Light and matter waves propagation in artificial atomic crystals: periodic and disordered configurations

Markus K Oberthaler

Iva Březinová, Lee A. Collins, Katharina Ludwig +2 more

Roland Abfalterer, Stefan Bernet, Claudia Keller +3 more

Atoms interacting with standing light waves are a model system for the propagation of waves in static and time varying periodic media. We present here experiments studying the coherent motion of atomic deBroglie waves in periodic potentials made from on and off resonant light. We observe anomalous transmission of atoms through resonant standing light waves and experimentally confirm that atoms fulfilling the Bragg condition form a standing matter wave pattern. We furthermore demonstrate how Bragg diffraction of atomic matter waves at a time-modulated thick standing light wave can be used to coherently shift the deBroglie frequency of the diffracted atoms. Our frequency shifter for atomic matter waves is similar to an acousto-optic frequency shifter for photons.

Jeremy B. Reeves, Bryce Gadway, Ludwig Krinner +3 more

Nicola Bartolo

The experimental achievement of Bose-Einstein condensation and Fermi degeneracy with ultracold gases boosted tremendous progresses both in theoretical methods and in the development of new experimental tools. Among them, intriguing possibilities have been opened by the implementation of optical lattices: periodic potentials for neutral atoms created by interfering laser beams. Degenerate gases in optical lattices can be forced in highly anisotropic traps, reducing the effective dimensionality of the system. From a fundamental point of view, the behavior of matter waves in reduced dimensions sheds light on the intimate properties of interparticle interactions. Furthermore, such reduced-dimensional systems can be engineered to quantum-simulate fasci- nating solid state systems, like bidimensional crystals, in a clean and controllable environment. Motivated by the exciting perspectives of this field, we devote this Thesis to the theoretical study of two systems where matter waves propagate in reduced dimensions. The long-range and anisotropic character of the dipole-dipole interaction critically affects the behavior of dipolar quantum gases. The continuous experimental progresses in this flourishing field might lead very soon to the creation of degenerate dipolar gases in optical potentials. In the first part of this Thesis, we investigate the emergence of a single dipolar-induced resonance in the two-body scattering process in quasi-one dimensional geometries. We develop a two-channel approach to describe such a resonance in a highly elongated cigar-shaped harmonic trap, which approximates the single site of a quasi-one-dimensional optical lattice. At this stage, we develop a novel atom-dimer extended Bose-Hubbard model for dipolar bosons in this quasi-one-dimensional optical lattice. Hence we investigate the T = 0 phase diagram of the model by exact diagonalization of a small-sized system, highlighting the effects of the dipolar-induced resonance on the many-body behavior in the lattice. In the second part of the Thesis, we present a general scheme to realize cold-atom quantum simulators of bidimensional atomic crystals, based on the possibility to independently trap two different atomic species. The first one constitutes a two-dimensional matter wave which interacts only with the atoms of the second species, deeply trapped around the nodes of a two-dimensional optical lattice. By introducing a general analytic approach, we investigate the matter-wave transport properties. We propose some illustrative applications to both Bravais (square, triangular) and non-Bravais (graphene, kagomeÌ ) lattices, studying both ideal periodic systems and experimental- sized, eventually disordered, ones. The features of the artificial atomic crystal critically depend on the two-body interspecies interaction strength, which is shown to be widely tunable via 0D-2D mixed-dimensional resonances. Keywords: matter waves, reduced dimensions, dipolar-induced resonances, mixed-dimensional resonances, extended Bose-Hubbard model, atomic artificial crystals.

Markus K Oberthaler, Roland Abfalterer, Stefan Bernet +3 more

Atoms in light crystals formed by a standing light wave are a model system to study the propagation of matter waves in periodic potentials. The encountered phenomena can be described by dynamical diffraction theory which has been extensively studied for x-ray, electron, and neutron scattering from solid state crystals. In this paper we show that an atomic de Broglie wave traversing a standing light wave allows investigation of predictions of dynamical diffraction theory which were previously experimentally not accessible. We present standard diffraction efficiency characterizations for pure absorptive and pure refractive crystals. Additionally we were able to measure directly the total atomic wave field formed inside a refractive and an absorptive crystal and to confirm the predicted absolute position of the atomic wave field with respect to the lattice planes. By superposing two standing light waves of different frequency we tailored a new kind of crystal potential where Friedel's law about usual diffraction symmetries is maximally violated.