Abstract

The characteristics of two coupled Bose-Einstein Condensate (BEC) bright solitons trapped in an optical lattice are investigated with the variational approach and direct numerical simulations of the Gross-Pitaevskii equation. It is found that the optical lattice can be controllably used to capture and drag the coupled BEC solitons. Its effect depends on the initial location of the BEC solitons, the lattice amplitude and wave-number, and the amplitude of the coupled BEC solitons. The effective interaction between the two coupled solitons is the attractive effect.

© 2006 Optical Society of America

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  1. M. H. Anderson, J. R. Matthews, and C. E. Wieman, “Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor,” Science 269,198 (1995)
    [Crossref] [PubMed]
  2. K. E. Strecker, G. B. Partridge, and A. G. Truscott, “Formation and propagation of matter-wave soliton trains,” Nature 417, 150(2002)
    [Crossref] [PubMed]
  3. L. Khaykovich, F. Schreck, and G. Ferrari, “Formation of a Matter-Wave Bright Soliton,” Science 296, 1290(2002)
    [Crossref] [PubMed]
  4. I. Carusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611(2002)
    [Crossref]
  5. Y. S. Cheng, H. Li, and R. Z. Gong, “Effects of parameters on the stationary state and self-trapping of three coupled Bose-Einstein Condensate solitons,” Chin. Opt. Lett. 3, 715(2005)
  6. P. Massignan and M. Modugno, “One-dimensional model for the dynamics and expansion of elongated Bose-Einstein condensates,” Phys. Rev. A 67, 023614(2003)
    [Crossref]
  7. C. Lee, W. Hai, and X. Luo, “Quasispin model for macroscopic quantum tunneling between two coupled Bose-Einstein condensates,” Phys. Rev. A 68, 053614(2003)
    [Crossref]
  8. E. A. Ostrovskaya and Y. S. Kivshar, “Localization of Two-Component Bose-Einstein Condensates in Optical Lattices,” Phys. Rev. Lett. 92, 180405(2004)
    [Crossref] [PubMed]
  9. A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates,” Phys. Rev. Lett. 79, 4950(1997)
    [Crossref]
  10. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620(1999)
    [Crossref]
  11. G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55, 4318(1997)
    [Crossref]
  12. J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, “Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate,” Phys. Rev. A 59, R31(1999)
    [Crossref]
  13. B. P. Anderson and M. A. Kasevich, “Macroscopic Quantum Interference from Atomic Tunnel Arrays,” Science 282, 1686(1998)
    [Crossref] [PubMed]
  14. D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, “Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1538(1998)D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of Relative Phase in Two-Component Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1543(1998)
  15. R. Carretero-Gonzalez and K. Promislow, “Localized breathing oscillations of Bose-Einstein condensates in periodic traps,” Phys. Rev. A 66, 033610(2002)
    [Crossref]
  16. C. Pare and M. Florjariczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287–6295(1990)
    [Crossref] [PubMed]
  17. H. Li, Y. S. Cheng, and D. X. Huang, “Effects of traps on dynamics of two coupled Bose-Einstein condensates,” Opt. Commun. 258, 306–314 (2006)
    [Crossref]
  18. S. Raghavan and G. P. Agrawal, “Switching and self-trapping dynamics of Bose-Einstein solitons,” J. Mod. Opt. 47, 1155(2000)
  19. P. Ohberg and L. Santos, “Dark Solitons in a Two-Component Bose-Einstein Condensate,” Phys. Rev. Lett. 86, 2918–2921(2001)
    [Crossref] [PubMed]
  20. D. J. Frantzeskakis, G. Theocharis, and F. K. Diakonos, “Interaction of dark solitons with localized impurities in Bose-Einstein condensates,” Phys. Rev. A 66, 053608(2002)
    [Crossref]
  21. R. G. Scott, A. M. Martin, and S. Bujkiewicz, “Transport and disruption of Bose-Einstein condensates in optical lattices,” Phys. Rev. A 69, 033605(2004)
    [Crossref]

2006 (1)

