Topological Properties of Ultracold Bosons in One-Dimensional Quasiperiodic Optical Lattice

Abstract

We analyze topological properties of the one-dimensional Bose-Hubbard model with a quasiperiodic superlattice potential. This system can be realized in interacting ultracold bosons in optical lattice in the presence of an incommensurate superlattice potential. We first analyze the quasiperiodic superlattice made by the cosine function, which we call Harper-like Bose-Hubbard model. We compute the Chern number and observe a gap-closing behavior as the interaction strength $U$ is changed. Also, we discuss the bulk-edge correspondence in our system. Furthermore, we explore the phase diagram as a function of $U$ and a continuous deformation parameter $\beta$ between the Harper-like model and another important quasiperiodic lattice, the Fibonacci model. We numerically confirm that the incommensurate charge density wave (ICDW) phase is topologically non-trivial and it is topologically equivalent in the whole ICDW region.

4 pages, 5 figures, submitted to JPSJ

References in corpus (4)

• Cold Bosons in Optical Lattices
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Lattice modulation spectroscopy of strongly interacting bosons in disordered and quasi-periodic optical lattices
• Ground-state and dynamic properties of hard-core bosons in one-dimensional incommensurate optical lattices with harmonic trap

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• Colloquium: Synthetic quantum matter in non-standard geometries
• Doped Mott insulator on Penrose tiling
• Topological end states in a one-dimensional spatially modulated interaction spinless fermion model
• Solution of one-dimensional Bose Hubbard model in large-$U$ limit