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.
Similar content being viewed by others
References
M. Greiner, O. Mandel, T. Esslinger, T.W. Hänsch, I. Bloch, Nature 415, 39 (2002)
B. Paredes, A. Widera, V. Murg, O. Mandel, S. Fölling, I. Cirac, G.V. Shlyapnikov, T.W. Hänsch, I. Bloch, Nature 429, 277 (2004)
W.H. Kuan, T.F. Jiang, S.C. Cheng, Chin. J. Phys. 45, 219 (2007)
D. Jaksch, P. Zoller, Ann. Phys. 315, 52 (2005)
O. Mandel, M. Greiner, A. Widera, T. Rom, T.W. Hänsch, I. Bloch, Nature 425, 937 (2003)
K.G.H. Vollbrecht, E. Solano, J.I. Cirac, Phys. Rev. Lett. 93, 220502 (2004)
P. Douglas, S. Bergamini, F. Renzoni, Phys. Rev. Lett. 96, 110601 (2006)
J. Jersblad, H. Ellmann, K. St, A. Kastberg, L. Sanchez-Palencia, R. Kaiser, Phys. Rev. A 69, 013410 (2004)
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)
G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature 453, 895 (2008)
J. Chabe, G. Lemarie, B. Gremaud, D. Delande, P. Szriftgiser, J.C. Garreau, Phys. Rev. Lett. 101, 255702 (2008)
D.A. Steck, V. Milner, W.H. Oskay, M.G. Raizen, Phys. Rev. E 62, 3461 (2000)
H. Lignier, J. Chabe, D. Delande, J.C. Garreau, P. Szriftgiser, Phys. Rev. Lett. 95, 234101 (2005)
A.L. Lichtenberg, M.A. Lieberman, Regular and chaotic dynamics (Springer Verlag, Berlin, 1991)
H. Guo, Y. Wen, S. Feng, Phys. Rev. A 79, 035401 (2009)
D.K. Chaikovsky, G.M. Zaslavsky, Chaos 1, 463 (1991)
N.C. Panoiu, Chaos 10, 166 (2000)
D. Hennequin, Ph. Verkerk, e-print arXiv:0906.2121 [physics.atom-ph]
E. Courtade, O. Houde, J.-F. Clément, P. Verkerk, D. Hennequin, Phys. Rev. A 74, 031403(R) (2006)
L. Guidoni, Ph. Verkerk, J. Opt. B: Quantum Semiclass. Opt. 1, R23 (1999)
L. Guidoni, C. Triche, P. Verkerk, G. Grynberg, Phys. Rev. Lett. 79, 3363 (1997)
M. Greiner, I. Bloch, O. Mandel, T.W. Hänsch, T. Esslinger, Phys. Rev. Lett. 87 160405 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hennequin, D., Verkerk, P. Synchronization in non dissipative optical lattices. Eur. Phys. J. D 57, 95–104 (2010). https://doi.org/10.1140/epjd/e2009-00324-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjd/e2009-00324-1