Abstract

By using the multiple-scale method, we study analytically the formation and stability of two-component spatial optical solitons in a cold, lifetime-broadened resonant four-level double-Λ type atomic system via electromagnetically induced transparency. It is shown that stable two-component (1+1) dimension spatial optical solitons with extremely weak light intensity can occur, which is different from the passive ones with photorefractive and planar waveguides. Furthermore, the interaction characteristics between two solitons are studied by numerical simulations. We find that the collisional dynamics and the energy transfer of the two solitons are closely correlated with their relative phase shift. Our results may provide a good idea to obtain useful spatial optical solitons for application in optical soliton communications.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. A. Haus and W. S. Wong, “Solitons in optical communications,” Rev. Mod. Phys. 68, 423-444 (1996).
    [CrossRef]
  2. Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81-197 (1998).
    [CrossRef]
  3. G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583-1586 (1991).
    [CrossRef] [PubMed]
  4. G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518-1523 (1999).
    [CrossRef] [PubMed]
  5. Y. S. Kivshar and G. I. Stegeman, “Spatial optical solitons,” Opt. Photonics News 13, 59-63 (2002).
    [CrossRef]
  6. G. X. Huang, K. J. Jiang, M. G. Payne, and L. Deng, “Formation and propagation of coupled ultraslow optical soliton pairs in a cold three-state double-Λ system,” Phys. Rev. E 73, 056606 (2006).
    [CrossRef]
  7. M. Fleischhauer, A. Imamŏglu, and J. P. Marangos, “Electromagnetically induced transparency: optics in coherent media,” Rev. Mod. Phys. 77, 633-673 (2005).
    [CrossRef]
  8. S. E. Harris, “Electromagnetically induced transparency,” Phys. Today 50, 36-42 (1997).
    [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] [PubMed]
  10. 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] [PubMed]
  11. H. Kang and Y. F. Zhu, “Observation of large Kerr nonlinearity at low light intensities,” Phys. Rev. Lett. 91, 093601 (2003).
    [CrossRef] [PubMed]
  12. T. Hong, M. W. Jack, M. Yamashita, and T. Mukai, “Enhanced Kerr nonlinearity for self-action via atomic coherence in a four-level atomic system,” Opt. Commun. 214, 371-380 (2002).
    [CrossRef]
  13. T. Hong, “Spatial weak-light solitons in an electromagnetically induced nonlinear waveguide,” Phys. Rev. Lett. 90, 183901 (2003).
    [CrossRef] [PubMed]
  14. H. Michinel, M. J. Paz-Alonso, and V. M. Perez-Garcia, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
    [CrossRef] [PubMed]
  15. C. Hang, G. X. Huang, and L. Deng, “Stable high-dimensional spatial weak-light solitons in a resonant three-state atomic system,” Phys. Rev. E 74, 046601 (2006).
    [CrossRef]
  16. P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20, 982-984 (1995).
    [CrossRef] [PubMed]
  17. 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] [PubMed]
  18. 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]
  19. D. A. Braje, V. Bali, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93, 183601 (2004).
    [CrossRef] [PubMed]
  20. Y. Zhang, B. Anderson, and M. Xiao, “Efficient energy transfer between four-wave-mixing and six-wave-mixing processes via atomic coherence,” Phys. Rev. A 77, 061801 (2008).
    [CrossRef]
  21. Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
    [CrossRef]
  22. 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] [PubMed]
  23. D. Petrosyan, “Towards deterministic optical quantum computation with coherently driven atomic ensembles,” J. Opt. B. 7, S141-S151 (2005).
    [CrossRef]
  24. C. Hang, Y. Li, L. Ma, and G. X. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319 (2006).
    [CrossRef]
  25. 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]
  26. G. X. 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]
  27. L. Deng, M. G. Payne, G. X. Huang, and E. W. Hagley, “Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double-Λ system,” Phys. Rev. E 72, 055601(R) (2005).
    [CrossRef]
  28. J. Wang, C. Hang, and G. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528-533 (2007).
    [CrossRef]
  29. W. X. Yang, J. M. Hou, and R. K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838 (2008).
    [CrossRef]
  30. R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673 (1995).
    [CrossRef] [PubMed]
  31. C. Hang, V. V. Konotop, and G. X. Huang, “Spatial solitons and instabilities of light beams in a three-level atomic medium with a standing-wave control field,” Phys. Rev. A 79, 033826 (2009).
    [CrossRef]
  32. X. Wu, X. T. Xie, and X. X. Yang, “Dark and bright vortex solitons in electromagnetically induced transparent media,” J. Phys. B 39, 3263-3273 (2006).
    [CrossRef]
  33. X. T. Xie, W. B. Li, and X. X. Yang, “Bright, dark, bistable bright, and vortex spatial-optical solitons in a cold three-state medium,” J. Opt. Soc. Am. B 23, 1609-1614 (2006).
    [CrossRef]
  34. H. J. Li and G. X. Huang, “Two-component spatial optical solitons in a four-state ladder system via electromagnetically induced transparency,” Phys. Lett. A 372, 4127-4134 (2008).
    [CrossRef]
  35. B. Hu, G. X. Huang, and M. G. Velarde, “Dynamics of coupled gap solitons in diatomic lattices with cubic and quartic nonlinearities,” Phys. Rev. E 62, 2827-2839 (2000).
    [CrossRef]
  36. F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
    [CrossRef] [PubMed]
  37. Z. G. Chen, A. Bezryadina, and I. Makasyuk, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29, 1656-1658 (2004).
    [CrossRef] [PubMed]
  38. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12, 614-616 (1987).
    [CrossRef] [PubMed]
  39. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871-873 (1988).
    [CrossRef] [PubMed]
  40. V. V. Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805-807 (1989).
    [CrossRef] [PubMed]
  41. Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18, 337-339 (1993).
    [CrossRef] [PubMed]
  42. C. Hang and G. Huang, “Weak-light ultraslow vector solitons via electromagnetically induced transparency,” Phys. Rev. A 77, 033830 (2008).
    [CrossRef]
  43. L. G. Si, W. X. Yang, and X. X. Yang, “Ultraslow temporal vector optical solitons in a cold four-level tripod atomic system,” J. Opt. Soc. Am. B 26, 478-486 (2009).
    [CrossRef]
  44. J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471-473 (1990).
    [CrossRef] [PubMed]
  45. W. J. Liu, B. Tian, H. Q. Zhang, L. L. Li, and Y. S. Xue, “Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method,” Phys. Rev. E 77, 066605 (2008).
    [CrossRef]

