Abstract

We investigate experimentally and theoretically the nonlinear propagation of 87Rb Bose Einstein condensates in a trap with cylindrical symmetry. An additional weak periodic potential which encloses an angle with the symmetry axis of the waveguide is applied. The observed complex wave packet dynamics results from the coupling of transverse and longitudinal motion. We show that the experimental observations can be understood applying the concept of effective mass, which also allows to model numerically the three dimensional problem with a one dimensional equation. Within this framework the observed slowly spreading wave packets are a consequence of the continuous change of dispersion. The observed splitting of wave packets is very well described by the developed model and results from the nonlinear effect of transient solitonic propagation.

© 2004 Optical Society of America

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References

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  1. �??Bose-Einstein condensation in atomic gases,�?? ed. by M. Inguscio, S. Stringari, and C. Wieman, (IOS Press, Amsterdam 1999)
  2. F.S. Cataliotti, S. Burger, S. C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Ingusio, �??Josephson Junction Arrays with Bose-Einstein Condensates�??, Science 293 843 (2001).
    [CrossRef] [PubMed]
  3. A. Trombettoni and A. Smerzi, �??Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates,�?? Phys. Rev. Lett. 86 2353 (2001).
    [CrossRef] [PubMed]
  4. M. Steel and W. Zhang, �??Bloch function description of a Bose-Einstein condensate in a finite optical lattice,�?? cond-mat/9810284 (1998).
  5. P. Meystre, Atom Optics (Springer Verlag, New York, 2001) p 205, and references therein.
  6. The experimental realization in our group will be published elsewhere.
  7. V.V. Konotop, M. Salerno, �??Modulational instability in Bose-Einstein condensates in optical lattices,�?? Phys. Rev. A 65 021602 (2002).
    [CrossRef]
  8. N. Ashcroft and N. Mermin, Solid State Physics (Saunders, Philadelphia, 1976).
  9. A.A. Sukhorukov, D. Neshev, W. Krolikowski, and Y.S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically-induced lattices,�?? nlin.PS/0309075.
  10. B. Eiermann, P. Treutlein, Th. Anker, M. Albiez, M. Taglieber, K.-P. Marzlin, and M.K. Oberthaler, �??Dispersion Management for Atomic Matter Waves,�?? Phys. Rev. Lett. 91 060402 (2003).
    [CrossRef] [PubMed]
  11. M. Kozuma, L. Deng, E.W. Hagley, J.Wen, R. Lutwak, K. Helmerson, S.L. Rolston, andW.D. Phillips, �??Coherent Splitting of Bose-Einstein Condensed Atoms with Optically Induced Bragg Diffraction,�?? Phys. Rev. Lett. 82 871(1999).
    [CrossRef]
  12. B.P. Anderson, and M.A. Kasevich, �??Macroscopic Quantum Interference from Atomic Tunnel Arrays,�?? Science 282 1686 (1998);
    [CrossRef] [PubMed]
  13. O. Morsch, J. M¨uller, M. Cristiani, D. Ciampini, and E. Arimondo, �??Bloch Oscillations and Mean-Field Effects of Bose-Einstein Condensates in 1D Optical Lattices,�?? Phys. Rev. Lett. 87 140402 (2001).
    [CrossRef] [PubMed]
  14. C.F. Bharucha, K.W. Madison, P.R. Morrow, S.R.Wilkinson, Bala Sundaram, and M.G. Raizen, �??Observation of atomic tunneling from an accelerating optical potential,�?? Phys. Rev. A 55 R857 (1997)
    [CrossRef]
  15. L. Salasnich, A. Parola, and L. Reatto, �??Effective wave equations for the dynamics of cigar-shaped and diskshaped Bose condensates,�?? Phys. Rev. A 65 043614 (2002).
    [CrossRef]
  16. G.P. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, San Diego, 2001).
  17. G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 1995).
  18. R.G. Scott, A.M. Martin, T.M. Fromholz,S. Bujkiewicz, F.W. Sheard, and M. Leadbeater, �??Creation of Solitons and Vortices by Bragg Reflection of Bose-Einstein Condensates in an Optical Lattice,�?? Phys. Rev. Lett. 90 110404 (2003).
    [CrossRef] [PubMed]

Atom Optics (1)

P. Meystre, Atom Optics (Springer Verlag, New York, 2001) p 205, and references therein.

Phys. Rev. A (3)

V.V. Konotop, M. Salerno, �??Modulational instability in Bose-Einstein condensates in optical lattices,�?? Phys. Rev. A 65 021602 (2002).
[CrossRef]

C.F. Bharucha, K.W. Madison, P.R. Morrow, S.R.Wilkinson, Bala Sundaram, and M.G. Raizen, �??Observation of atomic tunneling from an accelerating optical potential,�?? Phys. Rev. A 55 R857 (1997)
[CrossRef]

