## Introduction

The rise of quantum networks depends crucially on scalable quantum systems that combine quantum memories with long coherence times1,2 and stable optical emission to mediate entanglement via interference of indistinguishable photons3,4,5,6,7,8. In this regard, solid-state quantum systems are very appealing thanks to well-established fabrication techniques that promise chip-based integration and mass production9. A caveat coming along with many solid-state systems is strong coupling to charge fluctuations, which leads to large spectral diffusion and ionisation, especially under off-resonant laser excitation and in surface proximity10,11. Recently, spectral stability has been greatly improved for divacancy centres in charge-depleted semiconductor diode structures, albeit ionisation remains an issue12. Alternatively, one can resort to systems with inversion symmetry, e.g. with germanium-vacancy13,14, tin-vacancy centres15, and silicon-vacancy16 centres in diamond. For the latter, practical multi-millisecond spin coherence times have been demonstrated at ultracold temperatures in the millikelvin range17.

Here, we use semiconductor colour centres that provide a naturally stable spin–photonic interface at temperatures up to 6.9 K and demonstrate spin-controlled quantum optical interference of indistinguishable and distinguishable photons. This milestone experiment demonstrates that the system possesses the necessary prerequisites for remote entanglement generation as targeted in scalable quantum networks.

Our technological platform is silicon carbide (SiC), which has recently acquired great interest in the quantum community as it is industrially compatible and hosts several appealing optically addressable spin-active quantum defects18,19,20,21. We investigate here the negatively charged silicon vacancy centre at hexagonal lattice site (h-VSi) in the common 4H polytype of SiC22. Despite the lack of inversion symmetry, it was recently shown that the optical transition of h-VSi is decoupled from charge fluctuations through identical wavefunction symmetries in the ground and V1 excited states (ESs)23. Thanks to weak phonon coupling in the ground state (GS), millisecond spin coherence times are achieved20,24.

## Results

### Spin-optical system of silicon vacancies in silicon carbide

Our 4H-SiC host crystal is an isotopically purified (0001) epitaxial layer (28Si ~99.85%, 12C 99.98%), which is irradiated with 2 MeV electrons to generate isolated single h-VSi centres as shown in Fig. 1a. The crystal is slightly n-type to ensure that h-VSi centres are in the desired negatively charged state (see “Methods”). As shown in Fig. 1b, the h-VSi centre presents a spin quartet system $$(S = {\textstyle{3 \over 2}})$$. At zero external magnetic field, spin sublevels $$m_{{{\mathrm{S}}}} = \pm {\textstyle{1 \over 2}}$$ and $$m_{{{\mathrm{S}}}} = \pm {\textstyle{3 \over 2}}$$ are pairwise degenerate in the GS and the V1 ES. As the GS zero field splitting is relatively small at 4.5 MHz22, we apply a magnetic field (B ≈ 9 G) along the system’s symmetry axis (c-axis). This lifts the degeneracy and suppresses parasitic spin mixing due to external stray fields. Optical transitions are linearly polarised and associated with two zero phonon line (ZPL) transitions at 861.7 nm. They are assigned to $$\left| { \pm 1/2} \right\rangle _{{{{\mathrm{GS}}}}} \leftrightarrow \left| { \pm 1/2} \right\rangle _{{{{\mathrm{ES}}}}}$$ and $$\left| { \pm 3/2} \right\rangle _{{{{\mathrm{GS}}}}} \leftrightarrow \left| { \pm 3/2} \right\rangle _{{{{\mathrm{ES}}}}}$$ transitions and labelled A1 and A2, respectively. The energy separation between the two transitions is about 1 GHz, which is mainly determined by the ES zero field splitting22. It was recently shown that all optical transitions are fully spin conserving, which provides several pathways for spin–photon entanglement generation9,25. However, spin-flip processes can still be mediated by non-radiative intersystem crossing involving metastable states, which allows e.g. for deterministic spin state initialisation22,26. Note that we do not consider the system’s second ES, V1’, whose fluorescence at 858 nm is strongly reduced at cryogenic temperatures due to ultrafast relaxation to the V1 state20. Thus, and as shown in Fig. 1c, off-resonant excitation results in photoluminescence in the V1 ZPL (with 8% Debye–Waller factor27) or the associated phonon side band (PSB) with 6 ns lifetime20.

