Simulation of the superradiant quantum phase transition in the superconducting charge qubits inside a cavity

In this paper, we propose an experimentally feasible scheme that the superconducting quantum interference devices are coupled with a high-quality cavity supporting a single-mode photon, to realize an effective Dicke model. By using several hundred artificial two-level atoms, the strong coupling regime can be successfully achieved. Moreover, in our proposal the superradiant phase transition for this model can be well controlled by the frequency of external magnetic flux when the superconducting charge qubits work at their optimal point, in which the qubits can be mostly immune from charge noise produced by uncontrollable charge fluctuations. Finally, we propose to observe this phase transition by detecting the intracavity intensity in terms of a heterodyne detector out of the cavity.