2009 (3)

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

C. Hang, V. V. Konotop, and G. X. Huang, “Spatial solitons and instabilities of light beams in a three-level atomic medium with a standing-wave control field,” Phys. Rev. A 79, 033826 (2009).
[CrossRef]

L. G. Si, W. X. Yang, and X. X. Yang, “Ultraslow temporal vector optical solitons in a cold four-level tripod atomic system,” J. Opt. Soc. Am. B 26, 478-486 (2009).
[CrossRef]

2008 (5)

C. Hang and G. Huang, “Weak-light ultraslow vector solitons via electromagnetically induced transparency,” Phys. Rev. A 77, 033830 (2008).
[CrossRef]

W. J. Liu, B. Tian, H. Q. Zhang, L. L. Li, and Y. S. Xue, “Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method,” Phys. Rev. E 77, 066605 (2008).
[CrossRef]

H. J. Li and G. X. Huang, “Two-component spatial optical solitons in a four-state ladder system via electromagnetically induced transparency,” Phys. Lett. A 372, 4127-4134 (2008).
[CrossRef]

W. X. Yang, J. M. Hou, and R. K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838 (2008).
[CrossRef]

Y. Zhang, B. Anderson, and M. Xiao, “Efficient energy transfer between four-wave-mixing and six-wave-mixing processes via atomic coherence,” Phys. Rev. A 77, 061801 (2008).
[CrossRef]

2007 (1)

J. Wang, C. Hang, and G. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528-533 (2007).
[CrossRef]

2006 (6)

X. Wu, X. T. Xie, and X. X. Yang, “Dark and bright vortex solitons in electromagnetically induced transparent media,” J. Phys. B 39, 3263-3273 (2006).
[CrossRef]

X. T. Xie, W. B. Li, and X. X. Yang, “Bright, dark, bistable bright, and vortex spatial-optical solitons in a cold three-state medium,” J. Opt. Soc. Am. B 23, 1609-1614 (2006).
[CrossRef]

C. Hang, Y. Li, L. Ma, and G. X. 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. X. Huang, K. J. Jiang, M. G. Payne, and L. Deng, “Formation and propagation of coupled ultraslow optical soliton pairs in a cold three-state double-Λ system,” Phys. Rev. E 73, 056606 (2006).
[CrossRef]

H. Michinel, M. J. Paz-Alonso, and V. M. Perez-Garcia, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

C. Hang, G. X. Huang, and L. Deng, “Stable high-dimensional spatial weak-light solitons in a resonant three-state atomic system,” Phys. Rev. E 74, 046601 (2006).
[CrossRef]

2005 (4)

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

G. X. 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. G. Payne, G. X. Huang, and E. W. Hagley, “Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double-Λ system,” Phys. Rev. E 72, 055601(R) (2005).
[CrossRef]

D. Petrosyan, “Towards deterministic optical quantum computation with coherently driven atomic ensembles,” J. Opt. B. 7, S141-S151 (2005).
[CrossRef]

