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.

We investigate the long-term dynamics of spin textures prepared by cooling unmagnetized spinor gases of F = 1 87 Rb to quantum degeneracy, observing domain coarsening and a strong dependence of the equilibration dynamics on the quadratic Zeeman shift q. For small values of |q|, the textures arrive at a configuration independent of the initial spin-state composition, characterized by large length-scale spin domains and the establishment of easy-axis (negative q) or easy-plane (positive q) magnetic anisotropy. For larger |q|, equilibration is delayed as the spin-state composition of the degenerate spinor gas remains close to its initial value. These observations support the mean-field equilibrium phase diagram predicted for a ferromagnetic spinor Bose-Einstein condensate and also illustrate that equilibration is achieved under a narrow range of experimental settings, making the F = 1 87 Rb gas more suitable for studies of nonequilibrium quantum dynamics.

The mean-field treatment of the Bose-Hubbard model predicts properties of lattice-trapped gases to be insensitive to the specific lattice geometry once system energies are scaled by the lattice coordination number z. We test this scaling directly by comparing coherence properties of 87 Rb gases that are driven across the superfluid to Mott insulator transition within optical lattices of either the kagome (z = 4) or the triangular (z = 6) geometries. The coherent fraction measured for atoms in the kagome lattice is lower than for those in a triangular lattice with the same interaction and tunneling energies. A comparison of measurements from both lattices agrees quantitatively with the scaling prediction. We also study the response of the gas to a change in lattice geometry, and observe the dynamics as a strongly interacting kagome-lattice gas is suddenly "hole-doped" by introducing the additional sites of the triangular lattice.

The structure of a two-dimensional honeycomb optical lattice potential with small inversion asymmetry is characterized using coherent diffraction of 87 Rb atoms. We demonstrate that even a small potential asymmetry, with peak-to-peak amplitude of ≤ 2.3% of the overall lattice potential, can lead to pronounced inversion asymmetry in the momentum-space diffraction pattern. The observed asymmetry is explained quantitatively by considering both Kapitza-Dirac scattering in the RamanNath regime, and also either perturbative or full-numerical treatment of the band structure of a periodic potential with a weak inversion-symmetry-breaking term. Our results have relevance for both the experimental development of coherent atom optics and the proper interpretation of timeof-flight assays of atomic materials in optical lattices. DOI: 10.1103/PhysRevA.93.063613 In x-ray crystallography, the diffraction of light is analyzed to determine the exact crystalline structure of a material. Similarly, with the availability of ultracold sources of coherent matter waves of atoms, one can use atomic diffraction to characterize potentials experienced by the atoms. Of particular interest are the optical lattice potentials produced by periodic patterns of light intensity and polarization, formed by the intersection of several coherent plane waves of light or by direct imaging. Lattice potentials of various geometries and dimensionalities, some incorporating atomic-spin dependence and gauge fields, have been produced or proposed for the purpose of creating synthetic atomic materials by placing quantum-degenerate atoms within them [1][2][3]. Just as in condensed matter, the characteristics of such synthetic atomic materials derive from the nature of the optical crystal upon which they are based. Matter-wave crystallography therefore becomes a vital tool in the study of such synthetic quantum matter [4].A key first step in determining the structure of a lattice is the assignment of its point-group and space-group symmetries. The violation of a symmetry is identified in x-ray crystallography by a difference in the intensities of diffraction spots [5]. Following such work, here we detect the inversion asymmetry of an optical lattice by observing significant asymmetries in the diffraction of a coherent matter wave from the potential. For this, we produce a spin-polarized 87 Rb Bose-Einstein condensate at rest, and then impose for a variable pulse duration the two-dimensional honeycomb optical lattice potential produced by three light beams intersecting at equal angles [6]. The resulting Kapitza-Dirac diffraction is quantified by imaging the gas after it is allowed to expand freely. By tuning the pulse time and working with a deep optical lattice, we produce highly visible (over 50% contrast) * Electronic address: dmsk@berkeley.edu inversion asymmetry in the populations of the first-order diffraction peaks even while the inversion-asymmetric part of the potential is ≤ 2.3% of the overall lattice potential. This observation highlights the extre...