Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator

This paper investigates theoretically the evolutions of the entanglement entropy of a system of two coupled-charge-qubits interacting with an LC-resonator. It is found that when the initial states of the two qubits are prepared in a given superposition excited state, the evolution of the von Neumann entropy of the system depends significantly on the coupling strength between the two Josephson charge qubits. With the variation of the coupling strength, the evolution of the entanglement entropy of the system forms some structures, especially the periodically bistable properties, which are the first discovered for such a system to our knowledge. It is found that the relative entropy entanglement of the system is also sensitive to the variation of the coupling strength between the two charge qubits, some novel 'collective oscillations' of the relative entropy are found for the system.