Phonon-induced multicolor correlations in hBN single-photon emitters

Color centers in hexagonal boron nitride have shown enormous promise as single-photon sources, but a clear understanding of the electron-phonon interaction dynamics is critical to developing the material for quantum communications or quantum simulations. We demonstrate photon antibunching in the filtered auto- and cross-correlations $g_{lm}^{\left(2\right)}\left(\tau \right)$ between zero-, one-, and two-phonon replicas of defect luminescence. With no background correction, we observe a single-photon purity of $g^{\left(2\right)}\left(0\right)=0.20$ in a phonon replica and cross-spectral correlations of $g_{lm}^{\left(2\right)}\left(0\right)=0.18$ between a phonon replica and the zero-phonon line. Moreover, we combine a violation of the Cauchy-Schwarz inequality and a phenomenological model of the phonon-mediated emission cross section to distinguish a low quantum-efficiency defect from phonon replicas of a bright defect.

Figure 1

Background corrected defect $\mu \mathrm{PL}$ spectrum (blue) collected at 3.6 K, calculated $\mu \mathrm{PL}$ with (red dashed curve) and without (black curve) Lorentzian filters. The calculated one-phonon DOS is shown in the inset. The $\mu \mathrm{PL}$ spectrum calculated with the one-phonon DOS and Lorentzian filters approximating the selection rules present in this material provides a reasonable reproduction of the ZPL and the one-phonon replicas, but an additional transition appears in the experimental $\mu \mathrm{PL}$ spectrum that is not present in the calculated filtered two-phonon replicas.

Figure 2

(a) Background corrected room-temperature (blue) and 3.6-K (red) PL spectrum of a hBN defect [the inset illustrates a HBT interferometer with two single-photon detectors (D1 and D2), tunable bandpass filters (F1 and F2), and high-speed time correlation electronics (TC)]. The filters are actively tunable from 1.75 to 2.95 eV, enabling spectrally resolved single-photon detection across the bandwidth of all observed SPEs. (b)–(e) Frequency-filtered two-photon autocorrelations $g_{ll}^{\left(2\right)}\left(\tau \right)$ (blue), median fits (red), and $95\%$ credibility intervals (black) for the two-phonon replicas (2), LO($\mathrm{\Gamma }$) and LO($T$) replicas ($1^{\prime }$), TO($M$)/LO($K$) replicas (1), and ZPL (0), respectively. The colored bands ($0,1^{\prime },1,2$) in (a) are the spectral ranges of the bandpass filters used for each of the autocorrelation measurements in (b)–(e). The mean and standard deviations for $g_{ll}^{\left(2\right)}\left(0\right)$ are inset in (a)–(e).

Figure 3

Frequency-filtered two-photon cross-correlations $g_{lm}^{\left(2\right)}\left(\tau \right)$ between each pair of spectral bands visible at room temperature, labeled in terms of the four spectral bands illustrated in Fig. 2. The mean and standard deviations for $g_{lm}^{\left(2\right)}\left(0\right)$ are inset in each panel.