Steady State Entanglement in Cavity QED.

We investigate steady state entanglement in an open quantum system, specifically a single atom in a driven optical cavity with cavity loss and spontaneous emission. The system reaches a steady pure state when driven very weakly. Under these conditions, there is an optimal value for atom-field coupling to maximize entanglement, as larger coupling favors a loss port due to the cavity enhanced spontaneous emission. We address ways to implement measurements of the entanglement and find that normalized cross-correlation functions are indicators of the entanglement in the system. The equal time intensity-field cross correlation between the transmitted field of the cavity and the fluorescence intensity is proportional to the entanglement of formation for weak driving fields.