Abstract

The nonlinear evolution of a Gaussian-shaped matter wave with weak interaction among atoms is investigated analytically. An effective complex curvature is introduced to describe the interacting matter wave, and the evolution formula of the effective complex curvature is derived. The conditions under which the analytic formula can be used are presented. As an example, focusing of a coherent matter wave with the repulsive interaction among atoms is calculated and analyzed. The evolution characteristics of the matter wave with and without interactions are compared and discussed.

©2008 Optical Society of America

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References

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  1. K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
    [Crossref]
  2. B.P. Anderson and P. Meystre, “Nonlinear atom optics,” Contemp. Phys. 44, 473–-483 (2003).
    [Crossref]
  3. P. Meystre, Atom Optics (Springer-Verlag New York, 2001).
  4. Ch. J. Bordé, “Theoretical tools for atom optics and interferometry,” C. R. Acad. Sci. Paris, t.  2, Sèrie IV, 509–530 (2001).
  5. Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
    [Crossref] [PubMed]
  6. Ch. Antoine and Ch. J. Bordè, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
    [Crossref]
  7. Ch. J. Bordè, “Atomic clocks and inertial sensors,” Metrologia 39, 435–463 (2002).
    [Crossref]
  8. S. Zheng and Q. Lin, “The matrix method in treating atom interferometer,” Acta Optica Sinica 25, 860–864 (2005).
  9. S. Zheng, J. Chen, and Q. Lin, “Improvement of the measuring precision by changing the pulse sequence in the three-level atom gravimeter,” Acta Physica Sinica 54, 3535–3541 (2005).
  10. F. Impens, P. Bouyer, and Ch. J. Bordè, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
    [Crossref]
  11. J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
    [Crossref] [PubMed]
  12. J. Yin, C. Liu, Y. Yang, J. Liu, and G. Fan, “Effective ABCD formulation of the propagation of the atom laser,” Acta Physica Sinica 53, 356–361 (2004).
  13. J. Chen, Q. Lin, and Y. Liu, “The general astigmatic matter wave,” Opt. Express 16, 3368–3375 (2008).
    [Crossref] [PubMed]
  14. J. Chen and Q. Lin, “Partially coherent matter wave and its evolution,” Opt. Commun. 281, 1300–1305 (2008).
    [Crossref]
  15. M. Edwards and K. Burnett “Numerical solution of the nonlinear Schrödinger equation for small samples of the trapped neutral atoms,” Phys. Rev. A 51, 1382 (1995).
    [Crossref] [PubMed]
  16. P. A. Ruprecht, M. J. Holland, and K. Burnett, “Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms,” Phys, Rev. A 51, 4704 (1995).
    [Crossref]
  17. B. M. Caradoc-Davies, “Vortex Dynamics in Bose-Einstein Condensates,” Ph.D. thesis, University of Otago, New Zealand, 2000.
  18. P. -A. Belanger and C. Pare, “Self-focusing of Gaussian beams: an alternate derivation,” Appl. Op..  22, 1293–1295 (1983).
    [Crossref]
  19. C. Pare and P. -A. Belanger, “Beam propagation in a linear or nonlinear lens-like medium using ABCD ray matrices: the method of moments,” Opt. Quant. Electron. 24, S1051–S1070 (1992).
    [Crossref]
  20. F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
    [Crossref]
  21. G. Whyte, p. Öhberg, and J. Courtial “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610 (2004).
    [Crossref]
  22. D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
    [Crossref]
  23. C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78, 985–989 (1997).
    [Crossref]
  24. T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and Rudolf Grimm,“Bose-Einstein Condensation of Cesium,” Science 299, 232–235 (2003).
    [Crossref]
  25. E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
    [Crossref] [PubMed]
  26. R. W. Boyd, Nonlinear Optics (Academic Press, (1992).

