Journal
NANOPHOTONICS
Volume 9, Issue 13, Pages 4199-4205Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/nanoph-2020-0256
Keywords
graph coloring; optical computing; parametric three-photon down-conversion; Potts model
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In recent years, there has been a growing interest in optical simulation of lattice spin models for applications in unconventional computing. Here, we propose optical implementation of a three-state Potts spin model by using networks of coupled parametric oscillators with phase tristability. We first show that the cubic nonlinear process of spontaneous three-photon down-conversion is accompanied by a tristability in the phase of the subharmonic signal between three states with 2 pi/3 phase contrast. The phase of such a parametric oscillator behaves like a three-state spin system. Next, we show that a network of dissipatively coupled three-photon down-conversion oscillators emulates the three-state planar Potts model. We discuss potential applications of the proposed system for all-optical optimization of combinatorial problems such as graph 3-COL and MAX 3-CUT.
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