## Abstract

The desiderata for an ideal photon source are high brightness, high single-photon purity, and high indistinguishability. Defining brightness at the first collection lens, these properties have been simultaneously demonstrated with solid-state sources; however, absolute source efficiencies remain close to the 1% level and indistinguishability has only been demonstrated for photons emitted consecutively on the few-nanoseconds scale. Here, we employ deterministic quantum dot-micropillar devices to demonstrate solid-state single-photon sources with scalable performances. In one device, an absolute brightness at the output of a single-mode fiber of 14% and purities of 97.1%–99.0% are demonstrated. When nonresontantly excited, it emits a long stream of photons that exhibit indistinguishability up to 70%—above the classical limit of 50%—even after 33 consecutively emitted photons with a 400 ns separation between them. Resonant excitation in other devices results in near-optimal indistinguishability values: 96% at short timescales, remaining at 88% in timescales as large as 463 ns after 39 emitted photons. The performance attained by our devices brings solid-state sources into a regime suitable for scalable implementations.

© 2016 Optical Society of America

## 1. INTRODUCTION

Photon indistinguishability—responsible for unique quantum phenomena with no classical counterpart, notably photon bunching via interference [1]—has been demonstrated in various physical systems [2–9], resulting in a broad range of applications in photonic quantum technologies [10], including quantum teleportation [11,12], generation of entangled photon sources [13–15], and linear-optics quantum computation [16,17]. However, achieving conclusive indistinguishability, i.e., above 50% (the classical limit), while simultaneously displaying high single-photon purity and high absolute brightness is experimentally challenging.

Semiconductor quantum dots (QDs) inserted in photonic structures [18–22] are a rapidly improving technology for generating bright sources of indistinguishable single photons. Addressing the excited states of the quantum dot using a nonresonant scheme early showed two-photon interference visibilities in the 70%–80% range [8], yet with limited collection efficiencies. Improvements in the efficiency have been made by deterministically placing the quantum dot in the center of a photonic micro-cavity. Here, the acceleration of photon emission into well-defined cavity modes [23] due to Purcell enhancement has enabled two-photon interference visibilities in the same range, with simultaneous efficiencies at the first collection lens around 80% [9]. Near-unity indistinguishability, in turn, has been achieved in recent years under strictly resonant excitation of the quantum dot [24–26], whereas the recent development of electric control on deterministically coupled devices [27]—thus with scalable fabrication—has now enabled strictly resonant excitation in combination with Purcell enhancement. This has resulted in near-optimal single-photon sources [28] with visibilities reaching the 99% mark, simultaneous state-of-the-art extraction efficiency of 65%, and polarized brightness at the first lens around 16%.

Although impressive, the reported efficiencies in these demonstrations are defined at the first lens, and poor optical collection results in low photon count rates available in practice. Consequently, absolute brightnesses remain around the 1% mark, too low for practical scalable applications [10]. In addition, direct measurements of indistinguishability via two-photon interference so far only employed photons consecutively emitted with a few nanoseconds of separation, while a key question regarding the scalable potential of the developed sources is to determine how many consecutive photons exhibit high indistinguishability. A recent work on quantum dots in microlenses reported a 40% drop in the indistinguishability over 10 ns only [29].

In the present work, we demonstrate high absolute brightness and generation of indistinguishable photons consecutively emitted over 463 ns. Our measurements were performed on various quantum dot-micropillar devices, all obtained using a deterministic and thus scalable technology. Using a simple micropillar (*Device* 1) [9], we demonstrate a high-purity single-photon source with an absolute brightness of 14%. That is, about one in seven laser pulses creates a high-purity single photon at the output of a single-mode fiber. We also demonstrate robust and conclusive quantum interference between consecutively emitted photon pulses up to the first and thirty-third, separated by 400 ns. Interference visibilities, under nonresonant excitation, reach maximum values of 70% in short timescales, decreasing to plateaus above 60% at longer temporal separations, and remain above the classical limit of 50% even at high pump powers. Using electrically controlled pillar devices [28] (*Devices* 2 and 3) we demonstrate, under strictly resonant excitation, indistinguishability reaching near-optimal values: 96% at short timescales, remaining above 88% at 463 ns separation.

