Dissipative Topological Defects in Coupled Laser Networks

TL;DR

This paper demonstrates the formation and control of dissipative topological defects in a 1-D ring laser network, linking defect formation to the Kibble-Zurek mechanism and system parameters, with implications for optimization problems.

Contribution

It introduces dissipative topological defects in laser networks and shows how their formation can be controlled via system parameters, connecting to the Kibble-Zurek mechanism.

Findings

Defects form in a universal manner governed by two competing time scales.

The ratio of phase locking to synchronization time depends on gain and coupling.

Controlling these parameters can suppress defects and reach a fully ordered state.

Abstract

Topologically protected defects have been observed and studied in a wide range of fields, such as cosmology, spin systems, cold atoms and optics as they are quenched across a phase transition into an ordered state. Revealing their origin and control is becoming increasingly important field of research, as they limit the coherence of the system and its ability to approach a fully ordered state. Here, we present dissipative topological defects in a 1-D ring network of phase-locked lasers, and show how their formation is related to the Kibble-Zurek mechanism and is governed in a universal manner by two competing time scales of the lasers, namely the phase locking time and synchronization time of their amplitude fluctuations. The ratio between these two time scales depends on the system parameters such as gain and coupling strength, and thus offers the possibility to control the probability of topological defects in the system. Enabling the system to dissipate to the fully ordered, defect-free state can be exploited for solving hard combinatorial optimization problems in various fields. As opposed to unitary systems where quenching is obtained via external cooling mostly through the edges, our dissipative system is kept strictly uniform even for fast quenches.