Observation of partial replica symmetry breaking in polarization space for modulation instability competed by self-phase modulation

Replica symmetry breaking provides a profound framework for understanding complex systems. However, a direct experimental confirmation of such complex statistical behavior within the polarization space of a fundamental nonlinear process like modulation instability has remained elusive. Here, exploiting advances in ultrafast optical polarization measurement, we report the first experimental observation of partial replica symmetry breaking in the polarization space, where polarization serves as a direct analogue of spin. By performing wavelength-resolved polarization measurements of modulation instability sidebands, we identify the replica symmetry breaking for specific wavelengths by calculating the overlapping parameter of fluctuations between any two arbitrary points in polarization space, while other wavelengths maintain replica symmetric behavior. The partial replica symmetry breaking in polarization space is attributed to the competition of modulation instability and self-phase modulation. Our results establish polarization as a natural platform for probing complex energy landscapes in disordered photonic systems.