## 2. ABSOLUTE BRIGHTNESS

*Device* 1 contains self-assembled InGaAs QDs grown by molecular beam epitaxy, positioned in between two layers of GaAs/AlAs distributed Bragg reflectors, consisting of 16 (36) pairs acting as a top (bottom) mirror. Note that *Device* 1 is a pillar from the same batch as in Ref. [9]. Low-temperature *in situ* lithography [30] was employed to fabricate micropillars centered around a single QD with 50 nm accuracy. The sample is mounted on a closed-cycle cryostat and is optically pumped by 5 ps laser pulses at an 80 MHz repetition rate with wavelength tuned to 905.3 nm, corresponding to one of the quantum dot excited states in its p-shell. We optimized our collection efficiency by judicious choice of optical elements, achieving an efficiency budget as follows. After emission from the micropillar, single photons travel across the following elements, with measured transmittances ${\eta}_{\text{elem}}$, before reaching the detectors: two cryostat windows with ${\eta}_{\text{cryo}}=(96\pm 1)\%$; a microscope objective (Olympus LMPLN10XIR) with $\text{N.A.}=0.3$ and ${\eta}_{\text{obj}}=(91\pm 1)\%$; a dichroic mirror (Alluxa filters) used to separate single photons from the laser path, with a measured attenuation at 905 nm bounded to $>60\text{\hspace{0.17em}}\mathrm{dB}$ extinction, while no appreciable loss is recorded at wavelengths corresponding to single-photon emission, we thus consider ${\eta}_{\text{dich}}=1$; 6 mirrors and 2 lenses, with an overall transmission of ${\eta}_{\mathrm{ml}}=(95\pm 1)\%$; and a 0.85 nm FWHM bandpass filter (Alluxa filters) with ${\eta}_{\mathrm{bp}}=(91\pm 1)\%$ used to ensure that any residual scattered laser light is filtered out. The remaining losses are due to coupling to a single-mode fiber, where we estimate a fiber-coupling efficiency of ${\eta}_{\mathrm{fc}}=(65\pm 4)\%$ by comparing our collection with a multimode fiber assumed to have a unity coupling efficiency. This results in an overall transmission of our optical setup of ${\eta}_{\text{setup}}=(49\pm 3)\%$.

We characterize this device in terms of absolute brightness and purity (see Fig. 1). We detect large count rates in a silicon avalanche photodiode (APD), as shown in the saturation measurements in Fig. 1(a). The saturation curves are fitted to ${R}_{0}(1-\mathrm{exp}(-P/{P}_{0}))$, where ${R}_{0}$ is an asymptotic rate value and ${P}_{0}$ is the saturation power. The inset figure shows *Device* 1 spectra with varying temperature $T$. The energy of the QD transition varies like the band gap of the semiconductor with the temperature [31], whereas the cavity mode energy follows the temperature variation of the refractive index. Adjusting the temperature thus allows tuning the QD cavity resonance. For the measurements presented in Fig. 1, the neutral exciton line is brought in resonance at $T=15\text{\hspace{0.17em}}\mathrm{K}$. The count rates in pulsed configurations reach values as high as 3.6 MHz. In fact, for this measurement, a known loss must be introduced in the optical path in order to properly quantify the available count rates, as they are beyond the APD’s (Perkin-Elmer SPCM-AQR-14-FC) linear regime. This allows us to accumulate a high amount of statistics with notably short integration times. For instance, the inset in Fig. 1(b) shows a ${g}^{(2)}(\mathrm{\Delta}t)$ measurement—second-order autocorrelation function with ${g}^{(2)}(0)=0$ corresponding to an ideal single-photon state—at $P={P}_{0}$, yielding a value of ${g}^{(2)}(0)=0.0130\pm 0.0002$, where the small error is reached with an integration time of only 29 s. We in fact used about half the available counts after selecting one linear polarization emitted by our device. Thus, in our setup, the same amount of statistics is achieved four times faster when the polarizer is removed. Remarkably, we observe low multi-photon emission at all pump powers, with a measured maximum value of ${g}^{(2)}(0)=0.0288\pm 0.0002$ at $P=3{P}_{0}$. We thus observe a single-photon purity $1-{g}^{(2)}(0)$ above 97% even at maximum brightness. These values were extracted from integrating raw counts in a 2 ns window—sufficiently larger than the $<0.5\text{\hspace{0.17em}}\mathrm{ns}$ lifetime [9]—around the peak at zero delay compared to the average of the 10 adjacent lateral peaks, without any background subtraction. The error bars in this work are deduced from assuming poissonian statistics in the detected events.