H. Li, Y. S. Cheng, and D. X. Huang, “Effects of traps on dynamics of two coupled Bose-Einstein condensates,” Opt. Commun. 258, 306–314 (2006)
[Crossref]

2005 (1)

2004 (2)

E. A. Ostrovskaya and Y. S. Kivshar, “Localization of Two-Component Bose-Einstein Condensates in Optical Lattices,” Phys. Rev. Lett. 92, 180405(2004)
[Crossref] [PubMed]

R. G. Scott, A. M. Martin, and S. Bujkiewicz, “Transport and disruption of Bose-Einstein condensates in optical lattices,” Phys. Rev. A 69, 033605(2004)
[Crossref]

2003 (2)

P. Massignan and M. Modugno, “One-dimensional model for the dynamics and expansion of elongated Bose-Einstein condensates,” Phys. Rev. A 67, 023614(2003)
[Crossref]

C. Lee, W. Hai, and X. Luo, “Quasispin model for macroscopic quantum tunneling between two coupled Bose-Einstein condensates,” Phys. Rev. A 68, 053614(2003)
[Crossref]

2002 (5)

K. E. Strecker, G. B. Partridge, and A. G. Truscott, “Formation and propagation of matter-wave soliton trains,” Nature 417, 150(2002)
[Crossref] [PubMed]

L. Khaykovich, F. Schreck, and G. Ferrari, “Formation of a Matter-Wave Bright Soliton,” Science 296, 1290(2002)
[Crossref] [PubMed]

I. Carusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611(2002)
[Crossref]

R. Carretero-Gonzalez and K. Promislow, “Localized breathing oscillations of Bose-Einstein condensates in periodic traps,” Phys. Rev. A 66, 033610(2002)
[Crossref]

D. J. Frantzeskakis, G. Theocharis, and F. K. Diakonos, “Interaction of dark solitons with localized impurities in Bose-Einstein condensates,” Phys. Rev. A 66, 053608(2002)
[Crossref]

2001 (1)

P. Ohberg and L. Santos, “Dark Solitons in a Two-Component Bose-Einstein Condensate,” Phys. Rev. Lett. 86, 2918–2921(2001)
[Crossref] [PubMed]

2000 (1)

S. Raghavan and G. P. Agrawal, “Switching and self-trapping dynamics of Bose-Einstein solitons,” J. Mod. Opt. 47, 1155(2000)

1999 (2)

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, “Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate,” Phys. Rev. A 59, R31(1999)
[Crossref]

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620(1999)
[Crossref]

1998 (2)

B. P. Anderson and M. A. Kasevich, “Macroscopic Quantum Interference from Atomic Tunnel Arrays,” Science 282, 1686(1998)
[Crossref] [PubMed]

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, “Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1538(1998)D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of Relative Phase in Two-Component Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1543(1998)

1997 (2)

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55, 4318(1997)
[Crossref]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates,” Phys. Rev. Lett. 79, 4950(1997)
[Crossref]

1995 (1)

M. H. Anderson, J. R. Matthews, and C. E. Wieman, “Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor,” Science 269,198 (1995)
[Crossref] [PubMed]

1990 (1)

C. Pare and M. Florjariczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287–6295(1990)
[Crossref] [PubMed]

Agrawal, G. P.

S. Raghavan and G. P. Agrawal, “Switching and self-trapping dynamics of Bose-Einstein solitons,” J. Mod. Opt. 47, 1155(2000)

Anderson, B. P.

B. P. Anderson and M. A. Kasevich, “Macroscopic Quantum Interference from Atomic Tunnel Arrays,” Science 282, 1686(1998)
[Crossref] [PubMed]

Anderson, M. H.

M. H. Anderson, J. R. Matthews, and C. E. Wieman, “Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor,” Science 269,198 (1995)
[Crossref] [PubMed]

Bujkiewicz, S.

R. G. Scott, A. M. Martin, and S. Bujkiewicz, “Transport and disruption of Bose-Einstein condensates in optical lattices,” Phys. Rev. A 69, 033605(2004)
[Crossref]

Carretero-Gonzalez, R.

