Bridging Photon Statistics and Phase Transitions in Random Fiber Lasers

Complex systems exhibit rich equilibrium states, yet the universal principles governing these systems remain unrevealed, motivating the search for novel experimental platforms. Random fiber lasers (RFLs), which generate partially-coherent light-wave through feedback from Rayleigh scattering, provide a photonic realization of such systems. Here we report a comprehensive theoretical and experimental investigation of photon statistics for RFLs based on classical second-order temporal correlation function $g^{(2)}(\tau )$, revealing unique statistical properties and introduce a two-dimensional framework for controlling photon statistics. Remarkably, we establish a unified landscape between photon correlation, intensity statistics governed by Levy statistics, and phase transitions with replica symmetry breaking. This multifaceted relationship, observed for the first time, bridges disordered photonics with statistical physics of complex system. Our results offer new pathways for engineering laser emission with controllable photon statistics, and more broadly, this work positions RFLs as a fertile land for exploring emergent behaviors in disordered systems.