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 deta
il 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.
We propose an experiment to generate deterministic entanglement between separate nitrogen vacancy (NV) centers mediated by the mode of a photonic crystal cavity. Using numerical simulations the applicability and robustness of the entanglement operati
on to parameter regimes achievable with present technology is investigated. We find that even with moderate cavity Q-factors of $10^{4}$ a concurrence of $c>0.6$ can be achieved within a time of $t_{max}approx150$~ns, while Q-factors of $10^{5}$ promise $c>0.8$. Most importantly, the investigated scheme is relative insensitive to spectral diffusion and differences between the optical transitions frequencies of the used NV centers.