R. Carretero-Gonzalez and K. Promislow, “Localized breathing oscillations of Bose-Einstein condensates in periodic traps,” Phys. Rev. A 66, 033610(2002)
[Crossref]

Carusotto, I.

I. Carusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611(2002)
[Crossref]

Cheng, Y. S.

H. Li, Y. S. Cheng, and D. X. Huang, “Effects of traps on dynamics of two coupled Bose-Einstein condensates,” Opt. Commun. 258, 306–314 (2006)
[Crossref]

Y. S. Cheng, H. Li, and R. Z. Gong, “Effects of parameters on the stationary state and self-trapping of three coupled Bose-Einstein Condensate solitons,” Chin. Opt. Lett. 3, 715(2005)

Cooper, J.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, “Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate,” Phys. Rev. A 59, R31(1999)
[Crossref]

Cornell, E.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, “Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate,” Phys. Rev. A 59, R31(1999)
[Crossref]

Cornell, E. A.

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, “Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1538(1998)D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of Relative Phase in Two-Component Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1543(1998)

Corney, J.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55, 4318(1997)
[Crossref]

Diakonos, F. K.

D. J. Frantzeskakis, G. Theocharis, and F. K. Diakonos, “Interaction of dark solitons with localized impurities in Bose-Einstein condensates,” Phys. Rev. A 66, 053608(2002)
[Crossref]

Embriaco, D.

I. Carusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611(2002)
[Crossref]

Ensher, J. R.

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, “Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1538(1998)D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of Relative Phase in Two-Component Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1543(1998)

Fantoni, S.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620(1999)
[Crossref]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates,” Phys. Rev. Lett. 79, 4950(1997)
[Crossref]

Ferrari, G.

L. Khaykovich, F. Schreck, and G. Ferrari, “Formation of a Matter-Wave Bright Soliton,” Science 296, 1290(2002)
[Crossref] [PubMed]

Florjariczyk, M.

C. Pare and M. Florjariczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287–6295(1990)
[Crossref] [PubMed]

Frantzeskakis, D. J.

D. J. Frantzeskakis, G. Theocharis, and F. K. Diakonos, “Interaction of dark solitons with localized impurities in Bose-Einstein condensates,” Phys. Rev. A 66, 053608(2002)
[Crossref]

Giovanazzi, S.

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates,” Phys. Rev. Lett. 79, 4950(1997)
[Crossref]

Gong, R. Z.

Hai, W.

C. Lee, W. Hai, and X. Luo, “Quasispin model for macroscopic quantum tunneling between two coupled Bose-Einstein condensates,” Phys. Rev. A 68, 053614(2003)
[Crossref]

Hall, D. S.

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, “Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1538(1998)D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of Relative Phase in Two-Component Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1543(1998)

Holland, M.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, “Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate,” Phys. Rev. A 59, R31(1999)
[Crossref]

Huang, D. X.

H. Li, Y. S. Cheng, and D. X. Huang, “Effects of traps on dynamics of two coupled Bose-Einstein condensates,” Opt. Commun. 258, 306–314 (2006)
[Crossref]

Kasevich, M. A.

B. P. Anderson and M. A. Kasevich, “Macroscopic Quantum Interference from Atomic Tunnel Arrays,” Science 282, 1686(1998)
[Crossref] [PubMed]

Khaykovich, L.

L. Khaykovich, F. Schreck, and G. Ferrari, “Formation of a Matter-Wave Bright Soliton,” Science 296, 1290(2002)
[Crossref] [PubMed]

Kivshar, Y. S.

E. A. Ostrovskaya and Y. S. Kivshar, “Localization of Two-Component Bose-Einstein Condensates in Optical Lattices,” Phys. Rev. Lett. 92, 180405(2004)
[Crossref] [PubMed]

La Rocca, G. C.

I. Carusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611(2002)
[Crossref]

Lee, C.