### High-resolution ZPL emission spectrum

Single h-VSi centres are addressed via confocal microscopy (see “Methods”). Figure 1d shows the fine structure of the V1 ZPL emission, recorded at a temperature of T = 5.0 K. To this end, we use continuous-wave off-resonant excitation at 730 nm with an optical power of about 0.15 mW, which is almost 3 times higher than the saturation power20. As a high-resolution spectrometer, we use a home-built tunable Fabry–Pérot filter cavity with a linewidth of 29 ± 2 MHz. By integrating the emission spectrum over 20 min, we clearly resolve the two optical lines corresponding to the spin-conserving A1 and A2 transitions. Surprisingly, even under strong off-resonant excitation, the linewidths remain very close to the lifetime limit (~27 MHz). Taking into account the finite spectral resolution of the filter cavity (29 ± 2 MHz) via deconvolution of two Lorentzians, we infer emission linewidths of 57 ± 6 and 48 ± 6 MHz for the A1 and A2 transitions, respectively.

### Single-photon emission purity

Aside from superior spectral purity and robustness, perfect two-photon interference crucially requires the interfering photons to be in pure single-photon states, i.e. not degraded by spurious multi-photon contributions28. To evaluate the quality of our quantum light source, we use pulsed off-resonant excitation at 780 nm (PicoQuant LDH-P-C-780, pulse length: 56 ps, repetition rate: 20.5 MHz) and record the second-order autocorrelation function g2 (τ) of ZPL photons in a standard Hanbury Brown and Twiss arrangement29. As shown in Fig. 1e, we observe a strong antibunching at zero time delay, clearly evidencing that the defect is a single-photon source (g2 (τ = 0) < 0.5). Figure 1f shows the recorded value of g2 (τ = 0) as a function of the laser pulse energy above saturation (4 pJ, see Supplementary Note 1). The increase of g2 (τ = 0) is mainly due to noise from background fluorescence below 6 pJ (see Supplementary Note 3). Above 6 pJ, the increased probability to induce two optical excitations during one laser pulse degrades g2 (τ = 0). However, under all conditions, we observe g2 (τ = 0) < 0.25 without any background subtraction, which underlines the h-VSi centre’s single-photon emission quality.

### Indistinguishable photon generation

To prove that the h-VSi centre generates streams of indistinguishable photons in the A1 and A2 transitions, we perform a Hong–Ou–Mandel (HOM) interference30 experiment on two consecutively emitted photons31. Figure 2a shows the related set-up schematically. We use the off-resonant picosecond laser to excite the single defect twice with an interval of δt = 48.7 ns, and we repeat this sequence every 10δt = 487 ns. The laser pulse energy is set to 5.5 pJ, corresponding to about 74% excitation probability per pulse and the detected ZPL photon count is about 10−4 per pulse (see Supplementary Note 1). The ZPL emission is coupled into a single-mode fibre-based unbalanced Mach–Zehnder interferometer with a path travel time difference of δt = 48.7 ns. The interferometer’s outputs are connected to superconducting nanowire single-photon detectors (SNSPDs; Photon Spot Inc.) with sub-ns time resolution. We record the time differences between both SNSPD detection events using a time tagger (Swabian Instruments). The timing jitter of our detection system is about 0.4 ns.

Let us assume now that two consecutive ZPL photons enter the interferometer during one experimental sequence (i.e. no non-radiative intersystem crossing occurred). The most interesting case occurs when the early and the late photons take the long and short interferometer paths, respectively, and thus arrive simultaneously at the output beam-splitter (BS2) through different inputs. Provided that both photons are indistinguishable, HOM interference occurs and they must leave BS2 as a pair through the same output port30. Experimentally, this is measured through the reduction of coincidence events at zero time delay between both SNSPDs. Note that the normalised coincidence rate reduction is a direct measure of the photon indistinguishability. The normalisation process is actually implemented automatically in our set-up. Namely, 25% of the successfully created photon pairs take wrong opposite paths, i.e. the early and the late photons take the short and long interferometer paths, respectively. In this case, they arrive at BS2 with a time difference of ±2δt. As this delay exceeds the ES lifetime (6 ns), no interference is observed. Similarly, the remaining 50% of the paired photons choose identical interferometer paths and arrive at BS2 without interference with a time difference of ±δt. Thus we expect that the five detection rates associated with the different coincidence time differences A−2δt, Aδt, A0, A+δt and A+2δt show the well-known ratio of 1:2:0:2:131.

