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

TL;DR

This paper investigates the topological properties of a one-dimensional Bose-Hubbard model with a quasiperiodic potential, revealing topological phases and phase transitions influenced by interactions and lattice deformation.

Contribution

It introduces a comprehensive analysis of topological phases in the Harper-like Bose-Hubbard model and explores the topological nature of the ICDW phase across different quasiperiodic lattices.

Findings

Chern number exhibits gap-closing at varying interaction strengths

Bulk-edge correspondence is confirmed in the system

ICDW phase is topologically non-trivial and consistent across parameter space

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.