2008 (2)

J. Chen and Q. Lin, “Partially coherent matter wave and its evolution,” Opt. Commun. 281, 1300–1305 (2008).
[Crossref]

J. Chen, Q. Lin, and Y. Liu, “The general astigmatic matter wave,” Opt. Express 16, 3368–3375 (2008).
[Crossref] [PubMed]

2006 (2)

F. Impens, P. Bouyer, and Ch. J. Bordè, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

2005 (3)

S. Zheng and Q. Lin, “The matrix method in treating atom interferometer,” Acta Optica Sinica 25, 860–864 (2005).

S. Zheng, J. Chen, and Q. Lin, “Improvement of the measuring precision by changing the pulse sequence in the three-level atom gravimeter,” Acta Physica Sinica 54, 3535–3541 (2005).

D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
[Crossref]

2004 (3)

G. Whyte, p. Öhberg, and J. Courtial “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610 (2004).
[Crossref]

K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
[Crossref]

J. Yin, C. Liu, Y. Yang, J. Liu, and G. Fan, “Effective ABCD formulation of the propagation of the atom laser,” Acta Physica Sinica 53, 356–361 (2004).

2003 (3)

B.P. Anderson and P. Meystre, “Nonlinear atom optics,” Contemp. Phys. 44, 473–-483 (2003).
[Crossref]

Ch. Antoine and Ch. J. Bordè, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
[Crossref]

T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and Rudolf Grimm,“Bose-Einstein Condensation of Cesium,” Science 299, 232–235 (2003).
[Crossref]

2002 (1)

Ch. J. Bordè, “Atomic clocks and inertial sensors,” Metrologia 39, 435–463 (2002).
[Crossref]

2001 (3)

Ch. J. Bordé, “Theoretical tools for atom optics and interferometry,” C. R. Acad. Sci. Paris, t.  2, Sèrie IV, 509–530 (2001).

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
[Crossref] [PubMed]

1999 (1)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

1997 (1)

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78, 985–989 (1997).
[Crossref]

1995 (2)

M. Edwards and K. Burnett “Numerical solution of the nonlinear Schrödinger equation for small samples of the trapped neutral atoms,” Phys. Rev. A 51, 1382 (1995).
[Crossref] [PubMed]

P. A. Ruprecht, M. J. Holland, and K. Burnett, “Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms,” Phys, Rev. A 51, 4704 (1995).
[Crossref]

1992 (1)

C. Pare and P. -A. Belanger, “Beam propagation in a linear or nonlinear lens-like medium using ABCD ray matrices: the method of moments,” Opt. Quant. Electron. 24, S1051–S1070 (1992).
[Crossref]

1983 (1)

P. -A. Belanger and C. Pare, “Self-focusing of Gaussian beams: an alternate derivation,” Appl. Op..  22, 1293–1295 (1983).
[Crossref]

Anderson, B.P.

B.P. Anderson and P. Meystre, “Nonlinear atom optics,” Contemp. Phys. 44, 473–-483 (2003).
[Crossref]

Antoine, Ch.

Ch. Antoine and Ch. J. Bordè, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
[Crossref]

Aspect, A.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

Belanger, P. -A.

C. Pare and P. -A. Belanger, “Beam propagation in a linear or nonlinear lens-like medium using ABCD ray matrices: the method of moments,” Opt. Quant. Electron. 24, S1051–S1070 (1992).
[Crossref]

P. -A. Belanger and C. Pare, “Self-focusing of Gaussian beams: an alternate derivation,” Appl. Op..  22, 1293–1295 (1983).
[Crossref]

Bongs, K.

K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
[Crossref]

Bordé, Ch. J.

Ch. J. Bordé, “Theoretical tools for atom optics and interferometry,” C. R. Acad. Sci. Paris, t.  2, Sèrie IV, 509–530 (2001).

Bordè, Ch. J.

F. Impens, P. Bouyer, and Ch. J. Bordè, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

Ch. Antoine and Ch. J. Bordè, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
[Crossref]

Ch. J. Bordè, “Atomic clocks and inertial sensors,” Metrologia 39, 435–463 (2002).
[Crossref]

Bouyer, P.

F. Impens, P. Bouyer, and Ch. J. Bordè, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, (1992).

Bradley, C. C.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78, 985–989 (1997).
[Crossref]

Burnett, K.