Figure 2b shows typical raw data for the HOM experiment. The central peak at τ = 0 ns is strongly suppressed compared to the side peaks at τ = ±δt and τ = ± 2δt. Each peak exhibits an exponential decay of 6 ns corresponding to the V1 ES lifetime. Following the analysis by Santori et al.31, we determine the raw HOM interference visibility $$V_0 = 1 - 2 \cdot \frac{{A_0}}{{A_{ - {\updelta}t} + A_{ + {\updelta}t}}} = 0.69 \pm 0.02$$. Since this value greatly exceeds 2g(2) (τ = 0), generation of two-photon entanglement can be straightforwardly implemented32,33,34. The HOM interference visibility is comparable to those reported for two consecutive photons from quantum dots with off-resonant excitation (0.53–0.86)35,36,37.

### Spin-controlled distinguishable photon generation

As mentioned earlier (see Fig. 1b, d), optical transitions are spin conserving and intimately linked to spin sublevels, i.e. $$\left| { \pm 1/2} \right\rangle _{{{{\mathrm{GS}}}}} \leftrightarrow \left| { \pm 1/2} \right\rangle _{{{{\mathrm{ES}}}}}$$ levels are connected via the A1 optical transition and $$\left| { \pm 3/2} \right\rangle _{{{{\mathrm{GS}}}}} \leftrightarrow \left| { \pm 3/2} \right\rangle _{{{{\mathrm{ES}}}}}$$ via A2. Consequently, without intersystem crossing, repeated off-resonant excitation leads to streams of consecutively emitted indistinguishable photons in the A1 or photons in the A2 transition, respectively. As one of the system’s key assets, we highlight that the h-VSi centre in SiC possesses a GS spin quartet with a coherence time that exceeds the ES lifetime by at least five orders of magnitude20,22. This provides a direct control mechanism of the colour of consecutively emitted photons, e.g. by flipping the GS spin from the subspace $$\left| { \pm 1/2} \right\rangle _{{{{\mathrm{GS}}}}}$$ to $$\left| { \pm 3/2} \right\rangle _{{{{\mathrm{GS}}}}}$$, the first and second photon will be in A1 and A2, respectively. Figure 3a shows the experimental sequence. The four GS spin levels are non-degenerate due to the external magnetic field. After the first excitation, we apply a short radiofrequency (RF) wave pulse at a frequency of 30.3 MHz. Note that, owing to the high RF pulse power and the short pulse duration, all GS spin transitions are driven simultaneously. However, our independent resonant excitation measurements and theoretical modelling show that spin driving between the $$\left| { \pm 1/2} \right\rangle _{{{{\mathrm{GS}}}}}$$ and $$\left| { \pm 3/2} \right\rangle _{{{{\mathrm{GS}}}}}$$ subspaces still reaches fidelities of about 70% (for more details, see Supplementary Note 4). Figure 3b shows the resulting HOM interference pattern at RF power of 30 dBm and a pulse length of 19 ns, which corresponds to a π/2-pulse (see Supplementary Note 4). The coincidence peak at zero time delay reappears clearly, due to the emission of distinguishable photons. In addition, as shown in Fig. 3c, the interference pattern around zero time delay shows the expected modulation with a frequency of ≈1 GHz, matching the frequency difference between A1 and A2 optical transitions38. We note that the high RF pulse power causes significant optical linewidth broadening due to thermal heating, limiting the maximum HOM visibility to 0.56 ± 0.04 and Vmax = 0.73 ± 0.05 after correcting for experimental imperfections (as discussed later and in Supplementary Note 4). By normalising the recorded and corrected visibility Vmeasured to Vmax, we obtain a corrected HOM visibility of $$V_{{{{\mathrm{norm}}}},\pi /2} = \frac{{V_{{{{\mathrm{measured}}}}}}}{{V_{{{{\mathrm{max}}}}}}} = 0.65 \pm 0.07$$, which matches the expectation for a π/2-pulse (for details, see Supplementary Note 4). To prove that our spin-to-photon interface is indeed based on coherent spin manipulation, we repeat the experiment with two additional RF pulse lengths of 10 and 29 ns (corresponding to a π/4-pulse and 3π/4-pulse, respectively). The observed visibilities are $$V_{{{{\mathrm{norm}}}},\pi /4} = 0.90 \pm 0.09$$ and $$V_{{{{\mathrm{norm}}}},3\pi /4} = 0.47 \pm 0.17$$, respectively. Data for the three measurements above is shown in Fig. 3d. The data match the theoretical model very precisely, which is based on independently measured Rabi oscillations (see Supplementary Note 4). Consequently, the results corroborate that the photonic emission of the h-VSi centre can be controlled by coherent spin manipulation, which is crucial for remote entanglement generation5,6,7,8,39,40.

