The European Physical Journal D

, Volume 57, Issue 1, pp 95–104 | Cite as

Synchronization in non dissipative optical lattices

Nonlinear Dynamics

Abstract

The dynamics of cold atoms in conservative optical lattices obviously depends on the geometry of the lattice. But very similar lattices may lead to deeply different dynamics. In a 2D optical lattice with a square mesh, it is expected that the coupling between the degrees of freedom leads to chaotic motions. However, in some conditions, chaos remains marginal. The aim of this paper is to understand the dynamical mechanisms inhibiting the appearance of chaos in such a case. As the quantum dynamics of a system is defined as a function of its classical dynamics – e.g. quantum chaos is defined as the quantum regime of a system whose classical dynamics is chaotic – we focus here on the dynamical regimes of classical atoms inside a well. We show that when chaos is inhibited, the motions in the two directions of space are frequency locked in most of the phase space, for most of the parameters of the lattice and atoms. This synchronization, not as strict as that of a dissipative system, is nevertheless a mechanism powerful enough to explain that chaos cannot appear in such conditions.

Keywords

Periodic Solution Periodic Orbit Optical Lattice Cold Atom Main Frequency 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002) Google Scholar
  2. B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hänsch, I. Bloch, Nature 429, 277 (2004) Google Scholar
  3. W.H. Kuan, T.F. Jiang, S.C. Cheng, Chin. J. Phys. 45, 219 (2007) Google Scholar
  4. D. Jaksch, P. Zoller, Ann. Phys. 315, 52 (2005) Google Scholar
  5. O. Mandel, M. Greiner, A. Widera, T. Rom, T.W. Hänsch, I. Bloch, Nature 425, 937 (2003) Google Scholar
  6. K.G.H. Vollbrecht, E. Solano, J.I. Cirac, Phys. Rev. Lett. 93, 220502 (2004) Google Scholar
  7. P. Douglas, S. Bergamini, F. Renzoni, Phys. Rev. Lett. 96, 110601 (2006) Google Scholar
  8. J. Jersblad, H. Ellmann, K. St, A. Kastberg, L. Sanchez-Palencia, R. Kaiser, Phys. Rev. A 69, 013410 (2004) Google Scholar
  9. J. Billy, V. Josse, Z.C. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, A. Aspect, Nature 453, 891 (2008) Google Scholar
  10. G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008) Google Scholar
  11. J. Chabe, G. Lemarie, B. Gremaud, D. Delande, P. Szriftgiser, J.C. Garreau, Phys. Rev. Lett. 101, 255702 (2008) Google Scholar
  12. D.A. Steck, V. Milner, W.H. Oskay, M.G. Raizen, Phys. Rev. E 62, 3461 (2000) Google Scholar
  13. H. Lignier, J. Chabe, D. Delande, J.C. Garreau, P. Szriftgiser, Phys. Rev. Lett. 95, 234101 (2005) Google Scholar
  14. A.L. Lichtenberg, M.A. Lieberman, Regular and chaotic dynamics (Springer Verlag, Berlin, 1991) Google Scholar
  15. H. Guo, Y. Wen, S. Feng, Phys. Rev. A 79, 035401 (2009) Google Scholar
  16. D.K. Chaikovsky, G.M. Zaslavsky, Chaos 1, 463 (1991) Google Scholar
  17. N.C. Panoiu, Chaos 10, 166 (2000) Google Scholar
  18. D. Hennequin, Ph. Verkerk, e-print arXiv:0906.2121 [physics.atom-ph] Google Scholar
  19. E. Courtade, O. Houde, J.-F. Clément, P. Verkerk, D. Hennequin, Phys. Rev. A 74, 031403(R) (2006) Google Scholar
  20. L. Guidoni, Ph. Verkerk, J. Opt. B: Quantum Semiclass. Opt. 1, R23 (1999) Google Scholar
  21. L. Guidoni, C. Triche, P. Verkerk, G. Grynberg, Phys. Rev. Lett. 79, 3363 (1997) Google Scholar
  22. M. Greiner, I. Bloch, O. Mandel, T.W. Hänsch, T. Esslinger, Phys. Rev. Lett. 87 160405 (2001) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Laboratoire PhLAM, UMR CNRS, CERLA, Université Lille 1Villeneuve d’AscqFrance

Personalised recommendations