Abstract

By accelerating a Bose-Einstein condensate in a controlled way across the edge of the Brillouin zone of a 1D optical lattice, we investigate the stability of the condensate in the vicinity of the zone edge. Through an analysis of the visibility of the interference pattern after a time-of-flight and the widths of the interference peaks, we characterize the onset of instability as the acceleration of the lattice is decreased. We briefly discuss the significance of our results with respect to recent theoretical work.

© 2004 Optical Society of America

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References

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  1. C. Menotti, A. Smerzi, and A. Trombettoni, �??Superfluid dynamics of a Bose-Einstein condensate in a periodic potential,�?? New J. Phys. 5, 112 (2003).
    [CrossRef]
  2. BiaoWu and Qian Niu, �??Superfluidity of Bose-Einstein condensate in an optical lattice: Landau-Zener tunneling and dynamical instability,�?? New J. Phys. 5, 104 (2003).
    [CrossRef]
  3. Pearl J. Y. Louis, Elena A. Ostrovskaya, Craig M. Savage, and Yuri S. Kivshar, �??Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,�?? Phys. Rev. A 67, 013602 (2003).
    [CrossRef]
  4. O. Morsch, J.H. Muller, M. Cristiani, D. Ciampini, and E. Arimondo, �??Bloch oscillations and mean-field effects of Bose-Einstein condensates in optical lattices,�?? Phys. Rev. Lett. 87, 140402 (2001).
    [CrossRef] [PubMed]
  5. M. Cristiani, O. Morsch, J.H. M¨uller, D. Ciampini, and E. Arimondo, �??Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects,�?? Phys. Rev. A 65, 063612 (2002).
    [CrossRef]
  6. M. Greiner, O. Mandel, T. Esslinger, T.W. Hansch, and I. Bloch, �??Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,�?? Nature (London) 415, 6867 (2002).
    [CrossRef]
  7. F. S. Cataliotti, L. Fallani, F. Ferlaino, C. Fort, P. Maddaloni and M. Inguscio, �??Superfluid current disruption in a chain of weakly coupled BoseEinstein condensates,�?? New J. Phys. 5, 71 (2003).
    [CrossRef]
  8. Yuri S. Kivshar and Mario Salerno, �??Modulational instabilities in the discrete deformable nonlinear Schrodinger equation,�?? Phys. Rev. E 49, 3543 (1994).
    [CrossRef]
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    [CrossRef]
  10. Karen Marie Hilligsøe, Markus K. Oberthaler, and Karl-Peter Marzlin, �??Stability of gap solitons in a Bose-Einstein condensate,�?? Phys. Rev. A 66, 063605 (2002).
    [CrossRef]
  11. R.G. Scott, A.M. Martin, T.M. Fromhold, 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]
  12. J.R. Anglin, �??Second-quantized Landau-Zener theory for dynamical instabilities,�?? Phys. Rev. A 67, 051601(R) (2003).
    [CrossRef]
  13. Yu. S. Kivshar and D. E. Pelinovsky, �??Self-focusing and transverse instabilities of solitary waves,�?? Phys. Rep. 331, 117 (2000).
    [CrossRef]
  14. Jason W. Fleischer, Mordechai Segev, Nikolaos K. Efrimidis, and Demetrios N. Christodoulides, �??Observation of two-dimensional discrete solitions in optically induced nonlinear photonic lattices,�?? Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  15. Dragomir Neshev, Andrey A. Sukhorukov, Yuri S. Kivshar, andWieslaw Krolikowski, �??Observation of transverse instabilities in optically-induced lattices,�?? nlin.PS/0307053.
  16. Andrey A. Sukhorukov, Dragomir Neshev, Wieslaw Krolikowski, and Yuris S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,�?? nlin.PS/0309075.
  17. J.H. Muller, D. Ciampini, O. Morsch, G. Smirne, M. Fazzi, P. Verkerk, F. Fuso, and E. Arimondo, �??Bose-Einstein condensation of rubidium atoms in a triaxial TOP trap,�?? J. Phys. B: At. Mol. Opt. Phys. 33, 4095 (2000).
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  18. Y.B. Band and M. Trippenbach, �??Bose-Einstein condensates in time-dependent light potentials: Adiabatic and nonadiabatic behavior of nonlinear wave equations,�?? Phys. Rev. A 65, 053602 (2002).
    [CrossRef]
  19. D. Choi and Q. Niu, �??Bose-Einstein Condensates in an Optical Lattice,�?? Phys. Rev. Lett. 82, 2022 (1999).
    [CrossRef]
  20. Mark Fromhold, University of Nottingham (U.K.), private communication.

