Observation of Distinct Phase Transitions in a Nonlinear Optical Ising Machine

TL;DR

This paper demonstrates that a nonlinear optical Ising machine can exhibit two different types of phase transitions, enhancing its potential for solving complex optimization problems.

Contribution

The study experimentally observes and explains two distinct phase transitions in a nonlinear optical Ising machine, supported by simulations and mean-field theory.

Findings

Observation of second-order phase transition with continuous magnetization change.

Detection of first-order phase transition with abrupt magnetization drop.

Validation of experimental results through Monte Carlo simulations.

Abstract

Optical Ising machines promise to solve complex optimization problems with an optical hardware acceleration advantage. Here we study the ground state properties of a nonlinear optical Ising machine realized by spatial light modulator, Fourier optics, and second harmonic generation in a nonlinear crystal. By tuning the ratio of the light intensities at the fundamental and second harmonic frequencies, we experimentally observe two distinct ferromagnetic-to-paramagnetic phase transitions: a second-order phase transition where the magnetization changes to zero continuously and a first-order phase transition where the magnetization drops to zero abruptly as the effective temperature increases. Our experimental results are corroborated by a numerical simulation based on the Monte Carlo Metropolis-Hastings algorithm, and the physical mechanism for the distinct phase transitions can be understood with a mean-field theory. Our results showcase the great flexibility of the nonlinear optical Ising machine, which may find important potential applications in solving combinatorial optimization problems.