2004 (4)

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]

D. A. Braje, V. Bali, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Z. G. Chen, A. Bezryadina, and I. Makasyuk, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29, 1656-1658 (2004).
[CrossRef] [PubMed]

2003 (3)

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] [PubMed]

H. Kang and Y. F. 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]

2002 (3)

Y. S. Kivshar and G. I. Stegeman, “Spatial optical solitons,” Opt. Photonics News 13, 59-63 (2002).
[CrossRef]

T. Hong, M. W. Jack, M. Yamashita, and T. Mukai, “Enhanced Kerr nonlinearity for self-action via atomic coherence in a four-level atomic system,” Opt. Commun. 214, 371-380 (2002).
[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] [PubMed]

2000 (1)

B. Hu, G. X. Huang, and M. G. Velarde, “Dynamics of coupled gap solitons in diatomic lattices with cubic and quartic nonlinearities,” Phys. Rev. E 62, 2827-2839 (2000).
[CrossRef]

1999 (2)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518-1523 (1999).
[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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

1998 (1)

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81-197 (1998).
[CrossRef]

1997 (1)

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

1996 (2)

1995 (3)

P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20, 982-984 (1995).
[CrossRef] [PubMed]

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] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

1993 (1)

1991 (1)

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583-1586 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

1988 (1)

1987 (1)

Afanasyev, V. V.

Agrawal, G. P.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Aitchison, J. S.

Andersen, D. R.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583-1586 (1991).
[CrossRef] [PubMed]

Anderson, B.

Y. Zhang, B. Anderson, and M. Xiao, “Efficient energy transfer between four-wave-mixing and six-wave-mixing processes via atomic coherence,” Phys. Rev. A 77, 061801 (2008).
[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] [PubMed]

Bali, V.

D. A. Braje, V. Bali, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

Bezryadina, A.

Braje, D. A.

D. A. Braje, V. Bali, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

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] [PubMed]

Chen, Z. G.

Cronin-Golomb, M.

Deng, L.

C. Hang, G. X. Huang, and L. Deng, “Stable high-dimensional spatial weak-light solitons in a resonant three-state atomic system,” Phys. Rev. E 74, 046601 (2006).
[CrossRef]

G. X. Huang, K. J. Jiang, M. G. Payne, and L. Deng, “Formation and propagation of coupled ultraslow optical soliton pairs in a cold three-state double-Λ system,” Phys. Rev. E 73, 056606 (2006).
[CrossRef]

G. X. 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. G. Payne, G. X. Huang, and E. W. Hagley, “Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double-Λ system,” Phys. Rev. E 72, 055601(R) (2005).
[CrossRef]

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]

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] [PubMed]

Donoghue, J.

Du, Y.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Dunn, M. H.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Fleischhauer, M.

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

Fulton, D. J.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

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] [PubMed]

Goda, S.

D. A. Braje, V. Bali, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

Hagley, E. W.

L. Deng, M. G. Payne, G. X. Huang, and E. W. Hagley, “Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double-Λ system,” Phys. Rev. E 72, 055601(R) (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] [PubMed]

Hang, C.

C. Hang, V. V. Konotop, and G. X. Huang, “Spatial solitons and instabilities of light beams in a three-level atomic medium with a standing-wave control field,” Phys. Rev. A 79, 033826 (2009).
[CrossRef]

C. Hang and G. Huang, “Weak-light ultraslow vector solitons via electromagnetically induced transparency,” Phys. Rev. A 77, 033830 (2008).
[CrossRef]

J. Wang, C. Hang, and G. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528-533 (2007).
[CrossRef]

C. Hang, Y. Li, L. Ma, and G. X. 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, G. X. Huang, and L. Deng, “Stable high-dimensional spatial weak-light solitons in a resonant three-state atomic system,” Phys. Rev. E 74, 046601 (2006).
[CrossRef]

Harris, S. E.

D. A. Braje, V. Bali, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

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

Haus, H. A.

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

Hemmer, P. R.

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]

Hong, T.

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

T. Hong, M. W. Jack, M. Yamashita, and T. Mukai, “Enhanced Kerr nonlinearity for self-action via atomic coherence in a four-level atomic system,” Opt. Commun. 214, 371-380 (2002).
[CrossRef]

Hou, J. M.

W. X. Yang, J. M. Hou, and R. K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838 (2008).
[CrossRef]

Hu, B.

B. Hu, G. X. Huang, and M. G. Velarde, “Dynamics of coupled gap solitons in diatomic lattices with cubic and quartic nonlinearities,” Phys. Rev. E 62, 2827-2839 (2000).
[CrossRef]

Huang, G.