C. Lee, W. Hai, and X. Luo, “Quasispin model for macroscopic quantum tunneling between two coupled Bose-Einstein condensates,” Phys. Rev. A 68, 053614(2003)
[Crossref]

Li, H.

H. Li, Y. S. Cheng, and D. X. Huang, “Effects of traps on dynamics of two coupled Bose-Einstein condensates,” Opt. Commun. 258, 306–314 (2006)
[Crossref]

Y. S. Cheng, H. Li, and R. Z. Gong, “Effects of parameters on the stationary state and self-trapping of three coupled Bose-Einstein Condensate solitons,” Chin. Opt. Lett. 3, 715(2005)

Luo, X.

C. Lee, W. Hai, and X. Luo, “Quasispin model for macroscopic quantum tunneling between two coupled Bose-Einstein condensates,” Phys. Rev. A 68, 053614(2003)
[Crossref]

Martin, A. M.

R. G. Scott, A. M. Martin, and S. Bujkiewicz, “Transport and disruption of Bose-Einstein condensates in optical lattices,” Phys. Rev. A 69, 033605(2004)
[Crossref]

Massignan, P.

P. Massignan and M. Modugno, “One-dimensional model for the dynamics and expansion of elongated Bose-Einstein condensates,” Phys. Rev. A 67, 023614(2003)
[Crossref]

Matthews, J. R.

M. H. Anderson, J. R. Matthews, and C. E. Wieman, “Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor,” Science 269,198 (1995)
[Crossref] [PubMed]

Matthews, M. R.

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, “Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1538(1998)D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of Relative Phase in Two-Component Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1543(1998)

Milburn, G. J.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55, 4318(1997)
[Crossref]

Modugno, M.

P. Massignan and M. Modugno, “One-dimensional model for the dynamics and expansion of elongated Bose-Einstein condensates,” Phys. Rev. A 67, 023614(2003)
[Crossref]

Ohberg, P.

P. Ohberg and L. Santos, “Dark Solitons in a Two-Component Bose-Einstein Condensate,” Phys. Rev. Lett. 86, 2918–2921(2001)
[Crossref] [PubMed]

Ostrovskaya, E. A.

E. A. Ostrovskaya and Y. S. Kivshar, “Localization of Two-Component Bose-Einstein Condensates in Optical Lattices,” Phys. Rev. Lett. 92, 180405(2004)
[Crossref] [PubMed]

Pare, C.

C. Pare and M. Florjariczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287–6295(1990)
[Crossref] [PubMed]

Partridge, G. B.

K. E. Strecker, G. B. Partridge, and A. G. Truscott, “Formation and propagation of matter-wave soliton trains,” Nature 417, 150(2002)
[Crossref] [PubMed]

Promislow, K.

R. Carretero-Gonzalez and K. Promislow, “Localized breathing oscillations of Bose-Einstein condensates in periodic traps,” Phys. Rev. A 66, 033610(2002)
[Crossref]

Raghavan, S.

S. Raghavan and G. P. Agrawal, “Switching and self-trapping dynamics of Bose-Einstein solitons,” J. Mod. Opt. 47, 1155(2000)

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620(1999)
[Crossref]

Santos, L.

P. Ohberg and L. Santos, “Dark Solitons in a Two-Component Bose-Einstein Condensate,” Phys. Rev. Lett. 86, 2918–2921(2001)
[Crossref] [PubMed]

Schreck, F.

L. Khaykovich, F. Schreck, and G. Ferrari, “Formation of a Matter-Wave Bright Soliton,” Science 296, 1290(2002)
[Crossref] [PubMed]

Scott, R. G.

R. G. Scott, A. M. Martin, and S. Bujkiewicz, “Transport and disruption of Bose-Einstein condensates in optical lattices,” Phys. Rev. A 69, 033605(2004)
[Crossref]

Shenoy, S. R.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620(1999)
[Crossref]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates,” Phys. Rev. Lett. 79, 4950(1997)
[Crossref]

Smerzi, A.

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620(1999)
[Crossref]

A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, “Quantum Coherent Atomic Tunneling between Two Trapped Bose-Einstein Condensates,” Phys. Rev. Lett. 79, 4950(1997)
[Crossref]

Strecker, K. E.

