Fiber-taper collected emission from NV centers in high-$Q/V$ diamond microdisks

Fiber-coupled microdisks are a promising platform for enhancing the spontaneous emission from color centers in diamond. The measured cavity-enhanced emission from the microdisk is governed by the effective volume ($V$) of each cavity mode, the cavity quality factor ($Q$), and the coupling between the microdisk and the fiber. Here we observe photoluminescence from an ensemble of nitrogen-vacancy centers into high $Q/V$ microdisk modes, which when combined with coherent spectroscopy of the microdisk modes, allows us to elucidate the relative contributions of these factors. The broad emission spectrum acts as an internal light source facilitating mode identification over several cavity free spectral ranges. Analysis of the fiber-taper collected microdisk emission reveals spectral filtering both by the cavity and the fiber-taper, the latter of which we find preferentially couples to higher-order microdisk modes. Coherent mode spectroscopy is used to measure $Q\sim 1\times10^{5}$ -- the highest reported values for diamond microcavities operating at visible wavelengths. With realistic optimization of the microdisk dimensions, we predict that Purcell factors of $\sim 50$ are within reach.