  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.
