  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 entanglement witnesses and find that normalized
cross-correlation functions are indicators of the entanglement in the system.
The magnitude of the equal time intensity-field cross correlation between the
transmitted field of the cavity and the fluorescence intensity is proportional
to the concurrence for weak driving fields.
