Dynamics of two dipole-coupled superconducting qubits interacting with two independent cavity modes

In this paper, we have investigated the entanglement dynamics between two dipole-coupled superconducting qubits not resonantly interacting with two microwave modes of independent coplanar resonators. The case of different atom-field couplings has been under consideration. Using the dressed-states technique we have derived the exact solution of the evolution equation for separable initial qubits states and field modes in the vacuum states. On its basis the negativity as a measure of qubit-qubit entanglement has been calculated. The time dependence of negativity for different values of detuning between the qubits and fields frequencies, atom-field couplings and strength of the dipole-dipole interaction has been investigated for different separable initial qubits states. (paper)