M. Edwards and K. Burnett “Numerical solution of the nonlinear Schrödinger equation for small samples of the trapped neutral atoms,” Phys. Rev. A 51, 1382 (1995).
[Crossref] [PubMed]

P. A. Ruprecht, M. J. Holland, and K. Burnett, “Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms,” Phys, Rev. A 51, 4704 (1995).
[Crossref]

Caradoc-Davies, B. M.

B. M. Caradoc-Davies, “Vortex Dynamics in Bose-Einstein Condensates,” Ph.D. thesis, University of Otago, New Zealand, 2000.

Chen, J.

J. Chen and Q. Lin, “Partially coherent matter wave and its evolution,” Opt. Commun. 281, 1300–1305 (2008).
[Crossref]

J. Chen, Q. Lin, and Y. Liu, “The general astigmatic matter wave,” Opt. Express 16, 3368–3375 (2008).
[Crossref] [PubMed]

S. Zheng, J. Chen, and Q. Lin, “Improvement of the measuring precision by changing the pulse sequence in the three-level atom gravimeter,” Acta Physica Sinica 54, 3535–3541 (2005).

Claussen, N. R.

E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
[Crossref] [PubMed]

Coq, Y. Le.

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

Cornell, E. A.

E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
[Crossref] [PubMed]

Cornish, S. L.

E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
[Crossref] [PubMed]

Courtial, J.

G. Whyte, p. Öhberg, and J. Courtial “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610 (2004).
[Crossref]

Dalfovo, F.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

Delannoy, G.

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

Donley, E. A.

E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
[Crossref] [PubMed]

Edwards, M.

M. Edwards and K. Burnett “Numerical solution of the nonlinear Schrödinger equation for small samples of the trapped neutral atoms,” Phys. Rev. A 51, 1382 (1995).
[Crossref] [PubMed]

Fan, G.

J. Yin, C. Liu, Y. Yang, J. Liu, and G. Fan, “Effective ABCD formulation of the propagation of the atom laser,” Acta Physica Sinica 53, 356–361 (2004).

Fauqembergue, M.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

Gerbier, F.

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

Giorgini, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

Grimm, Rudolf

T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and Rudolf Grimm,“Bose-Einstein Condensation of Cesium,” Science 299, 232–235 (2003).
[Crossref]

Guerin, W.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

Herbig, J.

T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and Rudolf Grimm,“Bose-Einstein Condensation of Cesium,” Science 299, 232–235 (2003).
[Crossref]

Holland, M. J.

P. A. Ruprecht, M. J. Holland, and K. Burnett, “Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms,” Phys, Rev. A 51, 4704 (1995).
[Crossref]

Hulet, R. G.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78, 985–989 (1997).
[Crossref]

Impens, F.

F. Impens, P. Bouyer, and Ch. J. Bordè, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

Josse, V.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

Le Coq, Y.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

Lin, Q.

J. Chen and Q. Lin, “Partially coherent matter wave and its evolution,” Opt. Commun. 281, 1300–1305 (2008).
[Crossref]

J. Chen, Q. Lin, and Y. Liu, “The general astigmatic matter wave,” Opt. Express 16, 3368–3375 (2008).
[Crossref] [PubMed]

S. Zheng, J. Chen, and Q. Lin, “Improvement of the measuring precision by changing the pulse sequence in the three-level atom gravimeter,” Acta Physica Sinica 54, 3535–3541 (2005).

S. Zheng and Q. Lin, “The matrix method in treating atom interferometer,” Acta Optica Sinica 25, 860–864 (2005).

Liu, C.

J. Yin, C. Liu, Y. Yang, J. Liu, and G. Fan, “Effective ABCD formulation of the propagation of the atom laser,” Acta Physica Sinica 53, 356–361 (2004).

Liu, J.

J. Yin, C. Liu, Y. Yang, J. Liu, and G. Fan, “Effective ABCD formulation of the propagation of the atom laser,” Acta Physica Sinica 53, 356–361 (2004).

Liu, Y.

Mark, M.

T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and Rudolf Grimm,“Bose-Einstein Condensation of Cesium,” Science 299, 232–235 (2003).
[Crossref]

Meystre, P.

B.P. Anderson and P. Meystre, “Nonlinear atom optics,” Contemp. Phys. 44, 473–-483 (2003).
[Crossref]

P. Meystre, Atom Optics (Springer-Verlag New York, 2001).

Murry, D. R.

