MACROSCOPIC COHERENT DYNAMICS IN
NETWORKS OF COUPLED MULTIMODE OSCILLATORS

The coherent dynamics of coupled oscillators is a pillar of optics and wave physics, both classical and quantum. Coupled lasers show a myriad of coherent effects, such as synchronization, phase locking and mode-locking; Whereas coupled parametric oscillators were considered as candidate solvers for calculating the ground state of a general Ising spin-network, which is known to be computationally hard. We explore the macroscopic coherent dynamics in multimode oscillators, where many coupled cavity modes (ranging from two to a million) oscillate simultaneously, realizing new regimes of coherent dynamics, as well as new effects of large-scale mode-locking in both lasers and parametric oscillators.

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Persistent beating in coupled parametric oscillators vs. Ising spin-networks:

While parametric oscillators may seem similar to lasers, their coherent dynamics is drastically different and was far less explored (since their phase dynamics is restricted by the coherent link to the pump). We recently demonstrated a new dynamical regime of persistent, full-scale, coherent beats in coupled parametric oscillators [1,5,6] with a beating frequency that reflects the coupling strength and its properties. We explore this dynamical regime with simple networks (2-3 oscillators) [1,4-6], in order to understand in depth its effect on the prospects for a coherent Ising solver [2].

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Pairwise mode-locking in parametric oscillators [3]:
When implemented in a multimode cavity, the regime of persistent beating evolves into active “pairwise mode-locking" – a macroscopic phase transition of the spectrum to a collective simultaneous oscillation on all available frequency-pairs with a locked phase-sum, although the phases of individual modes remain undefined. The multimode emission from a pairwise mode-locked parametric oscillator is therefore completely coherent in 2nd order, despite being totally incoherent in 1st order, which is highly unique.