Entanglement between two superconducting charge qubits

In this paper, we investigated the dynamics of entanglement of two identical charge qubits with Josephson junctions in the case when one of the qubits is exposed to a microwave field in a coherent or thermal state. We have found the exact solution of the quantum time equation of evolution of the system under consideration for the statistical operator in the case of initial separable and entangled states of qubits. The exact solution for the complete statistical operator is used to calculate the qubit entanglement criterion - concurrence. The results of numerical simulation of the time dependence of the concurrence in the case of the coherent field showed that, with a certain choice of model parameters, the system can realize long-lived entangled states. It is also shown that for the thermal state of the field and the entangled initial state of qubits, the qubits retain a certain degree of entanglement during evolution even in the case of very intensive fields. In this case, for any intensities of thermal noise, there is no effect of the sudden death of entanglement.