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Features of the Motion of Ultracold Atoms in Quasiperiodic Potentials

  • ATOMS, MOLECULES, OPTICS
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Abstract

We consider here quasiperiodic potentials on the plane, which can serve as a “transitional link” between ordered (periodic) and chaotic (random) potentials. As can be shown, in almost any family of quasiperiodic potentials depending on a certain set of parameters, it is possible to distinguish a set (in the parameter space) where, according to a certain criterion, potentials with features of ordered potentials arise, and a set where we have potentials with features of random potentials. These sets complement each other in the complete parameter space, and each of them has its own specific structure. The difference between “ordered” and “chaotic” potentials will manifest itself, in particular, in the transport properties at different energies, which we consider here in relation to systems of ultracold atoms. It should be noted here also that the transport properties of particles in the considered potentials can be accompanied by the phenomena of “partial integrability” inherent in two-dimensional Hamiltonian systems.

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Notes

  1. One of the main conditions imposed in [4, 5] on the function V(X1, X2, X3) and the rational direction of embedding \({{\mathbb{R}}^{2}}\) → \({{\mathbb{R}}^{3}}\), is the absence in all planes of this direction of singular level lines connecting two different singular points of the potential, at least at one of the energy levels in the interval of the existence of open level lines. For Morse functions V(X1, X2, X3) and rational directions of embedding \({{\mathbb{R}}^{2}}\) → \({{\mathbb{R}}^{3}}\) in general position, this condition is satisfied. In some physical examples, this condition may actually be violated due to the imposition of certain additional special symmetries. As we have already said, we do not assume here the special presence of such additional symmetries on the considered families of potentials. In this case, the violation of this condition an our only for some special rational directions of embedding, which, in reality, does not change the described picture in the corresponding family of quasi periodic potentials.

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  1. Steklov Mathematical Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    I. Dynnikov

  2. Landau Institute for Theoretical Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow region, Russia

    A. Maltsev

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Dynnikov, I., Maltsev, A. Features of the Motion of Ultracold Atoms in Quasiperiodic Potentials. J. Exp. Theor. Phys. 133, 711–736 (2021). https://doi.org/10.1134/S1063776121120025

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