Steady-state correlations of two atoms interacting with a reservoir

We consider two two-level atoms fixed at different positions, driven by a resonant monochromatic laser field, and interacting collectively with the quantum electromagnetic field. A Born-Markov-secular master equation is used to describe the dynamics of the two atoms and the steady-state is obtained analytically for a configuration of the atoms. The steady-state populations of the energy levels of the free atoms, entanglement, quantum and geometric discords and degree of mixedness are calculated analytically as a function of the laser field intensity and the distance between the two atoms. It is found that there is a possibility of considerable steady-state entanglement and left/right quantum discord and that these can be controlled either by increasing/decreasing the intensity of the laser field or by increasing/decreasing the distance between atoms. It is shown that the system of two atoms can be prepared in a separable mixed state with non-zero quantum discord that turns into an $X$-state for high laser field intensities. The behavior and relationships between the different correlations are studied and several limiting cases are investigated.