Abstract

We show that the dynamic range of delay lines based on slow light propagation in atomic coherent media is restricted due to absorptive, dispersive, and nonlinear properties of the media. We compare the electro-magnetically induced transparency based delay lines with optical fiber and resonator delays.

© 2005 Optical Society of America

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    [CrossRef]
  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]
  3. D. Budker, D. Kimball, S. Rochester, and V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,�?? Phys. Rev. Lett. 83, 1767-1770 (1999).
    [CrossRef]
  4. D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, "Storage of light in atomic vapor,�?? Phys. Rev. Lett. 86, 783-786 (2001).
    [CrossRef] [PubMed]
  5. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, "Observation of coherent optical information storage in an atomic medium using halted light pulses,�?? Nature 409, 490-493 (2001).
    [CrossRef] [PubMed]
  6. A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, "Slow, ultraslow, stored, and frozen light,�?? Adv. At. Mol. Opt. Phys. 46, 191 (2001).
    [CrossRef]
  7. R. W. Boyd and D. J. Gauther, �??Slow and Fast Light,�?? Prog. Optics 43, 497-530 (2002).
    [CrossRef]
  8. A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid,�?? Phys. Rev. Lett. 88, 023602 (2002).
    [CrossRef] [PubMed]
  9. M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, �??Observation of ultraslow light propagation in a ruby crystal at room temperature,�?? Phys. Rev. Lett. 90, 113903 (2003).
    [CrossRef] [PubMed]
  10. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, "Coherent resonant interactions and slow light with molecules band-gap fibers,�?? E-print archive: physics/0412018 (2004).
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    [CrossRef]
  12. P. C. Ku, C. J. Chang-Hasnain, and S. L. Chuang, "Variable semiconductor all-optical buffer,�?? Electron. Lett. 38, 1581- 1583 (2002).
    [CrossRef]
  13. J. B. Khurgin, "Comparative analysis of linear and nonlinear devices based on slow waves in periodic photonic structures and EIT media,�?? presented on "Nonlinear Optics�?? conference, Hawaii, (2004).
  14. 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]
  15. R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, "Maximum time delay achievable on propagation through a slow-light medium,�?? Phys. Rev. A 71, 023801 (2005).
    [CrossRef]
  16. E. B. Aleksandrov and V. S. Zapasski, "A fairy tale of stopped light,�?? Physics-Uspekhi 47, 1033-1036 (2004).
    [CrossRef]
  17. M. Fleischhauer and M. D. Lukin, "Dark-state polaritons in electromagnetically induced transparency,�?? Phys. Rev. Lett. 84, 5094-5097 (2000).
    [CrossRef] [PubMed]
  18. M. D. Eisaman, L. Childress, A. Andr, F. Massou, A. S. Zibrov, and M. D. Lukin, "Shaping quantum pulses of light via coherent atomic memory,�?? Phys. Rev. Lett. 93, 233602 (2004).
    [CrossRef] [PubMed]
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  20. S. E. Harris, J. E. Field, and A. Kasapi, "Dispersive properties of electromagnetically induced transparency,�?? Phys. Rev. A 46, R29-R32 (1992).
    [CrossRef] [PubMed]
  21. L. Deng, M. G. Payne, and E.W. Hagley, "Propagation of light pulses in an ultra-cold atomic vapor: mechanism for the loss of the probe field,�?? Opt. Commun. 198, 129-133 (2001).
    [CrossRef]
  22. M. Stahler, R. Wynands, S. Knappe, J. Kitching, L. Hollberg, A. Taichenachev, and V. Yudin, "Coherent population trapping resonances in thermal 85Rb vapor: D1 versus D2 line excitation,�?? Opt. Lett. 27, 1472-1474 (2002).
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  23. A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, "Narrowing of electromagnetically induced transparency resonance in a Doppler-broadened medium,�?? Phys. Rev. A 66, 013805 (2002).
    [CrossRef]
  24. Y. Rostovtsev, I. Protsenko, H. Lee, and A. Javan, "From laser-induced line narrowing to electromagnetically induced transparency in a Doppler-broadened system,�?? J. Mod. Opt. 49, 2501-2516 (2002).
    [CrossRef]
  25. H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, "From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,�?? Appl. Phys. B 76, 33-39 (2003).
    [CrossRef]
  26. M. D. Lukin, P. R. Hemmer, and M. O. Scully, "Resonant nonlinear optics in phase-coherent media,�?? Adv. Atom. Mol. Opt. Phys. 42, 347-386 (2000).
    [CrossRef]
  27. M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, "Spectroscopy in dense coherent media: line narrowing and interference effects,�?? Phys. Rev. Lett. 79, 2959-2962 (1997).
    [CrossRef]
  28. M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient Nonlinear Frequency Conversion with Maximal Atomic Coherence,�?? Phys. Rev. Lett. 77, 4326-4329 (1996).
    [CrossRef] [PubMed]
  29. A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, "Transporting and time reversing light via atomic coherence,�?? Phys. Rev. Lett. 88, 103601 (2002).
    [CrossRef] [PubMed]
  30. A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media,�?? Phys. Rev. Lett. 87, 133601 (2001).
    [CrossRef] [PubMed]
  31. J. E. Heebner, R. W. Boyd, and Q. H. Park, "Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,�?? Phys. Rev. E 65, 036619 (2002).
    [CrossRef]
  32. J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical transmission characteristics of fiber ring resonators,�?? IEEE J. Quantum. Electron. 40, 726-730 (2004).
    [CrossRef]

