (10). l=1 cm, τ=1.0×10-6 s, and the other parameters are explained in the text.

Equations (14)

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

A1t=iΔt+iγ1A1+iΩC*A2,
A2t=iΔs+iγ2A2+iΩCA1+iΩpA0,
Ωpz+1cΩpt=iκ02A2A0*.
ω+Δt+iγ1β11+ΩC*β21=0,
ω+Δs+iγ2β21+ΩCβ11=-Λp,
Λpz-iωcΛp=iκ02β21,
Λpz,ω=Λp0,ωexpiKz,
K=ωc+κ02ω+Δt+iγ1ΩC2-ω+Δt+iγ1ω+Δs+iγ2=K0+ωVg+K2ω2+,
-iz+1VgtΩP+K22t2ΩP=NLT,
Aj1=Δt+iγ1δj2-ΩC*δj1ΩC2-Δt+iγ1Δs+iγ2Ωp,  j=1,2,
iξΩP-K22η2ΩP=W exp-αξΩP2ΩP,
W=κ02Δt+iγ1ΩC2+Δt2+γ12DD2,
iξΩP-K2r2η2ΩP=WrΩP2ΩP.
ΩP=ΩP0 sechη/τexp-iξWrΩP02/2,

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