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

J.H. Muller, D. Ciampini, O. Morsch, G. Smirne, M. Fazzi, P. Verkerk, F. Fuso, and E. Arimondo, �??Bose-Einstein condensation of rubidium atoms in a triaxial TOP trap,�?? J. Phys. B: At. Mol. Opt. Phys. 33, 4095 (2000).
[CrossRef]

Nature (2)

Jason W. Fleischer, Mordechai Segev, Nikolaos K. Efrimidis, and Demetrios N. Christodoulides, �??Observation of two-dimensional discrete solitions in optically induced nonlinear photonic lattices,�?? Nature 422, 147 (2003).
[CrossRef] [PubMed]

M. Greiner, O. Mandel, T. Esslinger, T.W. Hansch, and I. Bloch, �??Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,�?? Nature (London) 415, 6867 (2002).
[CrossRef]

New J. Phys. (3)

F. S. Cataliotti, L. Fallani, F. Ferlaino, C. Fort, P. Maddaloni and M. Inguscio, �??Superfluid current disruption in a chain of weakly coupled BoseEinstein condensates,�?? New J. Phys. 5, 71 (2003).
[CrossRef]

C. Menotti, A. Smerzi, and A. Trombettoni, �??Superfluid dynamics of a Bose-Einstein condensate in a periodic potential,�?? New J. Phys. 5, 112 (2003).
[CrossRef]

BiaoWu and Qian Niu, �??Superfluidity of Bose-Einstein condensate in an optical lattice: Landau-Zener tunneling and dynamical instability,�?? New J. Phys. 5, 104 (2003).
[CrossRef]

Phys. Rep. (1)

Yu. S. Kivshar and D. E. Pelinovsky, �??Self-focusing and transverse instabilities of solitary waves,�?? Phys. Rep. 331, 117 (2000).
[CrossRef]

Phys. Rev. A (6)

Pearl J. Y. Louis, Elena A. Ostrovskaya, Craig M. Savage, and Yuri S. Kivshar, �??Bose-Einstein condensates in optical lattices: Band-gap structure and solitons,�?? Phys. Rev. A 67, 013602 (2003).
[CrossRef]

V.V. Konotop and M. Salerno, �??Modulational instability in Bose-Einstein condensates in optical lattices,�?? Phys. Rev. A 65, 021620(R) (2002).
[CrossRef]

Karen Marie Hilligsøe, Markus K. Oberthaler, and Karl-Peter Marzlin, �??Stability of gap solitons in a Bose-Einstein condensate,�?? Phys. Rev. A 66, 063605 (2002).
[CrossRef]

M. Cristiani, O. Morsch, J.H. M¨uller, D. Ciampini, and E. Arimondo, �??Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects,�?? Phys. Rev. A 65, 063612 (2002).
[CrossRef]

J.R. Anglin, �??Second-quantized Landau-Zener theory for dynamical instabilities,�?? Phys. Rev. A 67, 051601(R) (2003).
[CrossRef]

Y.B. Band and M. Trippenbach, �??Bose-Einstein condensates in time-dependent light potentials: Adiabatic and nonadiabatic behavior of nonlinear wave equations,�?? Phys. Rev. A 65, 053602 (2002).
[CrossRef]

Phys. Rev. E (1)

Yuri S. Kivshar and Mario Salerno, �??Modulational instabilities in the discrete deformable nonlinear Schrodinger equation,�?? Phys. Rev. E 49, 3543 (1994).
[CrossRef]

Phys. Rev. Lett. (3)

R.G. Scott, A.M. Martin, T.M. Fromhold, 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]

O. Morsch, J.H. Muller, M. Cristiani, D. Ciampini, and E. Arimondo, �??Bloch oscillations and mean-field effects of Bose-Einstein condensates in optical lattices,�?? Phys. Rev. Lett. 87, 140402 (2001).
[CrossRef] [PubMed]

D. Choi and Q. Niu, �??Bose-Einstein Condensates in an Optical Lattice,�?? Phys. Rev. Lett. 82, 2022 (1999).
[CrossRef]

Other (3)

Mark Fromhold, University of Nottingham (U.K.), private communication.

Dragomir Neshev, Andrey A. Sukhorukov, Yuri S. Kivshar, andWieslaw Krolikowski, �??Observation of transverse instabilities in optically-induced lattices,�?? nlin.PS/0307053.

Andrey A. Sukhorukov, Dragomir Neshev, Wieslaw Krolikowski, and Yuris S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,�?? nlin.PS/0309075.

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Figures (3)

Fig. 1.
Fig. 1.

Integrated longitudinal and transverse profiles of the interference pattern of a condensate released from an optical lattice after acceleration to a quasimomentum ≈0.9 and a subsequent time-of-flight of 21ms. In (a) and (b), the acceleration a was 5ms-2, whereas in (c) and (d) a=0.3ms-2. In (a) and (c), the horizontal axis has been rescaled in units of recoil momenta. Note the different vertical axis scales (by a factor 4) for the upper and lower graphs. The total number of atoms was measured to be the same in both cases.

Fig. 2.
Fig. 2.

Visibility and radial width as a function of quasimomentum (in units of prec ) for different accelerations. As the acceleration is lowered, instabilities close to quasimomentum 1 (corresponding to the edge of the Brillouin zone) lead to a decrease in visibility and increase in radial width. For comparison, in each graph the (linear) fits to the visibility and radial width for the a=5ms-2 data are included. The error bars on the visibility correspond to an estimated 10% systematic error, whereas the error bars on the radial width are the standard deviations of the Gaussian fits.

Fig. 3.
Fig. 3.

Results of a one-dimensional numerical simulation of our experiment for different values of the nonlinear parameter C and acceleration a=0.3ms-2. The open squares, circles and triangles correspond to C=0.008 (the value for our experiment), C=0.004 and C=0, respectively. The closed symbols are the experimental values of the visibility as reported in Fig. 2 for a=0.3ms-2. The dashed lines connect the theoretical points to guide the eye.

Equations (2)

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visibility = h peak h middle h peak + h middle ,
C = π n 0 a s k L 2 ,

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