C. Hang and G. Huang, “Weak-light ultraslow vector solitons via electromagnetically induced transparency,” Phys. Rev. A 77, 033830 (2008).
[CrossRef]

J. Wang, C. Hang, and G. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528-533 (2007).
[CrossRef]

Huang, G. X.

C. Hang, V. V. Konotop, and G. X. Huang, “Spatial solitons and instabilities of light beams in a three-level atomic medium with a standing-wave control field,” Phys. Rev. A 79, 033826 (2009).
[CrossRef]

H. J. Li and G. X. Huang, “Two-component spatial optical solitons in a four-state ladder system via electromagnetically induced transparency,” Phys. Lett. A 372, 4127-4134 (2008).
[CrossRef]

C. Hang, Y. Li, L. Ma, and G. X. 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. X. Huang, K. J. Jiang, M. G. Payne, and L. Deng, “Formation and propagation of coupled ultraslow optical soliton pairs in a cold three-state double-Λ system,” Phys. Rev. E 73, 056606 (2006).
[CrossRef]

C. Hang, G. X. Huang, and L. Deng, “Stable high-dimensional spatial weak-light solitons in a resonant three-state atomic system,” Phys. Rev. E 74, 046601 (2006).
[CrossRef]

G. X. 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. G. Payne, G. X. Huang, and E. W. Hagley, “Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double-Λ system,” Phys. Rev. E 72, 055601(R) (2005).
[CrossRef]

B. Hu, G. X. Huang, and M. G. Velarde, “Dynamics of coupled gap solitons in diatomic lattices with cubic and quartic nonlinearities,” Phys. Rev. E 62, 2827-2839 (2000).
[CrossRef]

Imamoglu, A.

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

Jack, M. W.

T. Hong, M. W. Jack, M. Yamashita, and T. Mukai, “Enhanced Kerr nonlinearity for self-action via atomic coherence in a four-level atomic system,” Opt. Commun. 214, 371-380 (2002).
[CrossRef]

Jackel, J. L.

Jiang, K. J.

G. X. Huang, K. J. Jiang, M. G. Payne, and L. Deng, “Formation and propagation of coupled ultraslow optical soliton pairs in a cold three-state double-Λ system,” Phys. Rev. E 73, 056606 (2006).
[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] [PubMed]

Kang, H.

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

Kaplan, A. E.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583-1586 (1991).
[CrossRef] [PubMed]

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]

Katz, D. P.

Kivshar, Y. S.

Y. S. Kivshar and G. I. Stegeman, “Spatial optical solitons,” Opt. Photonics News 13, 59-63 (2002).
[CrossRef]

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81-197 (1998).
[CrossRef]

Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18, 337-339 (1993).
[CrossRef] [PubMed]

V. V. Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805-807 (1989).
[CrossRef] [PubMed]

Knox, W. H.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Konotop, V. V.

C. Hang, V. V. Konotop, and G. X. Huang, “Spatial solitons and instabilities of light beams in a three-level atomic medium with a standing-wave control field,” Phys. Rev. A 79, 033826 (2009).
[CrossRef]

V. V. Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805-807 (1989).
[CrossRef] [PubMed]

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] [PubMed]

Kumar, P.

Leaird, D. E.

Lee, R. K.

W. X. Yang, J. M. Hou, and R. K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838 (2008).
[CrossRef]

Li, C.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Li, H. J.

H. J. Li and G. X. Huang, “Two-component spatial optical solitons in a four-state ladder system via electromagnetically induced transparency,” Phys. Lett. A 372, 4127-4134 (2008).
[CrossRef]

Li, L. L.

W. J. Liu, B. Tian, H. Q. Zhang, L. L. Li, and Y. S. Xue, “Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method,” Phys. Rev. E 77, 066605 (2008).
[CrossRef]

Li, W. B.

Li, Y.

C. Hang, Y. Li, L. Ma, and G. X. 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] [PubMed]

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] [PubMed]

Lin, Q.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Liu, W. J.

W. J. Liu, B. Tian, H. Q. Zhang, L. L. Li, and Y. S. Xue, “Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method,” Phys. Rev. E 77, 066605 (2008).
[CrossRef]

Lu, F.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Lu, K.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[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]

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81-197 (1998).
[CrossRef]

Ma, L.

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

Makasyuk, I.

Marangos, J. P.

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

Menyuk, C. R.

Michinel, H.

H. Michinel, M. J. Paz-Alonso, and V. M. Perez-Garcia, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

Moseley, R. R.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Mukai, T.

T. Hong, M. W. Jack, M. Yamashita, and T. Mukai, “Enhanced Kerr nonlinearity for self-action via atomic coherence in a four-level atomic system,” Opt. Commun. 214, 371-380 (2002).
[CrossRef]

Nie, Z.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Oliver, M. K.

