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arXiv:0906.3042 · Physical Review Letters

Optical Kagome Lattice for Ultracold Atoms with Nearest Neighbor Interactions

Janne Ruostekoski

Published Aug 21, 2009• 69 citations
arXivHTMLPDF

Abstract

We propose a scheme to implement an optical kagome lattice for ultracold atoms with controllable s-wave interactions between nearest neighbor sites and a gauge potential. The atoms occupy three different internal atomic levels with electromagnetically induced coupling between the levels. We show that by appropriately shifting the triangular lattice potentials, experienced by atoms in different levels, the kagome lattice can be realized using only two standing waves, generating a highly frustrated quantum system for the atoms.

DOI
10.1103/physrevlett.103.080406

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We propose a scheme to implement an optical kagome lattice for ultracold atoms with controllable s-wave interactions between nearest neighbor sites and a gauge potential. The atoms occupy three different internal atomic levels with electromagnetically induced coupling between the levels. We show that by appropriately shifting the triangular lattice potentials, experienced by atoms in different levels, the kagome lattice can be realized using only two standing waves, generating a highly frustrated quantum system for the atoms.
Abstract We propose a novel method for the realization of an optical Kagome lattice due to the Raman processes driven by additional light fields applied to the ultracold atoms of two hyperfine internal states trapped in a planar optical triangular lattice. The tunneling between the different internal states of the nearest-neighbor atoms in Kagome lattices can be adjusted by the additional light fields independently of the on-site interaction. This optical lattice protocol can be used to investigate the magnetic quantum phenomena and the nearest-neighbor magnetic coupling becomes strong enough by increasing the intensities of the additional light fields.
We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geometries using Kapitza-Dirac diffraction and by analyzing the Bloch-state composition of a superfluid released suddenly from the lattice. The Bloch-state analysis also allows us to determine the ground-state distribution within the superlattice unit cell. The lattices implemented in this work offer a near-ideal realization of a paradigmatic model of many-body quantum physics, which can serve as a platform for future studies of geometric frustration.
Quantum simulation is the study of one quantum mechanical system via analog with another. In this thesis we explore a simple model of interacting bosons on a lattice, known as the Bose-Hubbard model, by experimental investigation of ultracold rubidium atoms in an optical lattice made from laser light. We describe the construction and stabilization of an optical superlattice with threefold symmetry, and its use in studying the Bose-Hubbard model on triangular and trimerized kagome lattices. We study the short range phase coherence of a Mott insulator on the triangular lattice, and develop a scheme to mitigate out-of-equilibrium effects arising from the state preparation. We show the first experimental realization of an optical trimerized kagome lattice for cold atoms, and discuss experiments characterizing this lattice. Finally, we provide evidence for a Mott insulating state with fractional average particle number per site with measurements of the nearest-neighbor phase coherence of strongly interacting atoms in the trimerized kagome lattice.
We produce a trimerized kagome lattice for ultracold atoms using an optical superlattice formed by overlaying triangular lattices generated with two colors of light at a 2:1 wavelength ratio. Adjusting the depth of each lattice tunes the strong intratrimer (JJJ) and weak intertrimer (${J}^{\ensuremath{'}}$) tunneling energies, and also the on-site interaction energy UUU. Two different trimerization patterns are distinguished using matter-wave diffraction. We characterize the coherence of a strongly interacting Bose gas in this lattice, observing persistent nearest-neighbor spatial coherence in the large $U/{J}^{\ensuremath{'}}$ limit, and that such coherence displays asymmetry between the strongly and the weakly coupled bonds.
We propose a general method to realize frustrated tunneling of ultracold atoms in a state-dependent optical lattice. Two typical lattice configurations are considered, the square lattice with competing interaction and the kagom\'e lattice with geometrical frustration. The ideal can be extended to implement frustrated tunneling of ultracold atoms in various geometries, which enable us to investigate the physics of frustration in both bosonic and spin systems. We study the mean-field phase diagrams of the considered models and the experimental situations are also discussed.
Geometric frustration is a phenomenon where local energy constraints cannot be simultaneously satisfied because of geometric reasons. This leads to a manifold of degenerate ground states in which ordering can be highly nontrivial and exotic phases of matter could emerge. In a kagome lattice, both interaction energies of spins and kinetic energies of particles can be frustrated. In the latter case, a single-particle band structure with a flat (dispersionless) energy band results.In this dissertation, we report our experimental studies of interacting bosonic systems in kagome lattices. Such studies are performed with a quantum simulator based on ultracold atoms in optical lattices. We describe upgrades and development of the apparatus that constructs optical kagome lattices in our experiment. We briefly discuss results of an experiment studying the Bose-Hubbard model in a trimerized kagome lattice. We then report the details of an experiment investigating the interplay of kinetic frustration and interactions by probing the band structure of an optical kagome lattice with interacting ultracold bosonic atoms. Finally, we propose experimental ideas for exploring the properties of the singular band touching point in the kagome flat band.