Our APD efficiency of 32%—measured using the approach of Ref. [32]—80 MHz pump rate, and 3.6 MHz detected count rate corresponds to an absolute brightness—the probability-per-laser-pulse of finding a spectrally isolated high-purity single photon at the output of a single-mode fiber—of 14%, the highest reported to date. Such absolute brightness represents a clear improvement over what has been previously achieved with quantum dot-based photon sources. For instance, a drastic contrast between the performance at the first lens and the actual detected count rates has been common until now, e.g., reporting a brightness as high as 72% while detecting 65 kHz [33], or 143 MHz collected on the first lens but only 72 kHz available on detection [34]. Detected rates of 4.0 MHz at the single-photon level have been reported [35], but without coupling into a single-mode fiber and at the cost of high multi-photon contribution with ${g}^{(2)}(0)=0.4$. In fact, our source greatly exceeds, in terms of absolute brightness, the performance of any other single-photon source from any physical system, including the well-established spontaneous parametric down-conversion source—so far considered as the premier photon source—where the equivalent (triggered) absolute brightness is well below 1%.

We note that, given our setup collection efficiency of ${\eta}_{\text{set}\text{up}}=49\%$, *Device* 1 exhibits for the neutral exciton state a brightness at the first lens of 29%. Deducing the exciton lifetime from the correlation curves at a low excitation power, we estimate the Purcell factor of the device to be around ${F}_{p}=2$ and the fraction of emission into the cavity mode to be around 66%. Considering an output coupling efficiency of 90%, the measured brightness in the first lens could reach 60% with a unity probability to find the QD in the neutral exciton state. However, as evidenced in the inset of Fig. 1(a), the present QD also presents an non-negligible probability to emit from the positively or negatively charged exciton transitions that are brought in resonance at higher temperatures. As a result, the probability of the quantum dot to be in the neutral exciton is reduced, leading to the measured 29% brightness at the first lens. Note that this instability of the charge state was not observed originally in the devices under study (see Ref. [9]), but appeared after accidentally freezing the sample.

## 3. LONG TIMESCALE INDISTINGUISHABILITY

We now explore the indistinguishability of photons emitted by *Device* 1 with various temporal distances. We perform our measurements at $T=13\text{\hspace{0.17em}}\mathrm{K}$ to reduce phonon-induced dephasing [36], which is sufficiently close to the quantum dot cavity resonance at $T=15\text{\hspace{0.17em}}\mathrm{K}$. Note that contrary to most reports, the phonon sideband here is not filtered out by the 0.85 nm bandpass filter used to further suppress the laser light. Figure 2(a) depicts our experimental setup. Single photons are injected into an unbalanced Mach–Zehnder interferometer with a variable fiber-based path-length difference designed to match—by using multiple fibers of distinct lengths—an integer multiple of 12.5 up to 400 ns. The polarization control—a polarizer (Pol) and a half-wave plate (HWP)—and a polarizing beam splitter behave as a beamsplitter with tuneable reflectivity, thus balancing the photon flux entering the interference point inside a fiber beam splitter closing the Mach–Zehnder configuration. Quarter-wave plates and HWPs are used to tune the polarization of interfering photons in a parallel or orthogonal configuration. Time-correlation histograms from the output of this interferometer reveal the indistinguishability of photons emitted with a temporal distance $\mathrm{\Delta}{\tau}_{e}$. Fully distinguishable photons—e.g., with orthogonal polarization—meeting at a $50:50$ beam splitter, resulting in a 50% probability of being detected simultaneously at the output of the beam splitter. This results in the peak around $\mathrm{\Delta}t=0$ of the time-correlation measurement being about half of those at $\mathrm{\Delta}t>0$, with the exception of peaks at $\mathrm{\Delta}t=\mathrm{\Delta}{\tau}_{e}$, where the larger suppression indicates that the interfering photons were emitted with a temporal distance $\mathrm{\Delta}{\tau}_{e}$. In general, it can be shown for a pure single-photon source (see Supplement 1), the areas ${A}_{\mathrm{\Delta}t}$ centered around $\mathrm{\Delta}t$ are given by ${A}_{k}=N$, ${A}_{-\mathrm{\Delta}{\tau}_{e}}=N(1-{\mathcal{R}}^{2})$, ${A}_{\mathrm{\Delta}{\tau}_{e}}=N(1-{\mathcal{T}}^{2})$, and ${A}_{0}=N(({\mathcal{R}}^{2}+{\mathcal{T}}^{2})-2\mathcal{RT}V)$, where $k=\pm 12.5\text{\hspace{0.17em}}\mathrm{ns},\pm 25\text{\hspace{0.17em}}\mathrm{ns},\dots $, peaks are excluded at $\pm \mathrm{\Delta}{\tau}_{e}$, $N$ is an integration constant, $\mathcal{R}$ is the beam splitter’s reflectivity, and $\mathcal{T}=1-\mathcal{R}$.