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] [PubMed]

Payne, M. G.

G. X. Huang, K. J. Jiang, M. G. Payne, and L. Deng, “Formation and propagation of coupled ultraslow optical soliton pairs in a cold three-state double-Λ system,” Phys. Rev. E 73, 056606 (2006).
[CrossRef]

L. Deng, M. G. Payne, G. X. Huang, and E. W. Hagley, “Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double-Λ system,” Phys. Rev. E 72, 055601(R) (2005).
[CrossRef]

G. X. 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] [PubMed]

Paz-Alonso, M. J.

H. Michinel, M. J. Paz-Alonso, and V. M. Perez-Garcia, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

Perez-Garcia, V. M.

H. Michinel, M. J. Paz-Alonso, and V. M. Perez-Garcia, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[CrossRef] [PubMed]

Petrosyan, D.

D. Petrosyan, “Towards deterministic optical quantum computation with coherently driven atomic ensembles,” J. Opt. B. 7, S141-S151 (2005).
[CrossRef]

Regan, J. J.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583-1586 (1991).
[CrossRef] [PubMed]

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]

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]

Segev, M.

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518-1523 (1999).
[CrossRef] [PubMed]

Serkin, V. N.

Shahriar, M. S.

Shepherd, S.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Shi, M.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Si, L. G.

Silberberg, Y.

Sinclair, B. D.

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Smith, P. W. E.

Song, J.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Stegeman, G. I.

Y. S. Kivshar and G. I. Stegeman, “Spatial optical solitons,” Opt. Photonics News 13, 59-63 (2002).
[CrossRef]

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518-1523 (1999).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871-873 (1988).
[CrossRef] [PubMed]

Swartzlander, G. A.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583-1586 (1991).
[CrossRef] [PubMed]

Tian, B.

W. J. Liu, B. Tian, H. Q. Zhang, L. L. Li, and Y. S. Xue, “Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method,” Phys. Rev. E 77, 066605 (2008).
[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] [PubMed]

Trillo, S.

Turitsyn, S. K.

Velarde, M. G.

B. Hu, G. X. Huang, and M. G. Velarde, “Dynamics of coupled gap solitons in diatomic lattices with cubic and quartic nonlinearities,” Phys. Rev. E 62, 2827-2839 (2000).
[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] [PubMed]

Vogel, E. M.

Wabnitz, S.

Wang, J.

J. Wang, C. Hang, and G. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528-533 (2007).
[CrossRef]

Wang, R.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Weiner, A. M.

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]

Wong, W. S.

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

Wright, E. M.

Wu, X.

X. Wu, X. T. Xie, and X. X. Yang, “Dark and bright vortex solitons in electromagnetically induced transparent media,” J. Phys. B 39, 3263-3273 (2006).
[CrossRef]

Wu, Y.

Xiao, M.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Y. Zhang, B. Anderson, and M. Xiao, “Efficient energy transfer between four-wave-mixing and six-wave-mixing processes via atomic coherence,” Phys. Rev. A 77, 061801 (2008).
[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] [PubMed]

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] [PubMed]

Xie, X. T.

X. Wu, X. T. Xie, and X. X. Yang, “Dark and bright vortex solitons in electromagnetically induced transparent media,” J. Phys. B 39, 3263-3273 (2006).
[CrossRef]

X. T. Xie, W. B. Li, and X. X. Yang, “Bright, dark, bistable bright, and vortex spatial-optical solitons in a cold three-state medium,” J. Opt. Soc. Am. B 23, 1609-1614 (2006).
[CrossRef]

Xue, Y. S.

W. J. Liu, B. Tian, H. Q. Zhang, L. L. Li, and Y. S. Xue, “Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method,” Phys. Rev. E 77, 066605 (2008).
[CrossRef]

Yamashita, M.

T. Hong, M. W. Jack, M. Yamashita, and T. Mukai, “Enhanced Kerr nonlinearity for self-action via atomic coherence in a four-level atomic system,” Opt. Commun. 214, 371-380 (2002).
[CrossRef]

Yang, W. X.

L. G. Si, W. X. Yang, and X. X. Yang, “Ultraslow temporal vector optical solitons in a cold four-level tripod atomic system,” J. Opt. Soc. Am. B 26, 478-486 (2009).
[CrossRef]

W. X. Yang, J. M. Hou, and R. K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838 (2008).
[CrossRef]

Yang, X. X.

Yin, G. Y.

D. A. Braje, V. Bali, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

Yin, H.

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583-1586 (1991).
[CrossRef] [PubMed]

Zhang, H. Q.

