# Topological Phase Transition and Charge Pumping in a One-Dimensional Periodically Driven Optical Lattice

## TL;DR

This paper proposes a method to realize and detect topological phase transitions and charge pumping in a driven optical lattice, using tunable long-range hopping to achieve different topological phases in ultracold atomic systems.

## Contribution

It introduces a scheme to induce topological phases in a bichromatic optical lattice with periodic driving, enabling experimental observation of topological transitions and charge pumping.

## Key findings

- Topological phase transition from -1 to 2 in the lowest band.
- Quantized topological pumped charges for different phases.
- Scheme is feasible with current cold atom technology.

## Abstract

Experimental realizations of topological quantum systems and detections of topological invariants in ultracold atomic systems have been a greatly attractive topic. In this work, we propose a scheme to realize topologically different phases in a bichromatic optical lattice subjected to a periodically driven tilt harmonic oscillation, which can be effectively described by a superlattice model with tunable long-range hopping processes. By tuning the ratio of nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping amplitudes, the system undergoes a topological phase transition accompanied by the change of topological numbers of the lowest band from -1 to 2. Using a slowly time-periodic modulation, the system emerges distinct quantized topological pumped charges (TPCs) of atoms in the filled band for different topological phases. Our scheme is realizable in current cold atomic technique.