Dynamics of coupled parametric oscillators beyond coupled Ising spins.

Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We present a detailed study of the simplest coupled oscillator system - two degenerate parametric oscillators, exploring the entire phase diagram in terms of pump power, coupling nature (dissipative or energy conserving) and strength, both analytically and experimentally in a radio-frequency experiment. When the coupling between the oscillators includes a conservative component, we predict and observe a new dynamical regime, unique to parametric oscillators, where the spin-1/2 description does not apply. In a wide range of parameters near the oscillation threshold the oscillators never synchronize (in contrast to coupled spin-1/2), but show persistent, full-scale, coherent beats, whose frequency reflects the coupling strength. This new beating regime is a unique manifestation of coherent dynamics in coupled oscillators in general, and a building block for coherent Ising machines in particular.