We use the visibility $V$ to quantify the degree of indistinguishability of the source. Since the measured visibility depends both on the photon source and on the apparatus used to characterize it, the latter must be accounted for. Ideally, the apparatus is a beam splitter of reflectivity $\mathcal{R}=0.5$; in our experiment $\mathcal{R}=0.471$, $\mathcal{T}=0.529$, and the visibility $V$ is thus,

where $A$ is taken as the average value of ${A}_{k}$. Note that since the ${g}^{(2)}(0)$ values are intrinsic to the source, and hence affect any process in which we wish to use it, we do not correct for nonzero ${g}^{(2)}(0)$ in Eq. (1). The deduced $V$ therefore corresponds to the raw two-photon interference visibility and quantifies the degree of photon indistinguishability.Figure 2(b) shows histograms for the indistinguishability of orthogonally and parallelly polarized photons at $\mathrm{\Delta}{\tau}_{e}=50\text{\hspace{0.17em}}\mathrm{ns}$ and $P={P}_{0}$. In virtue of Eq. (1) and the measured $\mathcal{R}=0.471$, we obtain ${V}_{50\text{\hspace{0.17em}}\mathrm{ns}}^{{P}_{0}}=(0.71\pm 0.01)\%$ in the orthogonal configuration (red histogram) and ${V}_{50\text{\hspace{0.17em}}\mathrm{ns}}^{{P}_{0}}=(60.31\pm 0.60)\%$ for parallelly polarized photons (blue histogram), where ${V}_{\mathrm{\Delta}{\tau}_{e}}^{P}$ denotes the visibility taken at a power $P$ and temporal delay $\mathrm{\Delta}{\tau}_{e}$. We observe higher visibilities at lower powers and shorter delays. For instance, the measurements in Fig. 2(c) were taken at $P=0.5{P}_{0}$ and reveal ${V}_{12.5\text{\hspace{0.17em}}\mathrm{ns}}^{0.5{P}_{0}}=(67.52\pm 0.78)\%$ at a temporal delay (blue histogram) of $\mathrm{\Delta}{\tau}_{e}=12.5\text{\hspace{0.17em}}\mathrm{ns}$. Remarkably, we find that indistinguishability is robust in the temporal domain. Even after 33 consecutive emitted photons (orange histogram) at $\mathrm{\Delta}{\tau}_{e}=400\text{\hspace{0.17em}}\mathrm{ns}$, the value only decreases to ${V}_{400\text{\hspace{0.17em}}\mathrm{ns}}^{0.5{P}_{0}}=(59.97\pm 0.76)\%$. That is, there is a less than 8% visibility decrease in $\sim 400\text{\hspace{0.17em}}\mathrm{ns}$. All $V$ values with the nonresonant schemes are obtained without any background correction.

To thoroughly examine the indistinguishability properties of *Device* 1, we carried out power- and temporal-dependent measurements [see Fig. 3(a)]. All these measured $V$ are within the 50%–70% range, thus showing conclusive quantum interference at all measured powers and timescales. The large available photon flux allows us to gather more than 100 visibility values with measurement errors sufficiently small to identify an interesting behavior in this narrow visibility range. At any given $\mathrm{\Delta}{\tau}_{e}$, $V$ is linear in $P$, see (Supplement 1), and we simply use $\overline{V}={V}_{\mathrm{\Delta}{\tau}_{e}}^{\mathrm{max}}+{m}_{\mathrm{\Delta}{\tau}_{e}}P$ to characterize the $P$-dependence of $V$ at fixed $\mathrm{\Delta}{\tau}_{e}$. Conversely, at fixed $P$, $V$ decreases monotonically and asymptotically in $\mathrm{\Delta}{\tau}_{e}$, flattening to fixed values at longer timescales.