### Temperature stability of spin–photonic properties

In the last step, we provide a deeper insight into the system’s temperature-dependent spin–phonon–photon physics. For this, we consider the visibility reduction in the raw data of the HOM experiment without RF pulses. To explain deviations from non-unity visibility, we consider six detrimental factors: (i) pure dephasing in the ES due to phonon scattering41, (ii) spectral diffusion due to local charge redistribution42, (iii) two-photon emission during one laser pulse31,43, (iv) background counts, e.g. laser breakthrough, bulk and surface fluorescence, and Raman scattering, (v) interferometer imperfections, e.g. non-unity fringe contrast and unbalanced beam splitter transmissivity and reflectivity31, and (vi) the photon arrival timing jitter at BS2, e.g. due to finite laser pulse duration44 as well as timing jitter of the laser. We infer that factors (v) and (vi) amount to 1% and 0.8% contrast reduction, respectively (see Supplementary Notes 2 and 3). Experimentally, we minimise the fast components of factors (iii) and (iv) by time-gating the coincidence detection, i.e. detector clicks are only considered posterior to a delay time tStart (see “Methods”). Generally, we find that the visibility saturates for tStart > 1.5 ns, indicating that laser-induced noise is efficiently filtered out at this point. To infer the contribution of pure dephasing and spectral diffusion, we extend the analysis by Thoma et al.41 and include coincidence window gating with start and stop delays tStart and tStop, respectively (for more details, see Supplementary Note 5). This provides us with an additional tuning knob, as we can now actively control the time window Δt = tStop − tStart in which we give pure dephasing (single-phonon scattering in the ES) a chance to degrade the fringe visibility in the HOM experiments (see Fig. 4a). As an example, Fig. 4b shows the HOM pattern at T = 5.0 K for tStart = 3.5 ns and a short time window Δt = 4 ns. For those settings, we obtain an uncorrected raw visibility of V0,gated = 0.85 ± 0.04. For arbitrary time gating settings, we find an analytic expression for the expected HOM visibility:

$$\begin{array}{*{20}{c}} {V = \frac{1}{{\left( {1 - {{{\mathrm{e}}}}^{ - {{\Gamma }} \cdot {{\Delta }}t}} \right)^2}}\left[ {\frac{{\Gamma }}{{{{\Gamma }} + \gamma }} + \frac{{\Gamma }}{{{{\Gamma }} - \gamma }}{{{\mathrm{e}}}}^{ - 2{{\Gamma }} \cdot {{\Delta }}t} - \frac{{2{{\Gamma }}^2}}{{{{\Gamma }}^2 - \gamma ^2}}{{{\mathrm{e}}}}^{ - \left( {{{\Gamma }} + \gamma } \right){{\Delta }}t}} \right].} \end{array}$$
(1)

