A Polariton Graph Simulator

TL;DR

This paper introduces polariton graphs as a versatile platform for simulating classical XY and Kuramoto models, enabling exploration of complex phase transitions and synchronization phenomena in two-dimensional systems.

Contribution

It presents a novel approach to simulate XY and Kuramoto models using polariton condensates imprinted on arbitrary graphs, with analytical modeling connecting these systems.

Findings

Polariton graphs can be used to simulate XY and Kuramoto models.

Analytical solutions relate polariton condensates to classical spin models.

Potential to study large-scale synchronization and phase transitions.

Abstract

We discuss polariton graphs as a new platform for simulating the classical XY and Kuramoto models. Polariton condensates can be imprinted into any two-dimensional graph by spatial modulation of the pumping laser. Polariton simulators have the potential to reach the global minimum of the XY Hamiltonian in a bottom-up approach by gradually increasing excitation density to the threshold or to study large-scale synchronisation phenomena and dynamical phase transitions when operating above the threshold. We consider the modelling of polariton graphs using the complex Ginzburg-Landau model and derive analytical solutions for a single condensate, the XY model, two-mode model and the Kuramoto model establishing the relationships between them.