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, 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),
  15. 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)
    [CrossRef]
  16. R. Carretero-Gonzalez and K. Promislow, "Localized breathing oscillations of Bose-Einstein condensates in periodic traps," Phys. Rev. A 66,033610 (2002)
    [CrossRef] [PubMed]
  17. C. Pare and M. Florjariczyk, "Approximate model of soliton dynamics in all-optical couplers," Phys. Rev. A 41,6287-6295(1990)
    [CrossRef]
  18. 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)
  19. S. Raghavan and G. P. Agrawal, "Switching and self-trapping dynamics of Bose-Einstein Solitons," J. Mod. Opt. 47,1155 (2000)
    [CrossRef] [PubMed]
  20. P. Ohberg and L. Santos, "Dark Solitons in a two-component Bose-Einstein Condensate," Phys. Rev. Lett. 86,2918-2921(2001)
    [CrossRef]
  21. 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]
  22. 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)

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)

2005 (1)

2004 (2)

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)

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]

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)

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

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]

2001 (1)

P. Ohberg and L. Santos, "Dark Solitons in a two-component Bose-Einstein Condensate," Phys. Rev. Lett. 86,2918-2921(2001)
[CrossRef]

2000 (1)

S. Raghavan and G. P. Agrawal, "Switching and self-trapping dynamics of Bose-Einstein Solitons," J. Mod. Opt. 47,1155 (2000)
[CrossRef] [PubMed]

1999 (2)

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

1998 (3)

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)
[CrossRef]

1997 (2)

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]

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]

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]

Agrawal, G. P.

S. Raghavan and G. P. Agrawal, "Switching and self-trapping dynamics of Bose-Einstein Solitons," J. Mod. Opt. 47,1155 (2000)
[CrossRef] [PubMed]

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)

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] [PubMed]

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)

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)
[CrossRef]

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),

Fantoni, S.

S. Raghavan, A. Smerzi, S. Fantoni and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose-Einstein Condensates: Josephson effects, 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]

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)
[CrossRef]

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)

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)

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)

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)
[CrossRef]

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]

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]

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] [PubMed]

Raghavan, S.

S. Raghavan and G. P. Agrawal, "Switching and self-trapping dynamics of Bose-Einstein Solitons," J. Mod. Opt. 47,1155 (2000)
[CrossRef] [PubMed]

S. Raghavan, A. Smerzi, S. Fantoni and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose-Einstein Condensates: Josephson effects, 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]

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)

Shenoy, S. R.

S. Raghavan, A. Smerzi, S. Fantoni and S. R. Shenoy, "Coherent oscillations between two weakly coupled Bose-Einstein Condensates: Josephson effects, 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, 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)
[CrossRef]

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)
[CrossRef] [PubMed]

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)

Phys. Rev. A (10)

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]

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)

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

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

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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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