# Topological insulator and particle pumping in a one-dimensional shaken optical lattice

## TL;DR

This paper presents a method to simulate and detect topological insulators and particle pumping in a one-dimensional optical lattice using periodic modulation, linking it to a two-dimensional Chern insulator model.

## Contribution

It introduces a way to realize topological phases and particle pumping in a 1D optical lattice, mapping it to a 2D Chern insulator, and proposes a measurement method for the Chern number.

## Key findings

- The shaken 1D system maps to a 2D Chern insulator model.
- Topological phase exists within accessible experimental parameters.
- Chern number can be measured via density shift after one pumping cycle.

## Abstract

We propose a simple method to simulate and detect topological insulators with cold atoms trapped in a one-dimensional bichromatic optical lattice subjected to a time-periodic modulation. The tight-binding form of this shaken system is equivalent to the periodically driven Aubry-Andre model. We demonstrate that this model can be mapped into a two-dimensional Chern insulator model, whose energy spectrum hosts a topological phase within an experimentally accessible parameter regime. By tuning the laser phase adiabatically, such one-dimensional system constitutes a natural platform to realize topological particle pumping. We show that the Chern number characterizing the topological features of this system can be measured by detecting the density shift after one cycle of pumping.