Abstract

We study electromagnetically induced transparency (EIT) and nonlinear pulse propagation in a resonant atomic gas confined in a microwaveguide. We find that the quantum-interference effect in this system can be greatly enhanced due to the reduction of the mode volume of the optical field. In particular, compared with atomic gases in free space, the EIT transparency window in the present confined system can be much wider and deeper, the group velocity of the probe field can be much slower, and the Kerr nonlinearity of the system can be much stronger. We show that a more efficient production of ultraslow optical solitons in the present system may be achieved with much slower propagating velocity and lower generation power. Features of EIT and pulse propagation in the present system are very promising for practical applications in optical information processing and transmission.

© 2012 Optical Society of America

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  1. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
    [CrossRef]
  2. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
    [CrossRef]
  3. J. B. Khurgin and R. S. Tucker, eds., Slow Light: Science and Applications (CRC, 2009).
  4. A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
    [CrossRef]
  5. M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
    [CrossRef]
  6. C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
    [CrossRef]
  7. C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
    [CrossRef]
  8. Y. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. 21, 1064–1066 (1996).
    [CrossRef]
  9. L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).
    [CrossRef]
  10. Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
    [CrossRef]
  11. Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904 (2004).
    [CrossRef]
  12. G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
    [CrossRef]
  13. R. Santra, E. Arimondo, T. Ido, C. H. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic Sr88,” Phys. Rev. Lett. 94, 173002 (2005).
    [CrossRef]
  14. M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T137, 014001 (2009).
    [CrossRef]
  15. S. Ghosh, J. Sharping, D. Ouzounov, and A. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
    [CrossRef]
  16. P. S. Light, F. Benabid, F. Couny, M. Maric, and A. N. Luiten, “Electromagnetically induced transparency in Rb-filled coated hollow-core photonic crystal fiber,” Opt. Lett. 32, 1323–1325 (2007).
    [CrossRef]
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    [CrossRef]
  18. F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A 79, 013818 (2009).
    [CrossRef]
  19. D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
    [CrossRef]
  20. M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
    [CrossRef]
  21. C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
    [CrossRef]
  22. Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 063813 (2010).
    [CrossRef]
  23. Since in our model ωp≈ωc, the mode index n can be chosen according to the value of ωp, satisfying the condition (L/πc)ωp−1<n<(L/πc)ωp.
  24. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).

2011 (1)

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

2010 (2)

C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
[CrossRef]

Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 063813 (2010).
[CrossRef]

2009 (3)

F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A 79, 013818 (2009).
[CrossRef]

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T137, 014001 (2009).
[CrossRef]

2008 (1)

2007 (1)

2006 (2)

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

2005 (4)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[CrossRef]

R. Santra, E. Arimondo, T. Ido, C. H. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic Sr88,” Phys. Rev. Lett. 94, 173002 (2005).
[CrossRef]

S. Ghosh, J. Sharping, D. Ouzounov, and A. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

2004 (1)

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

2003 (2)

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

2002 (1)

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

2000 (1)

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef]

1997 (1)

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

1996 (1)

Ahmad, F. R.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Arimondo, E.

R. Santra, E. Arimondo, T. Ido, C. H. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic Sr88,” Phys. Rev. Lett. 94, 173002 (2005).
[CrossRef]

Artoni, M.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Benabid, F.

Biancalana, F.

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Cataliotti, F.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Chang, W.

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Couny, F.

Deng, L.

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[CrossRef]

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

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

Feng, M.

Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 063813 (2010).
[CrossRef]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Fu, G. S.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

Fu, P. M.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

Gaeta, A.

S. Ghosh, J. Sharping, D. Ouzounov, and A. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

Gaeta, A. L.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Gallagher, M. T.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Ghosh, S.

S. Ghosh, J. Sharping, D. Ouzounov, and A. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

Greene, C. H.

R. Santra, E. Arimondo, T. Ido, C. H. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic Sr88,” Phys. Rev. Lett. 94, 173002 (2005).
[CrossRef]

Hagley, E. W.

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

Hakuta, K.

F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A 79, 013818 (2009).
[CrossRef]

Hammerer, K.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T137, 014001 (2009).
[CrossRef]

Hang, C.

C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
[CrossRef]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

Harris, S. E.

S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50(7), 36–42 (1997).
[CrossRef]

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).

Hawkins, A. R.

Holzer, P.

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Huang, G.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[CrossRef]

Hulbert, J. E.