W. J. Liu, B. Tian, H. Q. Zhang, L. L. Li, and Y. S. Xue, “Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method,” Phys. Rev. E 77, 066605 (2008).
[CrossRef]

Zhang, Y.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Y. Zhang, B. Anderson, and M. Xiao, “Efficient energy transfer between four-wave-mixing and six-wave-mixing processes via atomic coherence,” Phys. Rev. A 77, 061801 (2008).
[CrossRef]

Zheng, H.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

Zhu, Y. F.

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

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]

Zuo, C.

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

J. Opt. B. (1)

D. Petrosyan, “Towards deterministic optical quantum computation with coherently driven atomic ensembles,” J. Opt. B. 7, S141-S151 (2005).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (1)

X. Wu, X. T. Xie, and X. X. Yang, “Dark and bright vortex solitons in electromagnetically induced transparent media,” J. Phys. B 39, 3263-3273 (2006).
[CrossRef]

Opt. Commun. (1)

T. Hong, M. W. Jack, M. Yamashita, and T. Mukai, “Enhanced Kerr nonlinearity for self-action via atomic coherence in a four-level atomic system,” Opt. Commun. 214, 371-380 (2002).
[CrossRef]

Opt. Lett. (9)

P. R. Hemmer, D. P. Katz, J. Donoghue, M. Cronin-Golomb, M. S. Shahriar, and P. Kumar, “Efficient low-intensity optical phase conjugation based on coherent population trapping in sodium,” Opt. Lett. 20, 982-984 (1995).
[CrossRef] [PubMed]

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] [PubMed]

Z. G. Chen, A. Bezryadina, and I. Makasyuk, “Observation of two-dimensional lattice vector solitons,” Opt. Lett. 29, 1656-1658 (2004).
[CrossRef] [PubMed]

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes,” Opt. Lett. 12, 614-616 (1987).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman, “Optical solitary waves induced by cross-phase modulation,” Opt. Lett. 13, 871-873 (1988).
[CrossRef] [PubMed]

V. V. Afanasyev, Y. S. Kivshar, V. V. Konotop, and V. N. Serkin, “Dynamics of coupled dark and bright optical solitons,” Opt. Lett. 14, 805-807 (1989).
[CrossRef] [PubMed]

Y. S. Kivshar and S. K. Turitsyn, “Vector dark solitons,” Opt. Lett. 18, 337-339 (1993).
[CrossRef] [PubMed]

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]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, M. K. Oliver, J. L. Jackel, D. E. Leaird, E. M. Vogel, and P. W. E. Smith, “Observation of spatial optical solitons in a nonlinear glass waveguide,” Opt. Lett. 15, 471-473 (1990).
[CrossRef] [PubMed]

Opt. Photonics News (1)

Y. S. Kivshar and G. I. Stegeman, “Spatial optical solitons,” Opt. Photonics News 13, 59-63 (2002).
[CrossRef]

Phys. Lett. A (2)

J. Wang, C. Hang, and G. Huang, “Weak-light gap solitons in a resonant three-level system,” Phys. Lett. A 366, 528-533 (2007).
[CrossRef]

H. J. Li and G. X. Huang, “Two-component spatial optical solitons in a four-state ladder system via electromagnetically induced transparency,” Phys. Lett. A 372, 4127-4134 (2008).
[CrossRef]

Phys. Rep. (1)

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298, 81-197 (1998).
[CrossRef]

Phys. Rev. A (6)

Y. Zhang, B. Anderson, and M. Xiao, “Efficient energy transfer between four-wave-mixing and six-wave-mixing processes via atomic coherence,” Phys. Rev. A 77, 061801 (2008).
[CrossRef]

Y. Du, Y. Zhang, C. Zuo, C. Li, Z. Nie, H. Zheng, M. Shi, R. Wang, J. Song, K. Lu, and M. Xiao, “Controlling four-wave mixing and six-wave mixing in a multi-Zeeman sublevel atomic system with electromagnetically induced transparency,” Phys. Rev. A 79, 063839 (2009).
[CrossRef]

C. Hang and G. Huang, “Weak-light ultraslow vector solitons via electromagnetically induced transparency,” Phys. Rev. A 77, 033830 (2008).
[CrossRef]

W. X. Yang, J. M. Hou, and R. K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838 (2008).
[CrossRef]

C. Hang, V. V. Konotop, and G. X. Huang, “Spatial solitons and instabilities of light beams in a three-level atomic medium with a standing-wave control field,” Phys. Rev. A 79, 033826 (2009).
[CrossRef]

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

Phys. Rev. E (6)

G. X. 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. G. Payne, G. X. Huang, and E. W. Hagley, “Formation and propagation of matched and coupled ultraslow optical soliton pairs in a four-level double-Λ system,” Phys. Rev. E 72, 055601(R) (2005).
[CrossRef]

