  Strong interaction between light and a single quantum emitter is essential to
a great number of applications, including single photon sources. Microcavities
and plasmonic antennas have been used frequently to enhance these interactions
through the Purcell effect. Both can provide large emission enhancements: the
cavity typically through long photon lifetimes (high $Q$), and the antenna
mostly through strong field enhancement (low mode volume $V$). In this work, we
demonstrate that a hybrid system, which combines a cavity and a dipolar
antenna, can achieve stronger emission enhancements than the cavity or antenna
alone. We show that such systems can be used as a versatile platform to tune
the bandwidth of enhancement to any desired value, while simultaneously
boosting emission enhancement. Our fully consistent analytical model allows to
identify the underlying mechanisms of boosted emission enhancement in hybrid
systems, which include radiation damping and constructive interference between
multiple-scattering paths. Additionally, we find excellent agreement between
strongly boosted enhancement spectra from our analytical model and from
finite-element simulations on a realistic cavity-antenna system. Finally, we
demonstrate that hybrid systems can simultaneously boost emission enhancement
and maintain a near-unity outcoupling efficiency into a single cavity decay
channel, such as a waveguide.
