Persistent dynamics in coupled non-degenerate parametric oscillators: pump saturation prevents mode competition

The coherent dynamics in networks of coupled oscillators is of great interest in wave-physics since the coupling produces various dynamical effects, such as coherent energy exchange (beats) between the oscillators. However, it is common wisdom that these coherent dynamics are transients that quickly decay in active oscillators (e.g. lasers) since pump saturation causes mode competition that results, for homogeneous gain, in the prevalence of the single winning mode. We observe that pump saturation in coupled parametric oscillators counter-intuitively encourages the multi-mode dynamics of beating and indefinitely preserves it, despite the existence of mode competition. We explore in detail the coherent dynamics of a pair of coupled parametric oscillators with a shared pump and arbitrary coupling in a radio frequency (RF) experiment, as well as in simulation. Specifically, we realize two parametric oscillators as different frequency-modes of a single RF cavity and couple them arbitrarily using a digital high-bandwidth FPGA. We observe persistent coherent beats that are maintained at any pump level, even high above the threshold. The simulation highlights how the interplay of pump depletion between the two oscillators prevents them from synchronizing, even when the oscillation is deeply saturated.