L. Salasnich, A. Parola, and L. Reatto, �??Effective wave equations for the dynamics of cigar-shaped and diskshaped Bose condensates,�?? Phys. Rev. A 65 043614 (2002).
[CrossRef]

Phys. Rev. Lett. (5)

B. Eiermann, P. Treutlein, Th. Anker, M. Albiez, M. Taglieber, K.-P. Marzlin, and M.K. Oberthaler, �??Dispersion Management for Atomic Matter Waves,�?? Phys. Rev. Lett. 91 060402 (2003).
[CrossRef] [PubMed]

M. Kozuma, L. Deng, E.W. Hagley, J.Wen, R. Lutwak, K. Helmerson, S.L. Rolston, andW.D. Phillips, �??Coherent Splitting of Bose-Einstein Condensed Atoms with Optically Induced Bragg Diffraction,�?? Phys. Rev. Lett. 82 871(1999).
[CrossRef]

O. Morsch, J. M¨uller, M. Cristiani, D. Ciampini, and E. Arimondo, �??Bloch Oscillations and Mean-Field Effects of Bose-Einstein Condensates in 1D Optical Lattices,�?? Phys. Rev. Lett. 87 140402 (2001).
[CrossRef] [PubMed]

R.G. Scott, A.M. Martin, T.M. Fromholz,S. Bujkiewicz, F.W. Sheard, and M. Leadbeater, �??Creation of Solitons and Vortices by Bragg Reflection of Bose-Einstein Condensates in an Optical Lattice,�?? Phys. Rev. Lett. 90 110404 (2003).
[CrossRef] [PubMed]

A. Trombettoni and A. Smerzi, �??Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates,�?? Phys. Rev. Lett. 86 2353 (2001).
[CrossRef] [PubMed]

Science (2)

F.S. Cataliotti, S. Burger, S. C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Ingusio, �??Josephson Junction Arrays with Bose-Einstein Condensates�??, Science 293 843 (2001).
[CrossRef] [PubMed]

B.P. Anderson, and M.A. Kasevich, �??Macroscopic Quantum Interference from Atomic Tunnel Arrays,�?? Science 282 1686 (1998);
[CrossRef] [PubMed]

Solid State Physics (1)

N. Ashcroft and N. Mermin, Solid State Physics (Saunders, Philadelphia, 1976).

Other (6)

A.A. Sukhorukov, D. Neshev, W. Krolikowski, and Y.S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically-induced lattices,�?? nlin.PS/0309075.

The experimental realization in our group will be published elsewhere.

�??Bose-Einstein condensation in atomic gases,�?? ed. by M. Inguscio, S. Stringari, and C. Wieman, (IOS Press, Amsterdam 1999)

M. Steel and W. Zhang, �??Bloch function description of a Bose-Einstein condensate in a finite optical lattice,�?? cond-mat/9810284 (1998).

G.P. Agrawal, Applications of Nonlinear Fiber Optics (Academic Press, San Diego, 2001).

G.P. Agrawal, Nonlinear Fiber Optics (Academic Press, San Diego, 1995).

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Figures (4)

Fig. 1.
Fig. 1.

(a) Band structure for atoms in an optical lattice with V 0=1.2Erec (solid), parabolic approximation to the lowest energy band at q=π/d=G/2 (dashed), corresponding group velocity (b) and effective mass (c) in the lowest energy band. The vertical dashed lines at q=q± indicate where |meff |=∞. The shaded region shows the range of quasimomenta where the effective mass is negative.

Fig. 2.
Fig. 2.

Scheme for wave packet preparation (a–d). (a) initial wave packet is obtained by condensation in a crossed dipole trap. (b) A stationary periodic potential is ramped up adiabatically preparing the atoms at quasimomentum qc =0 in the lowest band. (c),(d) The periodic potential is accelerated to a constant velocity. (e) shows the numerically deduced quasimomentum shift for the preparation method I described in the text. (f) The motion of the center quasimomentum for the preparation method II described in the text. The additional shift to higher quasimomenta for long times results from the residual trap in the direction of the waveguide. The shaded area represents the quasimomenta corresponding to negative effective mass.

Fig. 3.
Fig. 3.

Wave packet dynamics for preparation I. (a) Experimental observation of wave packet propagation. (b) Result of the numerical simulation as discussed in the text. The data is convoluted with the optical resolution of the experiment. The obtained results are in good agreement with the experimental observations. The theoretically obtained (c) quasi-momentum distribution and (d) real space distribution are given for the initial 14ms of propagation. The inset reveals the phase of the observed slowly spreading wave packet.

Fig. 4.
Fig. 4.

Wave packet dynamics for preparation II. (a) Experimental results on wave packet propagation. (b) Result of the numerical simulation as discussed in the text. The simulation reproduces the observed wave packet splitting. The theoretically obtained (c) quasimomentum distribution and (d) real space distribution are given for the initial 14ms of propagation. The inset reveals that the transient formed wave packet has a flat phase indicating solitonic propagation.

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