Realization of Fractional Chern Insulators in the Thin-Torus-Limit with Ultracold Bosons

TL;DR

This paper proposes an experimental setup using ultracold bosons in a 1D ladder to simulate fractional Chern insulators in the thin-torus limit, demonstrating a topological charge density wave phase with potential for observing fractional quantum Hall effects.

Contribution

It introduces a realistic method to realize fractional Chern insulators using ultracold bosons, linking 1D ladder systems with 2D topological phases through numerical and experimental techniques.

Findings

Ground state is an incompressible topological charge density wave

Simulation of fractional quantum Hall states in a 1D ladder

Implementation of a fractional Thouless pump

Abstract

Topological states of interacting many-body systems are at the focus of current research due to the exotic properties of their elementary excitations. In this paper we suggest a realistic experimental setup for the realization of a simple version of such a phase. We show how delta-interacting bosons hopping on the links of a one-dimensional (1D) ladder can be used to simulate the thin-torus-limit of the two-dimensional (2D) Hofstadter-Hubbard model at one-quarter magnetic flux per plaquette. Bosons can be confined to ladders by optical superlattices, and synthetic magnetic fields can be realized by far off-resonant Raman beams. We show that twisted boundary conditions can be implemented, enabling the realization of a fractionally quantized Thouless pump. Using numerical density-matrix-renormalization-group (DMRG) calculations we show that the groundstate of our model is an incompressible symmetry-protected topological charge density wave (CDW) phase at average filling $\rho = 1/8$ per lattice site, related to the 1/2 Laughlin-type state of the corresponding 2D model.