Phase-Controlled Non-Markovian Hysteresis in a Nonlinear, Non-Hermitian Silicon Microresonator

Non-Hermitian photonic systems, where gain, loss, and nonlinear interactions interplay, offer a fertile ground for realizing complex dynamical behavior such as broken reciprocity, self-oscillations, and excitable dynamics. Here we report experimental observations of phase-controlled hysteresis in a nonlinear, non-Hermitian silicon microring resonator with dynamically tunable coupling between counter-propagating modes. By integrating independent thermal phase shifters, we modulate the intermodal feedback phase in real time and access regimes with different energy stored in the cavity, allowing us to investigate conditions governed by thermo-optic and free-carrier nonlinearities. We observe non-Markovian memory effects in the form of path-dependent phase trajectories: forward and reverse phase sweeps lead to distinct steady or oscillatory states, despite identical boundary conditions. This hysteresis is underpinned by a nonlocal bifurcation, where the system transitions from a stable fixed point to a saddle-node annihilation, to finally ending in a distant limit cycle. Our results demonstrate coherent phase control as a tool for accessing novel bifurcation structures in photonics and establish a scalable platform for exploring neuromorphic dynamics beyond classical excitability.