Abstract
A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. The most fascinating concept is the breaking of replica symmetry: identical copies of the randomly interacting system that manifest completely different dynamics. Replica symmetry breaking has been predicted in nonlinear wave propagation, including Bose-Einstein condensates and optics, but it has never been observed. Here, we report the experimental evidence of replica symmetry breaking in optical wave propagation, a phenomenon that emerges from the interplay of disorder and nonlinearity. When mode interaction dominates light dynamics in a disordered optical waveguide, different experimental realizations are found to have an anomalous overlap intensity distribution that signals a transition to an optical glassy phase. The findings demonstrate that nonlinear propagation can manifest features typical of spin-glasses and provide a novel platform for testing so-far unexplored fundamental physical theories for complex systems.
Highlights
A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics
Replica symmetry breaking here indicates a global locking of several spatial modes so that completely anticorrelated states may emerge from equivalent conditions, the signature that different metastable states underlie dynamics
The replica symmetry breaking phenomenology we report hereafter has to be considered as averaged over different realizations of the disorder in analogy with results in non-static random laser systems[16]
Summary
A landmark of statistical mechanics, spin-glass theory describes critical phenomena in disordered systems that range from condensed matter to biophysics and social dynamics. From the equilibrium perspective of the spin-glass theory, the transition to a glassy phase is signaled by replica symmetry breaking (RSB), that is, a change in the statistical distribution of the overlap between measurements in different realizations of the dynamics[3,4]. Interacting localized modes propagating in nonlinear disordered media[35,36,37] and multiple laser filaments in gases[38,39] may lead to optical states whose complexity resembles glassy phases This suggests that the statistical properties of coupled nonlinear optical waves can be investigated statically by means of Hamiltonian models with quenched disordered interactions. Replica symmetry breaking here indicates a global locking of several spatial modes so that completely anticorrelated states may emerge from equivalent conditions, the signature that different metastable states underlie dynamics
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