  The Fano effect arises from the interference between a continuum of
propagating modes and a localised resonance. By using this resonance as one of
the mirrors in an optical cavity, a localised mode with a highly asymmetric
line shape is obtained. Placing a single quantum emitter inside the cavity
leads to a new regime of cavity quantum electrodynamics, where the light-matter
interaction dynamics is fundamentally different from that observed in a
conventional cavity with Lorenztian lineshape. Furthermore, when the
vibrational dynamics of the emitter is taken into account, an intricate
phonon-photon interplay arises, and the optical interference induced by the
Fano mirror significantly alters the leakage of energy into vibrational modes.
We demonstrate that this control mechanism improves the maximum attainable
indistinguishability of emitted photons, as compared to an equivalent cavity
with a conventional mirror.