Ido, T.

R. Santra, E. Arimondo, T. Ido, C. H. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic Sr88,” Phys. Rev. Lett. 94, 173002 (2005).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef]

Jiang, Q.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

Joly Philip, N. Y.

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Kien, F. L.

F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A 79, 013818 (2009).
[CrossRef]

Koch, K. W.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).

Konotop, V. V.

C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
[CrossRef]

Kozuma, M.

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

Li, Y.

Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 063813 (2010).
[CrossRef]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

Y. Li and M. Xiao, “Enhancement of nondegenerate four-wave mixing based on electromagnetically induced transparency in rubidium atoms,” Opt. Lett. 21, 1064–1066 (1996).
[CrossRef]

Light, P. S.

Liu, X.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

Luiten, A. N.

Lukin, M.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T137, 014001 (2009).
[CrossRef]

Lukin, M. D.

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef]

Lvovsky, A. I.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

Ma, L.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

Malomed, B. A.

Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 063813 (2010).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[CrossRef]

Maric, M.

Müller, D.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Nazarkin, A.

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Ottaviani, C.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Ouzounov, D.

S. Ghosh, J. Sharping, D. Ouzounov, and A. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

Ouzounov, D. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Payne, M. G.

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[CrossRef]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

Rabl, P.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T137, 014001 (2009).
[CrossRef]

Russell, St. J.

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Saleh, M. F.

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Sanders, B. C.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

Santra, R.

R. Santra, E. Arimondo, T. Ido, C. H. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic Sr88,” Phys. Rev. Lett. 94, 173002 (2005).
[CrossRef]

Schmidt, H.

Sharping, J.

S. Ghosh, J. Sharping, D. Ouzounov, and A. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

Silcox, J.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Sun, J.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

Thomas, M. G.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Tittel, W.

A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics 3, 706–714 (2009).
[CrossRef]

Tombesi, P.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Travers, J. C.

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Venkataraman, N.

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Vitali, D.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Wallquist, M.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T137, 014001 (2009).
[CrossRef]

Wu, B.

Wu, L. A.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

Wu, Y.

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

Xiao, M.

Ye, J.

R. Santra, E. Arimondo, T. Ido, C. H. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic Sr88,” Phys. Rev. Lett. 94, 173002 (2005).
[CrossRef]

Zhou, J.

Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 063813 (2010).
[CrossRef]

Zoller, P.

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T137, 014001 (2009).
[CrossRef]

Zuo, Z. C.

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

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Nat. Photonics (1)

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Phys. Rev. A (4)

F. L. Kien and K. Hakuta, “Slowing down of a guided light field along a nanofiber in a cold atomic gas,” Phys. Rev. A 79, 013818 (2009).
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C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
[CrossRef]

C. Hang and V. V. Konotop, “All-optical steering of light via spatial Bloch oscillations in a gas of three-level atoms,” Phys. Rev. A 81, 053849 (2010).
[CrossRef]

Y. Li, B. A. Malomed, M. Feng, and J. Zhou, “Arrayed and checkerboard optical waveguides controlled by the electromagnetically induced transparency,” Phys. Rev. A 82, 063813 (2010).
[CrossRef]

Phys. Rev. E (1)

G. Huang, L. Deng, and M. G. Payne, “Dynamics of ultraslow optical solitons in a cold three-state atomic system,” Phys. Rev. E 72, 016617 (2005).
[CrossRef]

Phys. Rev. Lett. (8)

R. Santra, E. Arimondo, T. Ido, C. H. Greene, and J. Ye, “High-accuracy optical clock via three-level coherence in neutral bosonic Sr88,” Phys. Rev. Lett. 94, 173002 (2005).
[CrossRef]

S. Ghosh, J. Sharping, D. Ouzounov, and A. Gaeta, “Resonant optical interactions with molecules confined in photonic band-gap fibers,” Phys. Rev. Lett. 94, 093902 (2005).
[CrossRef]

M. F. Saleh, W. Chang, P. Holzer, A. Nazarkin, J. C. Travers, N. Y. Joly Philip, St. J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
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L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).
[CrossRef]

Z. C. Zuo, J. Sun, X. Liu, Q. Jiang, G. S. Fu, L. A. Wu, and P. M. Fu, “Generalized n-photon resonant 2n-wave mixing in an (n+1)-level system with phase-conjugate geometry,” Phys. Rev. Lett. 97, 193904 (2006).
[CrossRef]

