The RSB transition from the photoni

The RSB transition from the photonic paramagnetic to the spin-glass can be calculated by a statistical mechanics method (i.e., replica method) [25] which relates to amplitudes or intensities of the coupled lasing modes. Evaluating the similarity between replicas can reveal the interval thermodynamic states of sample.[26] However, as far as we know, there is no successful experiment of complex amplitude measurement at present, because the measurement of complex amplitude needs the measured lasing’s mode phases in the coherent regime, which cannot be achieved in most experimental conditions.[9] Thus, in our experimental analysis, the RSB transition is estimated by calculating the overlap between intensity fluctuation intensities in different laser shots. The overlap parameter calculated by the intensity fluctuation method, which is coarse graining of the parameter calculated by the complex amplitude, but it can still reflect the change of phase.Here, we consider each shot of bandgap laser emission which is under identical experimental environments is a replica, i.e., a copy of the bandgap laser system. The overlap parameter of intensity fluctuation is quantified by the order parameter q_αβ as follow: