We study the kinetic temperature and the localization of cesium atoms in a three dimensional quasiperiodic optical potential created by the interference of five or six laser beams. Bragg scattering experiments show evidence of a quasiperiodic order for the atomic density. Temperature measurements are consistent with the topological invariance of the optical potential under phase variations of the laser beams. Numerical semiclassical Monte Carlo simulations show results in reasonable agreement with the experimental observations. [S0031-9007 (97)04387-1] PACS numbers: 32.80.Pj, 61.44.Br The discovery of quasicrystals by Shechtman et al. in 1984 [1] has opened a research field of considerable importance. Quasicrystals are long-range ordered materials that are not invariant under space translation [2,3]. For this reason, the electronic wave functions as well as the macroscopic properties of such materials display intriguing new features compared to crystals which possess translational and rotational symmetries [4]. The long-range order of quasicrystals appears, for example, in Bragg scattering experiments [1]where sharp diffraction peaks are observed. In optics, such kinds of long-range order can also be achieved by combining several monochromatic traveling waves to create an interference pattern. Indeed such a light field was used to trap polystyrene microspheres in a two dimensional (2D) quasiperiodic pattern by Burns et al. [5]. More recently, several groups used the interference pattern of several laser beams to cool and trap atoms in a lattice of micron-sized optical potential wells originating from the space-dependent light shift of the atomic levels. However, all the experiments on these structures, called optical lattices [6], used laser beam configurations that lead to periodic optical potentials. It is the aim of this paper to present an experimental and a numerical study of the behavior of cesium atoms in a quasiperiodic optical potential. We describe laser beam configurations suited to the generation of quasiperiodic potentials and show that atoms are efficiently trapped and cooled in such potentials. Using Bragg scattering [7,8], we show that the atomic density displays a quasiperiodic order. We also show that the atomic kinetic temperature does not depend on the relative phases of the laser beams in spite of the fact that phase variations are not equivalent to space translations for a quasiperiodic potential.

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We present experimental and numerical studies of the atomic motion in an optical lattice displaying a fivefold rotational symmetry. The atomic transport has been investigated by measuring the time evolution of the size of the atomic cloud. The experimental results are compared to those of a semiclassical Monte Carlo simulation of the atomic motion in a three-dimensional optical quasicrystal. A good agreement has been obtained on the anisotropy of the diffusive expansion of the cloud. ͓S1050-2947͑99͒50312-0͔PACS number͑s͒: 32.80.Pj, 61.44.Br RAPID COMMUNICATIONS R4234PRA 60 GUIDONI, DÉ PRET, DI STEFANO, AND VERKERK RAPID COMMUNICATIONS R4236PRA 60 GUIDONI, DÉ PRET, DI STEFANO, AND VERKERK

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For a laser with a saturable absorber ͑LSA͒ and for a subnormal glow discharge ͑GD͒, both displaying homoclinic chaos, it is shown that double-valued curves in the return time maps, reconstructed from the time evolution of appropriate variables, are related to different time scales associated with the two mechanisms present in the respective chaotic attractors: the escape from an unstable saddle cycle and the reinjection process. For the LSA the investigation is performed numerically on a 3-2 molecular level model and the results are compared with experimental ones obtained from a CO 2 -OsO 4 LSA system having the laser frequency detuning as the control parameter. The analysis is complemented with experimental results from the GD. For both systems we show how to obtain single-valued multibranched return time maps starting from doublevalued return time maps, enabling the characterization of homoclinic chaos.

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