K. E. Strecker, G. B. Partridge, and A. G. Truscott, “Formation and propagation of matter-wave soliton trains,” Nature 417, 150(2002)
[Crossref] [PubMed]

Theocharis, G.

D. J. Frantzeskakis, G. Theocharis, and F. K. Diakonos, “Interaction of dark solitons with localized impurities in Bose-Einstein condensates,” Phys. Rev. A 66, 053608(2002)
[Crossref]

Truscott, A. G.

K. E. Strecker, G. B. Partridge, and A. G. Truscott, “Formation and propagation of matter-wave soliton trains,” Nature 417, 150(2002)
[Crossref] [PubMed]

Walls, D. F.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55, 4318(1997)
[Crossref]

Walser, R.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, “Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate,” Phys. Rev. A 59, R31(1999)
[Crossref]

Wieman, C. E.

D. S. Hall, M. R. Matthews, J. R. Ensher, C. E. Wieman, and E. A. Cornell, “Dynamics of Component Separation in a Binary Mixture of Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1538(1998)D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of Relative Phase in Two-Component Bose-Einstein Condensates,” Phys. Rev. Lett. 81, 1543(1998)

M. H. Anderson, J. R. Matthews, and C. E. Wieman, “Observation of Bose-Einstein Condensation in a Dilute Atomic Vapor,” Science 269,198 (1995)
[Crossref] [PubMed]

Williams, J.

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, “Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate,” Phys. Rev. A 59, R31(1999)
[Crossref]

Wright, E. M.

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55, 4318(1997)
[Crossref]

Chin. Opt. Lett. (1)

J. Mod. Opt. (1)

S. Raghavan and G. P. Agrawal, “Switching and self-trapping dynamics of Bose-Einstein solitons,” J. Mod. Opt. 47, 1155(2000)

Nature (1)

K. E. Strecker, G. B. Partridge, and A. G. Truscott, “Formation and propagation of matter-wave soliton trains,” Nature 417, 150(2002)
[Crossref] [PubMed]

Opt. Commun. (1)

H. Li, Y. S. Cheng, and D. X. Huang, “Effects of traps on dynamics of two coupled Bose-Einstein condensates,” Opt. Commun. 258, 306–314 (2006)
[Crossref]

Phys. Rev. A (10)

R. Carretero-Gonzalez and K. Promislow, “Localized breathing oscillations of Bose-Einstein condensates in periodic traps,” Phys. Rev. A 66, 033610(2002)
[Crossref]

C. Pare and M. Florjariczyk, “Approximate model of soliton dynamics in all-optical couplers,” Phys. Rev. A 41, 6287–6295(1990)
[Crossref] [PubMed]

S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy, “Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping,” Phys. Rev. A 59, 620(1999)
[Crossref]

G. J. Milburn, J. Corney, E. M. Wright, and D. F. Walls, “Quantum dynamics of an atomic Bose-Einstein condensate in a double-well potential,” Phys. Rev. A 55, 4318(1997)
[Crossref]

J. Williams, R. Walser, J. Cooper, E. Cornell, and M. Holland, “Nonlinear Josephson-type oscillations of a driven, two-component Bose-Einstein condensate,” Phys. Rev. A 59, R31(1999)
[Crossref]

I. Carusotto, D. Embriaco, and G. C. La Rocca, “Nonlinear atom optics and bright-gap-soliton generation in finite optical lattices,” Phys. Rev. A 65, 053611(2002)
[Crossref]

P. Massignan and M. Modugno, “One-dimensional model for the dynamics and expansion of elongated Bose-Einstein condensates,” Phys. Rev. A 67, 023614(2003)
[Crossref]

C. Lee, W. Hai, and X. Luo, “Quasispin model for macroscopic quantum tunneling between two coupled Bose-Einstein condensates,” Phys. Rev. A 68, 053614(2003)
[Crossref]