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

M. D. Lukin and A. Imamoğlu, “Nonlinear optics and quantum entanglement of ultraslow single photons,” Phys. Rev. Lett. 84, 1419–1422 (2000).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization qubit phase gate in driven atomic media,” Phys. Rev. Lett. 90, 197902 (2003).
[CrossRef]

Phys. Scr. (1)

M. Wallquist, K. Hammerer, P. Rabl, M. Lukin, and P. Zoller, “Hybrid quantum devices and quantum engineering,” Phys. Scr. T137, 014001 (2009).
[CrossRef]

Phys. Today (1)

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M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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Science (1)

D. G. Ouzounov, F. R. Ahmad, D. Müller, N. Venkataraman, M. T. Gallagher, M. G. Thomas, J. Silcox, K. W. Koch, and A. L. Gaeta, “Generation of megawatt optical solitons in hollow-core photonic band-gap fibers,” Science 301, 1702–1704(2003).
[CrossRef]

Other (3)

J. B. Khurgin and R. S. Tucker, eds., Slow Light: Science and Applications (CRC, 2009).

Since in our model ωp≈ωc, the mode index n can be chosen according to the value of ωp, satisfying the condition (L/πc)ωp−1<n<(L/πc)ωp.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, 1995).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Waveguide consisting of two parallel perfect metal plates and filled with the atomic gas. (b) Specified coordinate system. (c) Energy-level diagram and excitation scheme of three-level Λ system, in which a weak (strong) probe (control) field of central angular frequency ωp (ωc) and half Rabi frequency Ωp (Ωc) couples to the atomic states |1, (|2), and |3. Γ13 and Γ23 are spontaneous-emission decay rates from |3 to |1 and |3 to |2, respectively; Γ12 and Γ21 denote incoherent population exchange between |1 and |2. Δ2 and Δ3 are two- and one-photon detunings, respectively.

Fig. 2.
Fig. 2.

Im(K) as a function of ω and L. The dot-dashed, dashed, and solid curves are for L=4.0, 2.0, and 1.0 μm, respectively.

Fig. 3.
Fig. 3.

(a) Group velocity vg as a function of L. (b) Effective refraction index nWG of the waveguide as a function of L.

Fig. 4.
Fig. 4.

Im(K0) as a function of |Ωc| with Γ21=0 (solid curve) and Γ21=γ21 (dashed curve). The inset shows the result of the function “ratio” /100, where “ratio” Im(K0)Γ21=0/Im(K0)Γ21=γ21.

Fig. 5.
Fig. 5.

Nonlinear coefficient Re(W) as a function of Δ3 evaluated at ω=0. The dashed and solid curves in panel (a) are for L=0.6 and 0.4 μm, respectively. The inset shows the profile of Re(W) as a function of L with Δ3=1.0×107s1. The dashed and solid curves in panel (b) are for L=4.0 and 1.0 μm, respectively. The inset shows the corresponding dispersion length LD for the two cases.

Fig. 6.
Fig. 6.

Density of maximum input power Pmax/S0 for producing the ultraslow optical soliton as a function of L.

Fig. 7.
Fig. 7.

Evolution of the dimensionless probe-field intensity |u|2 as a function of dimensionless time t/τ0. The curves from left to right are waveshapes after propagating y=0.0, 1.0LD, 2.0LD, and 3.0LD, respectively. (a) L=1.0μm. The soliton forms because the Kerr nonlinearity is strong enough (due to the strong confinement effect) to balance the dispersion. (b) L=4.0μm. The soliton does not form because the Kerr nonlinearity is too weak.

Equations (34)

