  We investigate the dynamics of two-photon correlations generated by the
interaction of a three-level atom in the $\Xi$, $\Lambda$ or V configuration,
with two classical external driving fields, under the rotating-wave
approximation, in the presence of level decays. Using the example of a rubidium
atom in each configuration, with field strengths validating the single-photon
approximation, we compute measurement based correlations, such as measurement
induced disturbance (MID), quantum discord (QD), and quantum work deficit (WD),
and compare the results with that of quantum entanglement (concurrence).
Certain correlation properties observed are generic, model independent and
consistent with known results, e.g., MID is an upper bound on QD, QD and WD are
monotonic, and the generic correlation behavior is strongly affected by the
purity of the photon states. We observe that the qualitative hierarchy,
monotonicity and steady-state behavior of the correlations can be controlled by
the choice of parameters such as atomic decay constants and external driving
field strengths. We point out how particular configurations are better suited
at generating monotonic correlations in specific regimes and how the
steady-state correlation behavior and hierarchy are affected by the population
dynamics of the density matrix for different parameters. The possibility of
using well studied quantum optical systems such as the three-level atom to
generate, characterize and parametrically control mixed state quantum
correlations establishes an important step in the direction of their
implementation in quantum information tasks.