C. Hang, G. X. Huang, and L. Deng, “Stable high-dimensional spatial weak-light solitons in a resonant three-state atomic system,” Phys. Rev. E 74, 046601 (2006).
[CrossRef]

B. Hu, G. X. Huang, and M. G. Velarde, “Dynamics of coupled gap solitons in diatomic lattices with cubic and quartic nonlinearities,” Phys. Rev. E 62, 2827-2839 (2000).
[CrossRef]

G. X. Huang, K. J. Jiang, M. G. Payne, and L. Deng, “Formation and propagation of coupled ultraslow optical soliton pairs in a cold three-state double-Λ system,” Phys. Rev. E 73, 056606 (2006).
[CrossRef]

W. J. Liu, B. Tian, H. Q. Zhang, L. L. Li, and Y. S. Xue, “Soliton interaction in the higher-order nonlinear Schrödinger equation investigated with Hirota's bilinear method,” Phys. Rev. E 77, 066605 (2008).
[CrossRef]

Phys. Rev. Lett. (11)

G. A. Swartzlander, D. R. Andersen, J. J. Regan, H. Yin, and A. E. Kaplan, “Spatial dark-soliton stripes and grids in self-defocusing materials,” Phys. Rev. Lett. 66, 1583-1586 (1991).
[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

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

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] [PubMed]

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

H. Michinel, M. J. Paz-Alonso, and V. M. Perez-Garcia, “Turning light into a liquid via atomic coherence,” Phys. Rev. Lett. 96, 023903 (2006).
[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, “Ultraslow group velocity and enhanced nonlinear optical effects in a coherently driven hot atomic gas,” Phys. Rev. Lett. 82, 5229-5232 (1999).
[CrossRef]

D. A. Braje, V. Bali, S. Goda, G. Y. Yin, and S. E. Harris, “Frequency mixing using electromagnetically induced transparency in cold atoms,” Phys. Rev. Lett. 93, 183601 (2004).
[CrossRef] [PubMed]

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

R. R. Moseley, S. Shepherd, D. J. Fulton, B. D. Sinclair, and M. H. Dunn, “Spatial consequences of electromagnetically induced transparency: observation of electromagnetically induced focusing,” Phys. Rev. Lett. 74, 670-673 (1995).
[CrossRef] [PubMed]

Phys. Today (1)

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

Rev. Mod. Phys. (2)

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

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

Science (1)

G. I. Stegeman and M. Segev, “Optical spatial solitons and their interactions: universality and diversity,” Science 286, 1518-1523 (1999).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Lifetime-broadened four-level double-Λ type atomic system interacts with two weak probe fields (of which center angular frequencies and Rabi frequencies are ω p ( m ) and Ω p ( m ) ) and two strong control fields (of which center angular frequencies and Rabi frequencies are ω a ( b ) and Ω a ( b ) ), respectively. Δ j ( j = 2 , 3 , 4 ) is the detuning.

Fig. 2
Fig. 2

Absorption coefficients α ± of two components of the probe field versus Rabi frequency Ω a obtained with | Ω b | = 1.0 × 10 9 s 1 . Other parameters of this system are κ 14 = 2 κ 13 = 2.0 × 10 12 m 1 s 1 , Δ 2 = Δ 3 = 1.0 × 10 8 s 1 , Δ 4 = 2.0 × 10 8 s 1 , γ 3 = γ 4 = 2.0 × 10 8 Hz , and γ 2 = 2.0 × 10 7 Hz .

Fig. 3
Fig. 3

Space evolution of the relative probe field intensity | Ω p | 2 in the case of bright–bright soliton solution as a function of dimensionless diffraction width X = x R x and propagation distance ξ = z L F with R x = 20 μ m and L F = 2.5 mm . Other parameters are γ 2 = 2.0 × 10 6 s 1 , γ 3 = 5 γ 4 = 5.0 × 10 7 s 1 , Δ 2 = 2.5 × 10 8 s 1 , Δ 3 = Δ 4 = 1.5 × 10 9 s 1 , λ m = λ p = 0.16 μ m , κ 13 = κ 14 = 1.0 × 10 10 m 1 s 1 , | Ω b | = 1.5 | Ω a | = 1.5 × 10 9 s 1 , A = 1.0 , B = 0.1 , and p 0 = 0.5 .

Fig. 4
Fig. 4

Spatial distribution of | Ω p | 2 for the interactions between two solitons with (a) ρ = 1.4 , φ 1 = 0 , (b) ρ = 1.4 , φ 1 = π , (c) ρ = 1.0 , φ 1 = π 2 , and (d) ρ = 1.0 , φ 1 = π 2 .