D. J. Frantzeskakis, G. Theocharis, and F. K. Diakonos, “Interaction of dark solitons with localized impurities in Bose-Einstein condensates,” Phys. Rev. A 66, 053608(2002)
[Crossref]

R. G. Scott, A. M. Martin, and S. Bujkiewicz, “Transport and disruption of Bose-Einstein condensates in optical lattices,” Phys. Rev. A 69, 033605(2004)
[Crossref]

Phys. Rev. Lett. (4)

P. Ohberg and L. Santos, “Dark Solitons in a Two-Component Bose-Einstein Condensate,” Phys. Rev. Lett. 86, 2918–2921(2001)
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

The effective potential V eff2 resulting from the weak mutual interaction of two BEC solitons versus the separation Δ of the two BEC solitons

Fig. 2
Fig. 2

The effective potential Veff versus the separation Δof the two coupled BEC solitons

Fig. 3
Fig. 3

The two coupled BEC soliton density evolve in an OL. The initial locations of the motionless BEC soliton center x 0i (i=1, 2) , the amplitude A and the lattice depth of the OL V 0 are: (a) x 01,2=±1, A=1 and V 0=0.5, (b) x 01,2=±6.28, A=2 and V 0=0.5, (c) x 01,2=±8, A=2 and V 0=0.5, (d) x 01,2=±8, A=2 and V 0=1.5.

Fig. 4
Fig. 4

The two coupled BEC soliton density evolve in a slowly tuning OL. The OL drags the solitons and takes them to another location. The center of the solitons is initialized at the respective effective potential minimum.

Equations (15)

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j u t = 1 2 2 u x + g u 2 u + V ( x ) u ,
V ( x ) = V con + V opt = 1 2 Ω 2 x 2 + V 0 cos ( k x ) ,
V ( x ) = V opt = V 0 cos ( k x ) .
j u 1 t + 1 2 2 u 1 x 2 + ( u 1 2 + 2 u 2 2 ) u 1 = V ( x ) u 1
j u 2 t + 1 2 2 u 2 x 2 + ( 2 u 1 2 + u 2 2 ) u 2 = V ( x ) u 2 ,
u i ( x , t ) = A i sech [ A i ( x x 0 i ) ] exp [ j x ˙ 0 j ( x x 0 j ) 2 + j ϕ i ] . i = 1,2
L ( t ) = + { i = 1 2 [ j 2 ( u i u i * t u i * u i t ) + 1 2 u i z 2 1 2 u i 4 + V ( x ) u i 2 ] 2 u 1 2 u 2 2 } d x
= i = 1 2 [ 3 4 A i x ˙ 0 i 2 1 3 A i 3 + 2 A i ϕ ˙ i + k π V 0 sinh ( k π 2 A i ) cos ( k x 0 i ) ] + L 12 ,
L 12 = 2 A 1 2 A 2 2 sech 2 [ A 1 ( x x 01 ) ] sech 2 [ A 2 ( x x 02 ) ] d x .
d A i d t = 0 ,
3 2 A i d 2 x 0 i d t 2 = x 0 i [ k π V 0 sinh ( k π 2 A i ) cos ( k x 0 i ) + L 12 ] ,
3 4 x ˙ 0 i 2 A i 2 + 2 ϕ ˙ i + cosh ( k π 2 A i ) sinh 2 ( k π 2 A i ) k 2 π 2 V 0 2 A i 2 cos ( k x 0 i ) + L 12 A i = 0 .
d 2 Δ d t 2 = 8 3 A Δ [ k π V 0 sinh ( k π 2 A ) cos ( k Δ 2 ) + L 12 ] .
L 12 = 8 A 3 [ 1 sinh 2 ( A Δ ) + cosh ( A Δ ) sinh 2 ( A Δ ) ln cosh ( A Δ ) + 1 + sinh ( A Δ ) cosh ( A Δ ) + 1 sinh ( A Δ ) ] ,
V eff = 8 3 A [ k π V 0 sinh ( k π 2 A ) cos ( k Δ 2 ) + L 12 ] V eff 1 + V eff 2 ,

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