Enhancing Ising Machine Robustness Through Period-2 Dynamics in Optical Resonators

Here we propose a novel coherent Ising machine (CIM) based upon spontaneous symmetry-breaking (SSB) in a driven Kerr resonator [Fig. 1a]. Specifically, we consider a ring resonator made of a Kerr nonlinear waveguide (e.g. optical fibre) that is coherently driven with a train of short pulses with a repetition rate an integer multiple of the cavity free-spectral range. For appropriate parameters, each of the pulses undergoes spontaneous polarization symmetry breaking [SSB] within the resonator, thus yielding independent spin-like states. By measuring the polarization states of each of the pulses and feeding the measurement results to a phase modulator that acts upon the driving field, we are able to obtain a network of spins that are coupled according in a desired manner. Scanning a control parameter (e.g. laser wavelength) across the SSB bifurcation point when the coupling is activated forces the spins to evolve towards the ground-state of the corresponding Ising problem. By operating in a recently-discovered period-2 (P2) regime, where the polarization modes of the resonator switch at each roundtrip due to the implementation of a
$\pi$
-phase shift between two orthogonal polarisation modes of the resonator, the SSB dynamics are completely protected against asymmetries [1]. This includes both asymmetries in the feedback mechanism and the driving laser polarization state.