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Frontiers in Optics

Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

Yutaka Takeda, Shuhei Tamate, Y. Yamamoto, Hiroki Takesue, Takahiro Inagaki, Shoko Utsunomiya

Published Jan 1, 2017• 5 citations
Publisher

Abstract

We built a non-degenerate optical parametric oscillator (NOPO) network to simulate a one-dimensional XY model in thermal equilibrium. We experimentally found that the effective temperature can be controlled via an external noise injection.
DOI
10.1364/fio.2017.fm4e.3

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We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.
We present an experimental scheme of implementing multiple spins in a classical XY model using a non-degenerate optical parametric oscillator (NOPO) network. We built an NOPO network to simulate a one-dimensional XY Hamiltonian with 5000 spins and externally controllable effective temperatures. The XY spin variables in our scheme are mapped onto the phases of multiple NOPO pulses in a single ring cavity and interactions between XY spins are implemented by mutual injections between NOPOs. We show the steady-state distribution of optical phases of such NOPO pulses is equivalent to the Boltzmann distribution of the corresponding XY model. Estimated effective temperatures converged to the setting values, and the estimated temperatures and the mean energy exhibited good agreement with the numerical simulations of the Langevin dynamics of NOPO phases.
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We developed a quantum analysis of the nondegenerate optical parametric oscillator (NOPO) with unequally injected signal and idler. Both the steady-state output field and the two-mode quantum correlation spectrum are investigated under the condition of different injected idler-to-signal ratios (ISRs) and the relative phase between the pump and the injected seed. It is found that when the seed is injected through the output coupler, the NOPO allows for the robust generation of two-mode quantum entanglement even if the relative phase is free running and the ISR is as high as 0.7. At the specific relative phase of zero, a high degree of entanglement can exist across a whole range of ISRs. An experimental study of the NOPO with unequal seeds is presented, and the observed results verify the theoretical predictions.
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