Fig. 3.

Autocorrelation measurements. a Schematic representation of the Hanbury–Brown and Twiss interferometer. b Normalised coincidences for ND#4. c Time slicing employed to evaluate the autocorrelation function. d Measured time-integrated autocorrelation function $\overline{g^{\left(2\right)}\left(\tau \right)}$, which approaches g ⁽²⁾(0) as $\tau \to 0$. For ND#4, $\overline{g^{\left(2\right)}\left(0\right)}$ crests at 1.14 ± 0.02 for a time-slice width of 0.5 ns; it drops considerably as the width increases above 2–3 ns (after which the SR burst has exhausted) to then converge to Poissonian/random photoemission $\overline{g^{\left(2\right)}\left(\tau \right)}~1$ expected from many NV centres at long times. Error bars are determined from the standard error of the area under the peaks, for each set of time slices, excluding the ‘0’ peak. e Measured maximum value of $\overline{g^{\left(2\right)}\left(0\right)}$ for ND#1–4, and corresponding theoretically estimated number N _max of NV centres acting cooperatively to produce such value of $\overline{g^{\left(2\right)}\left(0\right)}$ using the initial state assumed by our model. Because of the finite time window for averaging (~ 0.5 ns) this is an underestimate of g ⁽²⁾(0). The continuous line (red) sets the upper limit of our theoretical prediction for g ⁽²⁾(0)