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ETE(r,t)=exkEksin(nπzL)exp[i(kyω¯t)]+h.c.,
E(r,t)=exω¯Eω¯sin(nπzL)exp{i[k(ω¯)yω¯t)]}+h.c.
k(ω¯)=[(ω¯c)2(nπL)2]1/2.
E(r,t)=exl=p,cEl(x,y,t)sin(nπzL)exp[i(klyωlt)]+h.c.
H^I=[ζ(z)Ωp*ei[kpyωpt]|13|+ζ(z)Ωc*ei[kcyωct]|23|]+h.c.,
itσ˜11+iΓ21σ˜11iΓ12σ˜22iΓ13σ˜33+ζ*(z)Ωp*σ˜31ζ(z)Ωpσ˜31*=0,
itσ˜22iΓ21σ˜11+iΓ12σ˜22iΓ23σ˜33+ζ*(z)Ωc*σ˜32ζ(z)Ωcσ˜32*=0,
itσ˜33+iΓ3σ˜33ζ*(z)Ωp*σ˜31+ζ(z)Ωpσ˜31*ζ*(z)Ωc*σ˜32+ζ(z)Ωcσ˜32*=0,
(it+d21)σ˜21ζ(z)Ωpσ˜32*+ζ*(z)Ωc*σ˜31=0,
(it+d31)σ˜31ζ(z)Ωp(σ˜33σ˜11)+ζ(z)Ωcσ˜21=0,
(it+d32)σ˜32ζ(z)Ωc(σ˜33σ˜22)+ζ(z)Ωpσ˜21*=0
2E1c22Et2=1ε0c22Pt2,
ζ(z)[i(nWGy+1ct)+c2ωp2x2]Ωp(x,y,t)+κ13σ˜31(z;x,y,t)=0.
[i(nWGy+1ct)+c2ωp2x2]Ωp(x,y,t)+κ13σ˜31(z;x,y,t)=0,
nWGk(ωp)cωp=[1(cωpnπL)2]1/2
σ˜11(0)=X1Γ12Γ3+Γ12|ζ(z)Ωc|2+Γ13|ζ(z)Ωc|2X2,
σ˜22(0)=X1Γ21Γ3+Γ21|ζ(z)Ωc|2X2,
σ˜33(0)=Γ21|ζ(z)Ωc|2X2,
σ˜32(0)=ζ(z)Ωcd32X1Γ21Γ3X2,
K(ω)=ωcnWG+κ13nWG(ω+d21)(2σ˜11(0)+σ˜22(0)1)+ζ(z)Ωcσ˜32*(0)|ζ(z)Ωc|2(ω+d21)(ω+d31).
Im(K0)=κ13nWGγ21|ζ(z)Ωc|2+γ21Γ31Γ21|ζ(z)Ωc|2+2γ21Γ31.
Ωp(1)=Feiθ,
σ˜31(1)=(ω+d21)(2σ˜11(0)+σ˜22(0)1)+ζ(z)Ωcσ˜32(0)|ζ(z)Ωc|2(ω+d21)(ω+d¯31)Feiθ,
σ˜21(1)=(ω+d¯31)σ˜32*(0)+ζ(z)Ωc*(2σ˜11(0)+σ˜22(0)1)|ζ(z)Ωc|2(ω+d21)(ω+d¯31)Feiθ
σ˜11(2)={[i(Γ12+Γ23)+2|ζ(z)Ωc|2(1d32*1d32)][(ω+d21*)(2σ11(0)+σ22(0)1)+ζ(z)Ωc*σ32(0)|ζ(z)Ωc|2(ω+d21*)(ω+d31*)c.c.]i(Γ13Γ12)[ζ(z)Ωcd32*ζ(z)(ω+d31)σ32*(0)+Ωc*(2σ11(0)+σ22(0)1)|ζ(z)Ωc|2(ω+d21)(ω+d31)c.c.]}/[i|ζ(z)Ωc|2(2Γ21+Γ12+Γ13)(1d32*1d32)Γ3(Γ12+Γ21)],
σ˜22(2)=iΓ13Γ12{[(ω+d21*)(2σ11(0)+σ22(0)1)+ζ(z)Ωc*σ32(0)|ζ(z)Ωc|2(ω+d21)(ω+d31)c.c]i(Γ21+Γ13)a11(2)},
σ˜32(2)=1d32[ζ(z)(ω+d31*)σ32(0)+Ωc(2σ11(0)+σ22(0)1)|ζ(z)Ωc|2(ω+d21*)(ω+d31*)Ωc(a11(2)+2a22(2))].
iFy2+c2ωpnWG2x12F122Kω22Ft12W|F|2Fe2α¯y2=0
W=κ13nWG1ζ(z)ζ(z)Ωcσ˜32*(2)+(ω+d21)(2σ˜11(2)+σ˜22(2))|ζ(z)Ωc|2(ω+d21)(ω+d¯31)
i(y+α)U+c2ωpnWG2Ux2122Kω22Uτ2W|U|2Ue2αy=0,
ius+2uσ2+2|u|2u=id0u+d12uη2
Ωp=1τ0|K2||W|sech[1τ0(tyvg)]exp{i[Re(K0)y+y2LD]},
vg=2.62×107c.
Pmax=2.5×106W.

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