  We study the excitation of a two-level system (2LS) by quantum light, thereby
bringing our previous studies~(see part~I. of this series) to a target that is
quantum itself. While there is no gain for the quantum state of the target as
compared to driving it with classical light, its dynamical features, such as
antibunching, can be improved. We propose a chain of two-level systems, i.e.,
setting the emission of each 2LS as the driving source of the following one, as
an arrangement to provide better single-photon sources. At a fundamental level,
we discuss the notion of strong-coupling between quantum light from a source
and its target, and the several versions of the Mollow triplet that follow from
various types of driving light. We discuss the Heitler effect of antibunched
photons from the scattered light off a laser.