Adv. At. Mol. Opt. Phys.

A. B. Matsko, O. Kocharovskaya, Y. Rostovtsev, G. R. Welch, A. S. Zibrov, and M. O. Scully, "Slow, ultraslow, stored, and frozen light,�?? Adv. At. Mol. Opt. Phys. 46, 191 (2001).
[CrossRef]

Adv. Atom. Mol. Opt. Phys.

M. D. Lukin, P. R. Hemmer, and M. O. Scully, "Resonant nonlinear optics in phase-coherent media,�?? Adv. Atom. Mol. Opt. Phys. 42, 347-386 (2000).
[CrossRef]

Appl. Phys. B

H. Lee, Y. Rostovtsev, C. J. Bednar, and A. Javan, "From laser-induced line narrowing to electromagnetically induced transparency: closed system analysis,�?? Appl. Phys. B 76, 33-39 (2003).
[CrossRef]

E-print archive: physics

S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, "Coherent resonant interactions and slow light with molecules band-gap fibers,�?? E-print archive: physics/0412018 (2004).

Electron. Lett.

P. C. Ku, C. J. Chang-Hasnain, and S. L. Chuang, "Variable semiconductor all-optical buffer,�?? Electron. Lett. 38, 1581- 1583 (2002).
[CrossRef]

IEEE J. Quantum. Electron.

J. E. Heebner, V. Wong, A. Schweinsberg, R. W. Boyd, and D. J. Jackson, "Optical transmission characteristics of fiber ring resonators,�?? IEEE J. Quantum. Electron. 40, 726-730 (2004).
[CrossRef]

J. Mod. Opt.

Y. Rostovtsev, I. Protsenko, H. Lee, and A. Javan, "From laser-induced line narrowing to electromagnetically induced transparency in a Doppler-broadened system,�?? J. Mod. Opt. 49, 2501-2516 (2002).
[CrossRef]

Nature

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

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

Nonlinear Optics conference

J. B. Khurgin, "Comparative analysis of linear and nonlinear devices based on slow waves in periodic photonic structures and EIT media,�?? presented on "Nonlinear Optics�?? conference, Hawaii, (2004).

Opt. Commun.

L. Deng, M. G. Payne, and E.W. Hagley, "Propagation of light pulses in an ultra-cold atomic vapor: mechanism for the loss of the probe field,�?? Opt. Commun. 198, 129-133 (2001).
[CrossRef]

Opt. Lett.

