Scaling laws of the cavity enhancement for nitrogen-vacancy centers in diamond

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.

Figure 1

(a) Level scheme of phonon assisted optical transitions in the NV optical cycle. (b) Schematic of the cavity. (c) Experimental setup combining a confocal microscope and a tunable microcavity (LP, long pass; SP, short pass; NF, notch filter; $\lambda /4$, quarter-wave plate).

Figure 2

(a) Free space spectrum of a 100-nm diamond on a suprasil substrate (in units kilocounts per second). (b) Calculated transmission spectrum of the macroscopic mirror. (c) Emission spectrum of a FND placed inside the cavity. The transmissive part can be explained by the free space spectrum and the mirror transmission (blue line). Within the mirror stop band, cavity enhanced emission into narrow resonances is observed. (d) Confocal scan with $I=0.5I_{\mathrm{sat}}$ showing a single nanodiamond, mirror background, and the effect of bleaching. (e) Saturation of free space NV emission (blue data points). For comparison, we show the same measurement with the linear background subtracted (red data points). Solid lines are fits to a saturation model.

Figure 3

(a) Comparison of the FND spectrum as inferred for free space conditions ($S_{\text{FS}}$, blue), emission through the mirror with the fiber retracted ($S_m$, gray), and a cavity configuration with $d_{\mathrm{eff}}=5.0\mu$m ($S_c$, red). (b) Normalized spectra for decreasing cavity length from $d_{\mathrm{eff}}=39\mu$m (top) to $5.4\mu$m (bottom). (c) Scaling behavior of the Purcell enhancement in the bad emitter regime: effective Purcell factor evaluated for the strongest cavity resonance at ${\lambda }_0=710$ nm as a function of mode volume (blue data points). The red line shows the prediction of Eq. (2), and the black line shows the ideal Purcell factor as given by Eq. (1) divided by a factor of 100 for easier comparison.

Figure 4

(a) Tuning of a single cavity resonance across the accessible NV spectrum starting at $d_{\mathrm{eff}}=4.3\mu$m. (b) Cavity spectrum with multiple resonances for $d_{\mathrm{eff}}=39\mu$m. (c) Ideal Purcell factor as a function of the quality factor for the data set partially shown in (a) (light blue) and (b) (dark blue) together with the predictions of Eq. (1) (solid lines). (d) Measurement (blue data points) and calculation (solid line) of the cavity quality factor as a function of the wavelength for $d_{\mathrm{eff}}=39\mu$m.