Coherent dynamics in frustrated coupled parametric oscillators

Marcello Calvanese Strinati, Igal Aharonovich, Shai Ben-Ami, Emanuele G. Dalla Torre, Leon Bello, Avi Pe'Er

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8 Scopus citations


We explore the coherent dynamics in a small network of three coupled parametric oscillators and demonstrate the effect of frustration on the persistent beating between them. Since a single-mode parametric oscillator represents an analogue of a classical Ising spin, networks of coupled parametric oscillators are considered as simulators of Ising spin models, aiming to efficiently calculate the ground state of an Ising network - a computationally hard problem. However, the coherent dynamics of coupled parametric oscillators can be considerably richer than that of Ising spins, depending on the nature of the coupling between them (energy preserving or dissipative), as was recently shown for two coupled parametric oscillators. In particular, when the energy-preserving coupling is dominant, the system displays everlasting coherent beats, transcending the Ising description. Here, we extend these findings to three coupled parametric oscillators, focussing in particular on the effect of frustration of the dissipative coupling. We theoretically analyse the dynamics using coupled nonlinear Mathieu's equations, and corroborate our theoretical findings by a numerical simulation that closely mimics the dynamics of the system in an actual experiment. Our main finding is that frustration drastically modifies the dynamics. While in the absence of frustration the system is analogous to the two-oscillator case, frustration reverses the role of the coupling completely, and beats are found for small energy-preserving couplings.

Original languageEnglish
Article number085005
JournalNew Journal of Physics
Issue number8
StatePublished - Aug 2020

Bibliographical note

Publisher Copyright:
© 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.


  • coherent Ising machines
  • coherent dynamics
  • many-body time crystal
  • parametric oscillators


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