Here $${{\Gamma }} = {\textstyle{1 \over {6\,{{{\mathrm{ns}}}}}}}$$ is the inverse ES lifetime, and $$\gamma = {{\Gamma }}_0^\prime [{1 - {{{\mathrm{e}}}}^{ - \left( {\delta t/\tau _{{{\mathrm{c}}}}} \right)^2}}] + 2\gamma^\prime$$, with $${{\Gamma }}_0^\prime$$ being the amplitude of spectral diffusion, τc the associated time constant and γ' the pure dephasing rate of the single emitter. To infer γ, the experimental data has to be corrected for experimental imperfections (interferometer, finite signal-to-noise ratio and photon arrival timing jitter). Figure 4c shows the corrected HOM visibility as a function of Δt for fixed tStart = 3.5 ns. To gain more insights of the system, the measurements are performed by adjusting the cryostat to three different temperatures T = 5.0, 5.9, and 6.8 K. By fitting each data set with the model in Eq. (1), we extract γ. We note that one contribution to spectral diffusion is thermal ionisation of nearby charge traps, usually occurring at several tens of Kelvin45,46,47. Thus, in our experiments, spectral diffusion is attributed to laser ionisation, which depends very weakly on temperature and occurs usually at a microsecond time scales47. Consequently, we have τcδt, such that HOM visibility reduction is essentially only limited by pure dephasing (γ'). This permits us to provide an upper limit for the pure dephasing rate $$\gamma _{{{{\mathrm{max}}}}}^\prime$$ (obtained from the HOM experiments), as well as the associated amplitude of spectral diffusion $${{\Gamma }}_0^\prime$$ (obtained from slow absorption linewidth measurements). The results of the temperature-dependent measurements are summarised in Fig. 4d. As expected, we find that $${{\Gamma }}_0^\prime$$ remains nearly constant over the measured temperature range. The increase of $$\gamma _{{{{\mathrm{max}}}}}^\prime$$ is described by vibronic interaction of the V1 and V1’ ESs27, which are separated by a relatively small energy gap of ΔE = 4.4 meV. As we detail in Supplementary Note 6, at the experimental temperatures, single acoustic phonon scattering processes cause pure dephasing with a rate given by

$$\begin{array}{*{20}{c}} {\gamma _{{{{\mathrm{max}}}}}^\prime \left( T \right) = A \cdot \frac{{\left( {\Delta E} \right)^3}}{{{{{\mathrm{e}}}}^{\Delta E/k_{{{\rm{B}}}} \cdot T} - 1}}.} \end{array}$$
(2)

Here kB is Boltzmann’s constant and the prefactor A describes the phonon interaction strength. By fitting the data, we obtain A = 2π(237 ± 12) MHz (meV)−3. Interestingly, we find that pure dephasing for the h-VSi centre is comparatively low at cryogenic temperatures, e.g. considering photonic interference experiments without any time-gating, pure dephasing reduces the optical coherence time to half of the transform limit (2Γ−1 = 12 ns) only at Tcrit > 6.9 K. This temperature is comparable to quantum dot single-photon sources48 and conveniently surpassed with standard cryostat equipment. Below Tcrit, the remaining small emission linewidth broadening is mainly due to slow spectral diffusion. Although this does not present a significant influence for HOM experiments, it may be even further suppressed with improved crystal growth and associated annealing procedures to reduce charge traps. Alternatively, electronic device structures might be promising to control the charge environment12,49,50,51.

## Discussion

In summary, we have demonstrated spin-controlled generation of indistinguishable and distinguishable photons from a single h-VSi centre in SiC. Despite performing our experiments under strong off-resonant excitation, pure dephasing, and spectral diffusion are exceptionally low, such that the quality of our raw data is sufficient for photonic entanglement generation32,33,34. Our semiconductor platform has thus demonstrated a level of spectral stability, which is on par with inversion-symmetry defects in diamond13,14,15,16, quantum dots36,41, and single molecules34. Furthermore, we showed that the system possesses an intimate spin–photon interface through which we deterministically tuned the degree of photon indistinguishability via coherent spin manipulation. Note that the system’s millisecond spin coherence times22 are sufficient for high-level spin–photon manipulation, such as remote entanglement generation5,6,7 in a scalable quantum repeater network8. Implementing the related protocols necessitates optimised RF driving to reduce heating issues, which will suppress pure dephasing to negligible levels. To provide the necessary optical phase reference, resonant excitation is required, which requires several orders of magnitude lower optical powers, such that spectral diffusion will also be greatly suppressed52. In the perspective of quantum repeaters, long storage time quantum memories can be conveniently realised with recently demonstrated coupling to individual nuclear spins22. Implementation of state-of-the-art SiC photonic nanostructures would further increase light collection efficiency and ultra-compact chip-based integration53, such that it will become realistic to use our system for generation of high-photon-number cluster states54.