Equations (31)

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

( i t + d 2 ) A 2 + Ω a * A 3 + Ω b * A 4 = 0 ,
( i t + d 3 ) A 3 + Ω p A 1 + Ω a A 2 = 0 ,
( i t + d 4 ) A 4 + Ω m A 1 + Ω b A 2 = 0 ,
| A 1 | 2 + | A 2 | 2 + | A 3 | 2 + | A 4 | 2 = 1 ,
2 E 1 c 2 2 E t 2 = 1 ε 0 c 2 2 P t 2 ,
i ( z + 1 c t ) Ω p + c 2 ω p 2 x 2 Ω p + κ 13 A 1 * A 3 = 0 ,
i ( z + 1 c t ) Ω m + c 2 ω m 2 x 2 Ω m + κ 14 A 1 * A 4 = 0 ,
( i t 0 + d 2 ) A 2 ( j ) + Ω a * A 3 ( j ) + Ω b * A 4 ( j ) = α ( j ) ,
( i t 0 + d 3 ) A 3 ( j ) + Ω p ( j ) + Ω a A 2 ( j ) = β ( j ) ,
( i t 0 + d 4 ) A 4 ( j ) + Ω m ( j ) + Ω b A 2 ( j ) = γ ( j ) ,
i ( z 0 + 1 c t 0 ) Ω p ( j ) + κ 13 A 3 ( j ) = δ ( j ) ,
i ( z 0 + 1 c t 0 ) Ω m ( j ) + κ 14 A 4 ( j ) = ρ ( j ) .
Ω p ( 1 ) = F + e i [ K + ( ( ω ) z 0 ω t 0 ) ] + F e i [ K ( ω ) z 0 ω t 0 ] = F + e i θ + + F e i θ ,
Ω m ( 1 ) = 1 κ 13 Ω a Ω b * G + F + e i θ + + 1 κ 13 Ω a Ω b * G F e i θ ,
A 2 ( 1 ) = 1 Ω a H + F + e i θ + 1 Ω a H F e i θ ,
A 3 ( 1 ) = 1 κ 13 ( K + ω c ) F + e i θ + + 1 κ 13 ( K ω c ) F e i θ ,
A 4 ( 1 ) = 1 κ 13 κ 14 Ω a Ω b * ( K + ω c ) G + F + e i θ + + 1 κ 13 κ 14 Ω a Ω b * ( K + ω c ) G F e i θ ,
K = K ± ( ω ) = K ± ( 0 ) + K ± ω + K ± ω 2 + ,
i ( z 1 + 1 v g ± t 1 ) F ± = 0 ,
i U + z + i R U + τ + K 2 + 2 U + τ 2 + M + 2 U + x 2 + ( N 11 | U + | 2 + N 12 | U | 2 ) U + = 0 ,
i U z + i R U τ + K 2 2 U τ 2 + M 2 U x 2 + ( N 21 | U + | 2 + N 22 | U | 2 ) U = 0 ,
i v + ξ + d 1 F 2 v + X 2 + ( β 11 | v + | 2 + β 12 | v | 2 ) v + = 0 ,
i v ξ + d 2 F 2 v X 2 + ( β 21 | v + | 2 + β 22 | v | 2 ) v = 0 ,
v + = 2 p 0 sec h [ A ( X B ξ ) ] exp { i [ B 2 d 1 F X + ( A 2 d 1 F B 2 4 d 1 F ) ξ ] } ,
v = 2 q 0 sec h [ A ( X B ξ ) ] exp { i [ B 2 d 2 F X + ( A 2 d 2 F B 2 4 d 2 F ) ξ ] } ,
v + = 2 p 0 sec h [ A ( X B ξ ) ] exp { i [ B 2 d 1 F X + ( A 2 d 1 F 2 β 12 q 0 2 B 2 4 d 1 F ) ξ ] } ,
v = 2 q 0 tanh [ A ( X B ξ ) ] exp { i [ B 2 d 2 F X 2 ( A 2 d 2 F + β 21 p 0 2 + B 2 8 d 2 F ) ξ ] } ,
v + = 2 p 0 tanh [ A ( X B ξ ) ] exp { i [ B 2 d 1 F X 2 ( A 2 d 1 F + β 12 q 0 2 + B 2 8 d 1 F ) ξ ] } ,
v = 2 q 0 sec h [ A ( X B ξ ) ] exp { i [ B 2 d 2 F X + ( A 2 d 2 F 2 β 21 p 0 2 B 2 4 d 2 F ) ξ ] } ,
v + = 2 p 0 tanh [ A ( X B ξ ) ] exp { i [ B 2 d 1 F X 2 ( A 2 d 1 F + B 2 8 d 1 F ) ξ ] } ,
v = 2 q 0 tanh [ A ( X B ξ ) ] exp { i [ B 2 d 2 F X 2 ( A 2 d 1 F + B 2 8 d 2 F ) ξ ] } ,

Metrics