Phys. Rev. A

A. Javan, O. Kocharovskaya, H. Lee, and M. O. Scully, "Narrowing of electromagnetically induced transparency resonance in a Doppler-broadened medium,�?? Phys. Rev. A 66, 013805 (2002).
[CrossRef]

S. E. Harris, J. E. Field, and A. Kasapi, "Dispersive properties of electromagnetically induced transparency,�?? Phys. Rev. A 46, R29-R32 (1992).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, "Maximum time delay achievable on propagation through a slow-light medium,�?? Phys. Rev. A 71, 023801 (2005).
[CrossRef]

Phys. Rev. E

J. E. Heebner, R. W. Boyd, and Q. H. Park, "Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide,�?? Phys. Rev. E 65, 036619 (2002).
[CrossRef]

Phys. Rev. Lett.

M. D. Lukin, M. Fleischhauer, A. S. Zibrov, H. G. Robinson, V. L. Velichansky, L. Hollberg, and M. O. Scully, "Spectroscopy in dense coherent media: line narrowing and interference effects,�?? Phys. Rev. Lett. 79, 2959-2962 (1997).
[CrossRef]

M. Jain, H. Xia, G. Y. Yin, A. J. Merriam, and S. E. Harris, "Efficient Nonlinear Frequency Conversion with Maximal Atomic Coherence,�?? Phys. Rev. Lett. 77, 4326-4329 (1996).
[CrossRef] [PubMed]

A. S. Zibrov, A. B. Matsko, O. Kocharovskaya, Y. V. Rostovtsev, G. R. Welch, and M. O. Scully, "Transporting and time reversing light via atomic coherence,�?? Phys. Rev. Lett. 88, 103601 (2002).
[CrossRef] [PubMed]

A. B. Matsko, I. Novikova, M. O. Scully, and G. R. Welch, "Radiation trapping in coherent media,�?? Phys. Rev. Lett. 87, 133601 (2001).
[CrossRef] [PubMed]

M. Fleischhauer and M. D. Lukin, "Dark-state polaritons in electromagnetically induced transparency,�?? Phys. Rev. Lett. 84, 5094-5097 (2000).
[CrossRef] [PubMed]

M. D. Eisaman, L. Childress, A. Andr, F. Massou, A. S. Zibrov, and M. D. Lukin, "Shaping quantum pulses of light via coherent atomic memory,�?? Phys. Rev. Lett. 93, 233602 (2004).
[CrossRef] [PubMed]

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]

S. E. Harris and L. V. Hau, "Nonlinear optics at low light levels,�?? Phys. Rev. Lett. 82, 4611-4614 (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, "Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,�?? Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

D. Budker, D. Kimball, S. Rochester, and V. Yashchuk, "Nonlinear magneto-optics and reduced group velocity of light in atomic vapor with slow ground state relaxation,�?? Phys. Rev. Lett. 83, 1767-1770 (1999).
[CrossRef]

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

A. V. Turukhin, V. S. Sudarshanam, M. S. Shahriar, J. A. Musser, B. S. Ham, and P. R. Hemmer, "Observation of ultraslow and stored light pulses in a solid,�?? Phys. Rev. Lett. 88, 023602 (2002).
[CrossRef] [PubMed]

M. S. Bigelow, N. N. Lepeshkin, and R. W. Boyd, �??Observation of ultraslow light propagation in a ruby crystal at room temperature,�?? Phys. Rev. Lett. 90, 113903 (2003).
[CrossRef] [PubMed]

Physics-Uspekhi

E. B. Aleksandrov and V. S. Zapasski, "A fairy tale of stopped light,�?? Physics-Uspekhi 47, 1033-1036 (2004).
[CrossRef]

Prog. Optics

R. W. Boyd and D. J. Gauther, �??Slow and Fast Light,�?? Prog. Optics 43, 497-530 (2002).
[CrossRef]

Other

G. P. Agrawal, Nonlinear fiber optics, (Academic Press, New York, 2001).

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Figures (4)

Fig. 1.
Fig. 1.

Double-lambda scheme. (a) Usual level configuration for EIT observation. The atomic coherence is created through two-photon transition |c〉⃡|α〉⃡|b〉 while off resonant level |α 2〉 results in residual absorption of the light. (b) Four-wave mixing process that could mask EIT if ωbc >γ, where γ is the natural decay rate of state |a〉. Presence of the off resonant level shown by dashed line is not necessary to observe the wave mixing process.

Fig. 2.
Fig. 2.