## Methods

### Sample preparation

The 100-µm-thick 4H-28Si12C silicon carbide layer is grown by chemical vapour deposition on an n-type (0001) 4H-SiC substrate. The isotope purity is measured by secondary ion mass spectroscopy and inferred to be 99.85% for 28Si and 99.98% for 12C. Current–voltage measurements at room temperature shows that the layer is n-type with a free carrier concentration of 6 × 1013 cm−3, which is close to the concentration of shallow nitrogen donors of 3.5 × 1013 cm−3. Deep-level transient spectroscopic measurements show that the dominant electron trap in the layer is related to the carbon vacancy with a concentration in the mid 1012 cm−3 range. Minority carrier lifetime mapping of the carrier shows a homogeneous carrier lifetime of 0.6 µs. We expect the real value to be twice as high, as an optical method with high injection was used55. Thus the density of all electron traps should be limited to the mid 1013 cm−3 range56. Individually addressable silicon vacancy centres were created through room temperature electron beam irradiation at 2 MeV with a fluence of 1012 cm−2. Parasitic defects, such as carbon vacancies, interstitials, anti-sites, and their associated defects, are expected to be below mid 1012 cm−3. Some interstitial-related defects were removed by subsequent annealing at 300 °C for 30 min.

To improve light extraction efficiency out of the high refractive index material (n ≈ 2.6), we fabricate a solid immersion lens using a focussed ion beam milling machine (Helios NanoLab 650). The related surface contaminations and modifications are subsequently removed by wet and dry etching treatments19.

### Experimental set-up

All the experiments were performed at cryogenic temperatures in a Montana Instruments Cryostation. A home-built confocal microscope20 was used for optical excitation and subsequent fluorescence detection of single silicon vacancies.

Continuous-wave off-resonant optical excitation of single silicon vacancy centres was performed with a 730 nm laser diode. Pulsed off-resonant excitation at 780 nm was performed using a picosecond laser diode (PicoQuant LDH-P-C-780). For resonant optical excitation at 861.7 nm, we used an external cavity tunable diode laser (Toptica DLC DL PRO 850). All lasers are spatial-mode cleaned by coupling to a single-mode fibre. For the picosecond laser, we employ a 780-nm bandpass filter after the fibre output to suppress Raman noise. Light is focussed onto the sample with a vacuum-compatible microscope objective (Zeiss EC Epiplan-Neofluar ×100, NA = 0.9).

Note that the used 4H-SiC sample was flipped to the side, i.e. by 90° compared to the c-axis, such that the polarisation of the excitation lasers is parallel to the c-axis (E||c), which allows to excite the V1 ES with maximum efficiency20,57.

The fluorescence emission is collected by the same microscope objective and split by a dichroic mirror (Semrock Versa Chrome Edge) into two parts, i.e. ZPL (at 861.7 nm) and PSB (at 875–950 nm). PSB fluorescence is detected using a silicon avalanche photodiode (Excelitas SPCM-AQRH-W4).

ZPL emission is directed to a fully fibred Mach–Zehnder-type interferometer with a path length difference of ≈10 m. A fibre polarisation controller in the long interferometer arm allows to match the photon polarisation rotation experienced in both arms. Both interferometer outputs are directed to SNSPDs (PhotonSpot Inc.) with 80–85% detection efficiency and sub-Hz dark count rates.

In order to coherently manipulate GS spin populations, microwaves are applied through a 50-µm-thick copper wire spanned over the 4H-SiC sample in close proximity to the investigated h-VSi defect centre.

### Filter cavity for ZPL fine structure investigation

To investigate the fine structure of the ZPL, we use a home-built fibre-coupled plano-concave Fabry–Pérot cavity. The cavity has the following specifications: free spectral range: 5.145 GHz; finesse: 177 ± 10; linewidth: 29 ± 2 MHz; input-fibre-to-output-fibre transmission: 80%. The cavity length is tunable via a piezoelectric actuator on which one of the two mirrors is glued. The cavity housing is made from Invar to ensure good thermal stability. The typical drift of the cavity was measured to be on the order of 5 kHz s−1.

Further details on how the cavity was used for resolving the fine structure of the ZPL emission are given in Supplementary Note 8.

### Time-gating scheme

To filter out noise components induced by the off-resonant high-power pulsed laser excitation and to perform time-resolved HOM experiments for investigation of pure dephasing, a time-gated photon detection scheme is implemented by software. All photon click signals from the SNSPDs are time tagged by coincidence electronics (Swabian Instruments Time Tagger 20) and referenced to the laser pulse timing. Via software postprocessing, we then implement time-gating by validating only photon clicks between tStart ≤ t ≤ tStop (here t = 0 represents the earliest possible photon arrival time). Owing to the software implementation on the Time Tagger 20, the experimental data points with different settings of (tStart, tStop) are obtained within a single measurement.