Thouless pumping in a driven-dissipative Kerr resonator array

TL;DR

This paper demonstrates a topological Thouless pump in a driven-dissipative Kerr resonator array, utilizing nonlinear interactions and modulated parameters to achieve quantized transport and topological transitions.

Contribution

It introduces a novel nonlinear, driven-dissipative implementation of Thouless pumping in Kerr resonator arrays, revealing interaction-induced topological transitions.

Findings

Realistic parameters inspired by exciton polaritons enable the proposed pump.

Topological bands exhibit quantized transport linked to Chern numbers.

Interaction-driven band inversion indicates a topological phase transition.

Abstract

Thouless pumping is an emblematic manifestation of topology in physics, referring to the ability to induce a quantized transport of charge across a system by simply varying one of its parameters periodically in time. The original concept of Thouless pumping involves a non-interacting system, and has been implemented in several platforms. One current challenge in the field is to extend this concept to interacting systems. In this article, we propose a Thouless pump that solely relies on nonlinear physics, within a chain of coupled Kerr resonators. Leveraging the driven-dissipative nature of the system, we modulate in space and time the onsite Kerr interaction energies, and generate 1+1-dimensional topological bands in the Bogoliubov spectrum of excitations. These bands present the same topology as the ones obtained within the Harper-Hofstadter framework, and the Wannier states associated to each band experience a net displacement and show quantized transport according to the bands Chern numbers. Remarkably, we find driving configurations leading to band inversion, revealing an interaction-induced topological transition. Our numerical simulations are performed using realistic parameters inspired from exciton polaritons, which form a platform of choice for investigating driven topological phases of matter.