Synchronization of Networked Jahn-Teller Systems in Circuit QED

We consider the nonlinear effects in Jahn-Teller system of two coupled resonators interacting simultaneously with flux qubit using Circuit QED. Two frequency description of Jahn Teller system that inherits the networked structure of both nonlinear Josephson Junctions and harmonic oscillators is employed to describe the synchronous structures in multifrequency scheme. Emergence of dominating mode is investigated to analyze frequency locking by eigenvalue spectrum. Rabi Supersplitting is tuned for coupled and uncoupled synchronous configurations in terms of frequency entrainment switched by coupling strength between resonators. Second order coherence functions are employed to investigate self-sustained oscillations in resonator mode and qubit dephasing. Snychronous structure between correlations of priviledged mode and qubit is obtained in localization-delocalization and photon blockade regime controlled by the population imbalance.