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We present a quantum-state-diffusion equation to characterize the dynamics ofa generic atomic system coupled to a leaky cavity mode. As quantum resources,the population, the coherence and even the entanglement of the system wouldgradually leak out of the cavity. The effect from the leakage of thecavity-mode to the uncontrollable degree of freedom, e.g., environment, ishowever not always negative to particular targets. A well-established scenariois that a photon counter attached to the cavity would absorb and then recordthe leaking photon. As a medium between the system and the photon counter, astrong coupling between system and cavity is necessary to enhance themeasurement efficiency. While we find it also reduce the reading efficiency ofthe photon counter at the same time as fewer photons leak out of the cavity. Weinvestigate the competition between these two mechanisms in the framework ofnon-Markovian open-quantum-system dynamics, where the photon counter serves asa general bosonic environment. Our results provide an optimized parameter spacefor system entanglement preservation and generation.

Exact coherence dynamics mediated by a single cavity mode in the presence of leakage