  We employ a fiber-based optical microcavity with high finesse to study the
enhancement of phonon sideband fluorescence of nitrogen-vacancy centers in
nanodiamonds. Harnessing the full tunability and open access of the resonator,
we explicitly demonstrate the scaling laws of the Purcell enhancement by
varying both the mode volume and the quality factor over a large range. While
changes in the emission lifetime remain small in the regime of a broadband
emitter, we observe an increase of the emission spectral density by up to a
factor of 300. This gives a direct measure of the Purcell factor that could be
achieved with this resonator and an emitter whose linewidth is narrower than
the cavity linewidth. Our results show a method for the realization of
wavelength-tunable narrow-band single-photon sources and demonstrate a system
that has the potential to reach the strong-coupling regime.