D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
[Crossref]

Nägerl, H.-C.

T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and Rudolf Grimm,“Bose-Einstein Condensation of Cesium,” Science 299, 232–235 (2003).
[Crossref]

Öhberg, P.

D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
[Crossref]

G. Whyte, p. Öhberg, and J. Courtial “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610 (2004).
[Crossref]

Pare, C.

C. Pare and P. -A. Belanger, “Beam propagation in a linear or nonlinear lens-like medium using ABCD ray matrices: the method of moments,” Opt. Quant. Electron. 24, S1051–S1070 (1992).
[Crossref]

P. -A. Belanger and C. Pare, “Self-focusing of Gaussian beams: an alternate derivation,” Appl. Op..  22, 1293–1295 (1983).
[Crossref]

Pitaevskii, L. P.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

Rangwala, S. A.

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

Richard, S.

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

Riou, J.-F.

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

Roberts, J. L.

E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
[Crossref] [PubMed]

Ruprecht, P. A.

P. A. Ruprecht, M. J. Holland, and K. Burnett, “Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms,” Phys, Rev. A 51, 4704 (1995).
[Crossref]

Sackett, C. A.

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78, 985–989 (1997).
[Crossref]

Sengstock, K.

K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
[Crossref]

Stringari, S.

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

Thywissen, J. H.

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

Weber, T.

T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and Rudolf Grimm,“Bose-Einstein Condensation of Cesium,” Science 299, 232–235 (2003).
[Crossref]

Whyte, G.

G. Whyte, p. Öhberg, and J. Courtial “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610 (2004).
[Crossref]

Wieman, C. E.

E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
[Crossref] [PubMed]

Yang, Y.

J. Yin, C. Liu, Y. Yang, J. Liu, and G. Fan, “Effective ABCD formulation of the propagation of the atom laser,” Acta Physica Sinica 53, 356–361 (2004).

Yin, J.

J. Yin, C. Liu, Y. Yang, J. Liu, and G. Fan, “Effective ABCD formulation of the propagation of the atom laser,” Acta Physica Sinica 53, 356–361 (2004).

Zheng, S.

S. Zheng, J. Chen, and Q. Lin, “Improvement of the measuring precision by changing the pulse sequence in the three-level atom gravimeter,” Acta Physica Sinica 54, 3535–3541 (2005).

S. Zheng and Q. Lin, “The matrix method in treating atom interferometer,” Acta Optica Sinica 25, 860–864 (2005).

Acta Optica Sinica (1)

S. Zheng and Q. Lin, “The matrix method in treating atom interferometer,” Acta Optica Sinica 25, 860–864 (2005).

Acta Physica Sinica (2)

S. Zheng, J. Chen, and Q. Lin, “Improvement of the measuring precision by changing the pulse sequence in the three-level atom gravimeter,” Acta Physica Sinica 54, 3535–3541 (2005).

J. Yin, C. Liu, Y. Yang, J. Liu, and G. Fan, “Effective ABCD formulation of the propagation of the atom laser,” Acta Physica Sinica 53, 356–361 (2004).

Appl. Op. (1)

P. -A. Belanger and C. Pare, “Self-focusing of Gaussian beams: an alternate derivation,” Appl. Op..  22, 1293–1295 (1983).
[Crossref]

Appl. Phys. B (1)

F. Impens, P. Bouyer, and Ch. J. Bordè, “Matter-wave cavity gravimeter,” Appl. Phys. B 84, 603–615 (2006).
[Crossref]

C. R. Acad. Sci. Paris (1)

Ch. J. Bordé, “Theoretical tools for atom optics and interferometry,” C. R. Acad. Sci. Paris, t.  2, Sèrie IV, 509–530 (2001).

