  We present an analytical solution of the single photon quantum feedback in a
cavity quantum electrodynamics system based on a half cavity set-up coupled to
a structured continuum. The exact analytical expression we obtain allows us to
discuss in detail under which conditions a single emitter-cavity system, which
is initially in the weak coupling regime, can be driven into the strong
coupling regime via the proposed quantum feedback mechanism [Carmele et al,
Phys.Rev.Lett. 110, 013601]. Our results reveal that the feedback induced
oscillations rely on a well-defined relationship between the delay time and the
atom-light coupling strength of the emitter. At these specific values the
leakage into the continuum is prevented by a destructive interference effect,
which pushes the emitter to the strong coupling limit.
