Controlled asymmetric Ising model implemented with parametric micromechanical oscillators

TL;DR

This paper demonstrates that coupled parametric micromechanical oscillators can physically realize an asymmetric Ising model, revealing novel behaviors like circulating probability currents and enabling controlled exploration of such systems.

Contribution

It introduces a physical implementation of the asymmetric Ising model using parametric oscillators, with detailed characterization and observation of unique asymmetric phenomena.

Findings

Observation of probability currents in stationary states

Control of switching rates via periodic forcing

Implementation of asymmetric Ising interactions in micromechanical systems

Abstract

Asymmetric Ising model, in which coupled spins affect each other differently, plays an important role in diverse fields, from physics to biology to artificial intelligence. We show that coupled parametric oscillators provide a well-controlled and fully characterizable physical system to implement the model. Such oscillators are bistable. The coupling changes the rate of interstate switching of an oscillator depending on the state of other oscillators. Our experiment on two coupled micromechanical resonators reveals unusual features of asymmetric Ising systems, including the onset of a probability current that circulates in the stationary state. We relate the asymmetry to the exponentially strong effect of a periodic force on the switching rates of an individual parametric oscillator, which we measure. Our findings open the possibilities of constructing and exploring asymmetric Ising systems with controlled parameters and connectivity.