Contemp. Phys. (1)

B.P. Anderson and P. Meystre, “Nonlinear atom optics,” Contemp. Phys. 44, 473–-483 (2003).
[Crossref]

J. Phys. B: At. Mol. Opt. Phys. (1)

D. R. Murry and P. Öhberg, “Matter wave focusing,” J. Phys. B: At. Mol. Opt. Phys. 38, 1227–1234 (2005).
[Crossref]

Metrologia (1)

Ch. J. Bordè, “Atomic clocks and inertial sensors,” Metrologia 39, 435–463 (2002).
[Crossref]

Nature (1)

E. A. Donley, N. R. Claussen, S. L. Cornish, J. L. Roberts, E. A. Cornell, and C. E. Wieman “Dynamics of collapsing and exploding Bose-Einstein condensates,” Nature 412, 295–299 (2001).
[Crossref] [PubMed]

Opt. Commun. (1)

J. Chen and Q. Lin, “Partially coherent matter wave and its evolution,” Opt. Commun. 281, 1300–1305 (2008).
[Crossref]

Opt. Express (1)

Opt. Quant. Electron. (1)

C. Pare and P. -A. Belanger, “Beam propagation in a linear or nonlinear lens-like medium using ABCD ray matrices: the method of moments,” Opt. Quant. Electron. 24, S1051–S1070 (1992).
[Crossref]

Phys, Rev. A (1)

P. A. Ruprecht, M. J. Holland, and K. Burnett, “Time-dependent solution of the nonlinear Schrödinger equation for Bose-condensed trapped neutral atoms,” Phys, Rev. A 51, 4704 (1995).
[Crossref]

Phys. Lett. A (1)

Ch. Antoine and Ch. J. Bordè, “Exact phase shifts for atom interferometry,” Phys. Lett. A 306, 277–284 (2003).
[Crossref]

Phys. Rev. A (2)

M. Edwards and K. Burnett “Numerical solution of the nonlinear Schrödinger equation for small samples of the trapped neutral atoms,” Phys. Rev. A 51, 1382 (1995).
[Crossref] [PubMed]

G. Whyte, p. Öhberg, and J. Courtial “Transverse laser modes in Bose-Einstein condensates,” Phys. Rev. A 69, 053610 (2004).
[Crossref]

Phys. Rev. Lett. (3)

C. C. Bradley, C. A. Sackett, and R. G. Hulet, “Bose-Einstein Condensation of Lithium: Observation of Limited Condensate Number,” Phys. Rev. Lett. 78, 985–989 (1997).
[Crossref]

Y. Le. Coq, J. H. Thywissen, S. A. Rangwala, F. Gerbier, S. Richard, G. Delannoy, P. Bouyer, and A. Aspect, “Atom laser divergence,” Phys. Rev. Lett. 87, 170403 (2001).
[Crossref] [PubMed]

J.-F. Riou, W. Guerin, Y. Le Coq, M. Fauqembergue, V. Josse, P. Bouyer, and A. Aspect “Beam quality of a nonideal atom laser,” Phys. Rev. Lett. 96, 070404 (2006).
[Crossref] [PubMed]

Rep. Prog. Phys. (1)

K. Bongs and K. Sengstock, “Physics with coherent matter waves,” Rep. Prog. Phys. 67, 907–963 (2004).
[Crossref]

Rev. Mod. Phys (1)

F. Dalfovo, S. Giorgini, L. P. Pitaevskii, and S. Stringari, “Theory of Bose-Einstein condensation in trapped gases,” Rev. Mod. Phys,  71, 463–512 (1999).
[Crossref]

Science (1)

T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and Rudolf Grimm,“Bose-Einstein Condensation of Cesium,” Science 299, 232–235 (2003).
[Crossref]

Other (3)

R. W. Boyd, Nonlinear Optics (Academic Press, (1992).

B. M. Caradoc-Davies, “Vortex Dynamics in Bose-Einstein Condensates,” Ph.D. thesis, University of Otago, New Zealand, 2000.

