Quasiperiodic Optical Lattices

Abstract

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.

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

“…However, it is important to note that controlled disorder (or quasi-disorder) may also be created by means of different techniques. These include the use of two-color superlattice potentials [471][472][473], the employment of so-called quasi-crystal (i.e., quasi-periodic) optical lattices in 2D or 3D [474][475][476], the use of impurity atoms trapped at random positions in the nodes of a periodic optical lattice [477], random phase masks [478], or optical speckle patterns [479][480][481]. The latter is a random intensity pattern which is produced by the scattering of a coherent laser beam from a rough surface (see, e.g., Ref.…”

Spinor Bosonic Atoms in Optical Lattices: Symmetry Breaking and Fractionalization

“…It was pointed out that the ground state of atoms with antiferromagnetic interactions in an optical trap is not a usual condensate of a macroscopic number of atoms in a single quantum state, but, rather, a complicated many body state of atoms arranged into a total singlet [7][8][9][10]. In this article we examine the problem of Bose F 1 atoms with antiferromagnetic interaction (spin symmetric interactions are assumed throughout the paper) in optical latticesarrays of microscopic potentials created by interfering laser beams [11][12][13][14][15][16][17][18]. The dynamics of spinless bosonic atoms in arrays of optical wells may be described by a BoseHubbard model with the possibility of quantum phase transitions between insulating and superfluid phases induced by varying the properties of the laser light [19].…”

Commensurability Effects in Superconducting Nb Films with Quasiperiodic Pinning Arrays

“…We note that the discovery of quasicrystals [15] has, until today, stimulated intensive investigations of a large variety of artificially generated quasiperiodic systems, such as semiconductor heterostructures [16], optical superlattices [17], photonic quasicrystals [18], atoms in optical potentials [19], superconducting wire networks [20] and Josephson junction arrays [21]. The investigation of the static and dynamic properties of vortex quasicrystals, including phase transitions which may be tuned by temperature and magnetic field, is interesting, both from a practical point of view (regarding controllability and enhancement of critical currents in superconductors) and also with respect to our understanding of fundamental aspects related to the physics of quasicrystals.…”