We present a configuration of two coupled parametric oscillators where frequency pairs interact as coherent spins which are inherently frustrated, similar to the XY model. Spin models, like the Ising and XY models, describe the dynamics of large arrays of coupled spins [1, 2] and form the theoretical framework for a vast range of phenomena in solid-state physics,

Our configuration consists of two coupled parametric oscillators that generate broadband two-mode oscillation and squeezing. By changing the coupling between the oscillators, the frequency separation between the modes can be tuned from degeneracy up to the repetition rate of the oscillators. Modulation of the coupling in-time actively couples adjacent frequency pairs, stimulating a bright, broadband oscillation around the carrier frequency. These pairs interact as inherently frustrated coherent spins, mapping in steady-state to a non-ferromagnetic ground state of a spin-model [3].

We verify our ideas with numerical simulations and an experiment in the radio-frequency (RF) domain, which serves as a physical simulator of optical parametric squeezing. In our experiment we achieve pairwise mode-locking of   resonant modes filling the entire bandwidth between DC and the pump frequency.

References

1. Inagaki, T.; Inaba, K.; Hamerly, R.; Inoue, K.; Yamamoto, Y. & Takesue, H.
   Large-scale Ising spin network based on degenerate optical parametric oscillators
   Nature Photonics, Springer Nature, 2016, 10, 415-419
2. Micha Nixon, Eitan Ronen, A. A. F. & Davidson, N.
   Observing Geometric Frustration with Thousands of Coupled Lasers
   Physical Review Letters, American Physical Society (APS), 2013, 110
3. Weill, R.; Vodonos, B.; Gordon, A.; Gat, O. & Fischer, B.
   Statistical light-mode dynamics of multipulse passive mode locking
   Physical Review E, American Physical Society (APS), 2007, 76