P. Meystre, Atom Optics (Springer-Verlag New York, 2001).

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Figures (4)

Fig. 1.
Fig. 1. Comparison between the exact amplitude profile (solid line) and the ECC amplitude profile (dashed line). The evolution time is t = 1.4.
Fig. 2.
Fig. 2. Relative phase distribution of matter waves with different M 2-factors. The evolution time is t = 1.4.
Fig. 3.
Fig. 3. (a) Evolution of the density profile of the effective Gaussian-shaped matter wave after the interaction with a focusing pulse f =1. The M 2 factor of the interacting matter wave is 1.5; (b) comparison between the exact density profile (the solid line) and the effective density profile (the dashed line) at t = 0.8; (c) at t = 1.2; (d) at t = 1.6.
Fig. 4.
Fig. 4. Focusing time tf as a function of f , both in dimensionless units. The solid line is the graph of the noninteracting matter wave; The dashed line is the graph for an interacting matter wave with M 2 = 1.5.

Equations (29)

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i h ¯ t ϕ ( r , t ) = ( - h ¯ 2 2 m 2 + V ( r , t ) ) ϕ ( r , t ) ,
ϕ ( r , t ) = ψ ( x , y , t ) exp [ i h ¯ σ ( z , t ) ] .
V ( r , t ) = V t ( x , y , t ) + V z ( z , t ) .
t σ ( z , t ) = - i h ¯ 2 m 2 z 2 σ ( z , t ) + 1 2 m ( z σ ( z , t ) ) 2 + V z ( z , t ) σ ( z , t ) ,
i h ¯ t ψ ( x , y , t ) = ( - h ¯ 2 2 m 2 + V t ( x , y , t ) ) ψ ( x , y , t ) ,
V t ( x , y , t ) = U ψ ( x , y , t ) 2 ,
i h ¯ t ψ ( x , y , t ) = ( h ¯ 2 2 m 2 + U ψ ( x , y , t ) 2 ) ψ ( x , y , t ) .
ψ ( x , y , t ) = A ( t ) exp [ im 2 h ¯ x 2 + y 2 q ( t ) ] ,
1 q ( t ) = 1 ρ ( t ) + 2 i h ¯ m 1 w ( t ) 2
ψ ( x , y , t ) 2 A ( t ) 2 2 A ( t ) 2 ( x 2 + y 2 ) w ( t ) 2 .
( 1 q ( t ) ) + 1 q ( t ) 2 4 U A ( t ) 2 mw ( t ) 2 = 0 ,
A ( t ) A ( t ) + 1 q ( t ) + i U A ( t ) 2 h ¯ = 0 .
( A ( t ) 2 ) A ( t ) 2 + 2 ρ ( t ) = 0 .
1 ρ ( t ) = w ( t ) w ( t ) .
A ( t ) 2 = A ( 0 ) 2 w ( 0 ) 2 w ( t ) 2 ,
( 1 ρ ( t ) ) + 2 i h ¯ m ( 1 w ( t ) 2 ) + 1 ρ ( t ) 2 + 4 i h ¯ ( t ) w ( t ) 2 4 h ¯ 2 m 2 M 2 w ( t ) 4 = 0 ,
M 2 = 1 + mU h ¯ 2 A ( 0 ) 2 w ( 0 ) 2 .
( 1 ρ ( t ) ) + 1 ρ ( t ) 2 4 h ¯ 2 m 2 M 2 w ( t ) 4 = 0 ,
2 h ¯ m ( 1 w ( t ) 2 ) + 4 h ¯ ( t ) w ( t ) 2 = 0 .
( 1 ρ ( t ) ) + 1 ρ ( t ) 2 4 h ¯ 2 m 2 M 2 w ( t ) 4 + 2 i h ¯ m ( 1 w ( t ) 2 ) M + 4 i h ¯ M ( t ) w ( t ) 2 = 0 .
1 q eff ( t ) = 1 ρ ( t ) + 2 i h ¯ m M w ( t ) 2 ,
( q eff ( t ) ) 1 = 0 .
q eff ( t ) = q eff ( 0 ) + t .
q eff ( t ) = Aq eff ( 0 ) + B Cq eff ( 0 ) + D ,
A = 1 , B = t , C = 0 , D = 1 .
ψ ( x , t = 0 ) = exp [ x 2 ( 1 4 + i 100 ) ] .
M 2 = 1 + U h ¯ 2 ( 2 m ) = 1 + Ũ ,
ψ ( x , t = 0 ) = exp [ - x 2 4 ( 1 + i 1 f ) ] .
t f = f 1 + M 2 f 2 .

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