Topological defect formation in 1D and 2D spin chains realized by network of optical parametric oscillators

TL;DR

This paper demonstrates how a network of optical parametric oscillators can simulate classical spin chains, revealing defect formation dynamics driven by quantum noise, with predictions validated against experimental data.

Contribution

It introduces a novel optical network-based simulator for spin chains that captures defect formation and dynamics during phase transitions.

Findings

Topological defects form during the system's transition above threshold.

Predicted defect densities match experimental data for large spin systems.

The model combines linear growth and nonlinear saturation stages for accurate predictions.

Abstract

A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this "Ising machine" for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice, and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear "growth stage" and a nonlinear "saturation stage". These predictions are compared against recent data for a 10,000-spin 1D Ising machine.