  We address the consequences of backaction in the unidirectional coupling of
two cascaded open quantum subsystems connected to the same reservoir at
different spatial locations. In the spirit of [H. J. Carmichael, Phys. Rev.
Lett. 70, 2273 (1993)], the second subsystem is a two-level atom, while the
first transforms from a driven empty cavity to a perturbative QED configuration
and ultimately to a driven Jaynes-Cummings (JC) oscillator through a varying
light-matter coupling strength. For our purpose, we appeal at first to the
properties of resonance fluorescence in the statistical description of
radiation emitted along two channels -- those of forwards and sideways
scattering -- comprising the monitored output. In the simplest case of an empty
cavity coupled to an external atom, we derive analytical results for the
nonclassical fluctuations in the fields occupying the two channels, pursuing a
mapping to the bad-cavity limit of the JC model to serve as a guide for the
description of the more involved dynamics. Finally, we exemplify a conditional
evolution for the composite system of a critical JC oscillator on resonance
coupled to an external monitored two-level target, showing that coherent atomic
oscillations of the target probe the onset of a second-order dissipative
quantum phase transition in the source.
