Observation of Distinct Phase Transitions in a Nonlinear Optical Ising Machine

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.

7 pages, 4 figures

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• Wavelength-division multiplexing optical Ising simulator enabling fully programmable spin couplings and external magnetic fields
• Observing a Phase Transition in a Coherent Ising Machine
• Spatial-photonic Ising machine by space-division multiplexing with physically tunable coefficients of a multi-component model
• Spin Hamiltonians in the Modulated Momenta of Light
• An optical Ising spin glass simulator with tuneable short range couplings
• Spatial Optical Simulator for Classical Statistical Models
• Dense Associative Memory in a Nonlinear Optical Hopfield Neural Network