Geometric measure of nonlocality and quantum discord of two charge qubits with phase decoherence and dipole-dipole interaction

The effects of both phase decoherence and dipole-dipole interaction on quantum correlations of superconducting (SC) charge qubits, placed in a single-mode SC-cavity, are investigated. When the initial qubit-states are unentangled, measurement-induced nonlocality (MIN), geometric quantum discord (GQD) and quantum entanglement (QE) have different evolutions. They remain at stationary nonzero values with phase decoherence. These stationary correlations clearly appear with the photon number of Fock state. The quantum correlations can be enhanced by dipole-dipole interaction that can weaken the phase decoherence effect. When the initial states of charge qubits are entangled, the appearance of the stationary correlations can be accelerated by the photon number. The correlations can be also increased by the dipole-dipole interaction. These increases can be weaken by the photon number. The photon number also leads to sudden death and sudden birth for QE while MIN periodically reaches its maximum values, but GQD decays continuously with respect to time until it tends to be zero. When the states of the qubits have no entanglement nor entanglement sudden death, MIN and GQD keep nonzero values. The steady-state of correlations is calculated. It is found that these correlations depend on the initial states, the photon number and the dipole-dipole interaction.