Transient replica symmetry breaking in Brillouin random fiber lasers

Abstract Replica symmetry breaking (RSB), as a featured phase transition between paramagnetic and spin glass state in magnetic systems, has been predicted and validated among random laser-based complex systems, which involves numerous random modes interplayed via gain competition and exhibits disorder-induced frustration for glass behavior. However, the dynamics of RSB phase transition involving micro-state evolution of a photonic complex system have never been well investigated. Here, we report experimental evidence of transient RSB in a Brillouin random fiber laser (BRFL)-based photonic system through high-resolution unveiling of random laser mode landscape based on heterodyne technique. Thanks to the prolonged lifetime of activated random modes in BRFLs, an elaborated mapping of time-dependent statistics of the Parisi overlap parameter in both time and frequency domains was timely resolved, attributing to a compelling analogy between the transient RSB dynamics and the random mode evolution. These findings highlight that BRFL-based systems with the flexible harness of a customized photonic complex platform allow a superb opportunity for time-resolved transient RSB observation, opening new avenues in exploring fundamentals and application of complex systems and nonlinear phenomena.