Self-symmetrization of symmetry-breaking dynamics in passive Kerr resonators

Abstract: The realization of spontaneous symmetry breaking (SSB) requires a system that exhibits a near perfect symmetry. SSB manifests itself through a pitchfork bifurcation, but that bifurcation is fragile, and perturbed by any asymmetry or imperfections. Consequently, exploiting SSB for real-world applications is challenging and often requires cumbersome stabilization techniques. Here, we reveal a novel method that automatically leads to symmetric conditions, and demonstrate its practical application in coherently-driven, two-mode, passive Kerr resonators. More specifically, we show that introducing a $\pi$-phase defect between the modes of a driven nonlinear resonator makes SSB immune to asymmetries by means of a period-doubled dynamics of the system's modal evolution. The two-roundtrip evolution induces a self-symmetrization of the system through averaging of the parameters, hence enabling the realization of SSB with unprecedented robustness. This mechanism is universal: all symmetry-broken solutions of driven Kerr resonators have a period-doubled counterpart. We experimentally demonstrate this universality by considering the polarization symmetry breaking of several different nonlinear structures found in normal and anomalous dispersion fiber cavities, including homogeneous states, polarization domain walls, and bright vector cavity solitons.