Controlling synchronization in large laser networks using number theory

TL;DR

This paper demonstrates experimentally how number theory can be used to control multi-cluster synchronization in large laser networks, enabling remote phase coherence adjustments and potential applications in secure communications.

Contribution

It introduces a novel method linking network connectivity to synchronization clusters via number theory, validated through experimental laser network demonstrations.

Findings

Synchronization clusters correspond to the greatest common divisor of network loops.

Remote control of laser phase coherence is achieved by local connectivity adjustments.

The approach provides a benchmark for coupled oscillators and applications in optical communication.

Abstract

Synchronization in networks with delayed coupling are ubiquitous in nature and play a key role in almost all fields of science including physics, biology, ecology, climatology and sociology. In general, the published works on network synchronization are based on data analysis and simulations, with little experimental verification. Here we develop and experimentally demonstrate various multi-cluster phase synchronization scenarios within coupled laser networks. Synchronization is controlled by the network connectivity in accordance to number theory, whereby the number of synchronized clusters equals the greatest common divisor of network loops. This dependence enables remote switching mechanisms to control the optical phase coherence among distant lasers by local network connectivity adjustments. Our results serve as a benchmark for a broad range of coupled oscillators in science and technology, and offer feasible routes to achieve multi-user secure protocols in communication networks and parallel distribution of versatile complex combinatorial tasks in optical computers.