Normalized absorption and refractivity of the double-Λ system shown in Fig. 1a. Red (solid) curves correspond to the exact solution of the Maxwell-Bloch equations for the system, while blue (dashed) lines stand for the analytical approximations (9) and (5). The parameters used in the calculations are |Ω|=0.1γ, |Ω p |=0.01γ, γbc =0.001γ, and Δ=200γ

Fig. 3.
Fig. 3.

Normalized absorption and refractivity of the Doppler-broadened double-Λ system shown in Fig. 1a. Red (solid) curves correspond to the exact solution of the Maxwell-Bloch equations for the system, while blue (dashed) lines stand for the analytical approximations (16) and (12). The parameters used in the calculations are |Ω|=10γ, |Ω p |=0.3γ, γbc =0.004γ, Δ D =100γ, and Δ=300γ.

Fig. 4.
Fig. 4.

Left: Transmission of a bi-rectangular probe pulse. Relative power of the probe pulse at the entrance (blue) and exit (red) of the atomic cell. The probe power transmission is 20%. Right: Transmission of a comb of short rectangular probe pulses. The color indicates here simultaneous reduction of the both pump and probe power (from red to blue). The corresponding relative probe power transmission is 40, 30, 25, 20, 15 and 10 % (from red to blue). All output probe pulses are normalized to unity for convenience of perception.

Equations (28)

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

N B = BL V g ,
τ g τ B = L τ B V g N B Δ ν B B .
B ( β 2 L ) 1 2 0.25 ,
B ( β 3 L ) 1 3 0.324 .
β κ [ γ δ ( Ω 2 δ 2 ) ( Ω 2 δ 2 + γ γ bc ) 2 + γ 2 δ 2 + γ a 2 Δ δ ] ,
β 1 = 1 V g κ γ Ω 2 ,
β 2 0 ,
β 3 6 κ γ 3 Ω 6 ( 1 Ω 2 γ 2 ) .
α 2 κ [ γ γ bc ( Ω 2 δ 2 + γ γ bc ) + γ 2 δ 2 ( Ω 2 δ 2 + γ γ bc ) 2 + γ 2 δ 2 + γ a 2 2 Δ 2 ] ,
P out P in = exp [ 2 κ L ( γ γ bc Ω 2 + γ a 2 2 Δ 2 ) ] exp [ 2 κ L γ 2 δ 2 Ω 4 ] .
δ EIT = Ω 2 γ ( 2 ln 2 κ L ) 1 2 .
β D κ [ γ δ ( Ω 2 δ 2 ) ( Ω 2 δ 2 + Δ D γ bc ) 2 + Δ D 2 δ 2 + γ a 2 Δ Δ D 2 + Δ 2 ] .
β D 1 1 V g = κ γ Ω 2 ,
β D 2 0 ,
β D 3 6 κ γ Δ D 2 Ω 6 .
α D 2 κ [ γ γ bc ( Ω 2 δ 2 + Δ D γ bc ) + Δ D γ δ 2 ( Ω 2 δ 2 + Δ D γ bc ) 2 + Δ D 2 δ 2 + γ a 2 Δ D Δ D 2 + Δ 2 ] .
P out P in = exp [ 2 κ L ( γ γ bc Ω 2 + γ a 2 Δ D Δ D 2 + Δ 2 ) ] ×
exp [ 2 κ L γ Δ D δ 2 Ω 4 ] .
δ DEIT = Ω 2 γ Δ D ( 2 ln 2 κ L ) 1 2 .
B Ω 2 γ 0.18 ( 1 Ω 2 γ 2 1 3 + 0.18 ξ 1 6 ) ξ 1 3 ,
B D Ω 2 Δ D 0.18 ( 1 + 0.18 ξ D 1 6 ) ξ D 1 2 ,
N B 0.18 ξ 2 3 1 Ω 2 γ 2 1 3 + 0.18 ξ 1 6 ,
N B D 0.18 ξ D 2 3 1 + 0.18 ξ D 1 6 .
ξ Δ 2 2 γ a 2 2 ,
ξ D γ γ a 2 Δ 2 + Δ D 2 2 Δ D 2 .
ξ ω bc γ ,
ξ D ω bc Δ D .
L f = N B c B n f ,

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