  We address the problem of optically controlling and quantifying the
dissipative dynamics of quantum and classical correlations in a set-up of
individual quantum emitters under external laser excitation. We show that both
types of correlations, the former measured by the quantum discord, are present
in the system's evolution even though the emitters may exhibit an early stage
disentanglement. In the absence of external laser pumping,we demonstrate
analytically, for a set of suitable initial states, that there is an entropy
bound for which quantum discord and entanglement of the emitters are always
greater than classical correlations, thus disproving an early conjecture that
classical correlations are greater than quantum correlations. Furthermore, we
show that quantum correlations can also be greater than classical correlations
when the system is driven by a laser field. For scenarios where the emitters'
quantum correlations are below their classical counterparts, an optimization of
the evolution of the quantum correlations can be carried out by appropriately
tailoring the amplitude of the laser field and the emitters' dipole-dipole
interaction. We stress the importance of using the entanglement of formation,
rather than the concurrence, as the entanglement measure, since the latter can
grow beyond the total correlations and thus give incorrect results on the
actual system's degree of entanglement.