We model this behavior by considering a time-dependent wandering of the spectral line as the origin of the temporal modulation. That is, the frequency of every emitted photon $\omega (t)={\omega}_{0}+\delta \omega (t)$ varies in time according to some wandering function $\delta \omega (t)$ occurring in timescales much longer than the photon lifetime. Our problem is then equivalent to finding the mutual interference visibility between independent sources with finite frequency detuning [37], which is given by $V(0)/(1+\delta {\omega}_{r}^{2})$ in the case where $V(0)$ is the degree of indistinguishability for each source alone (equal value for both) and $\delta {\omega}_{r}$ is the ratio of the frequency detuning to the spectral linewidth of the sources (equal linewidth for both). If this mismatch arises due to spectral wandering within the same source, then the time-averaged relative detuning squared is given by $2\delta {\omega}_{r}^{2}(1-\mathrm{exp}(-\mathrm{\Delta}{\tau}_{e}/{\tau}_{c}))$, with ${\tau}_{c}$ a characteristic wandering timescale (see Supplement 1 for more details). We thus derive the visibility of temporally distant photons as follows:

The decrease of the indistinguishability by a few percents for temporally distant photons demonstrates a very limited spectral diffusion in our micropillar devices. This observation is in striking contrast to previous measurements on single-photon sources based on alternative approaches for efficient photon extraction, such as nanowires [38], or micro lenses [29]. A significantly lower stability of the electrostatic environment of the QD can reasonably be attributed to the close proximity of free surfaces in the latter. Indeed, as indicated by the observation of three emission lines from the same QD, even the micropillar devices under study do not provide a fully stable charge state for the QDs, an effect that we observe to be dependent on the quality of the etched surfaces. This makes strictly resonant spectroscopy difficult without an additional nonresonant excitation, a situation also observed in other micropillar devices [26].

Therefore, to explore the indistinguishability of temporally distant photons under strictly resonant excitation, we turn to electrically controlled micropillars and present data on two devices, *Device* 2 and *Device* 3. These devices consist of quantum dots deterministically coupled to micropillars embedded in cylindrical gated structures with $p$- and $n$-contacts, respectively, defined on the top and bottom sides of the device, resulting in an effective $p\text{-}i\text{-}n$ diode structure onto which an electric field can be applied (see Ref. [28] for a detailed description of the device). We perform our measurements at $T=9\text{\hspace{0.17em}}\mathrm{K}$ and tune the emission into cavity resonance via an applied bias voltage of $-0.3\text{\hspace{0.17em}}\mathrm{V}$. This sample is cooled by gas exchange in a closed-cycle cryostat and is pumped by shaped 15 ps laser pulses at an 82 MHz repetition rate. The experimental setup used for photon collection is reported in Ref. [28], and the apparatus used for the temporal-dependent measurements is conceptually identical to that in Fig. 2(a).

Resonant excitation allows us to probe two-photon interference in a regime excelling in indistinguishability performance. Indeed, for *Device* 2, we obtain ${V}_{12.2\text{\hspace{0.17em}}\mathrm{ns}}^{\pi}=(95.0\pm 1.0)\%$ at a short temporal separation, decreasing only to ${V}_{158.5\text{\hspace{0.17em}}\mathrm{ns}}^{\pi}=(90.6\pm 1.7)\%$ at long timescales [see Figs. 4(a) and 4(b)]. We observe a high single-photon purity quantified by ${g}^{(2)}(0)=0.015\pm 0.007$ at the $\pi $-pulse [see Fig. 4(c)], where the nonvanishing ${g}^{(2)}(0)$ primarily consists of background noise and thus a value $1-{g}^{(2)}(0)$ of 98.5% represents a lower bound on the intrinsic single-photon purity. Indistinguishability measurements at various temporal distances [see Fig. 4(d)], reveal plateaus at high values: up to a first and fourteenth photon, separated by $\sim 150\text{\hspace{0.17em}}\mathrm{ns}$, exhibit an indistinguishability greater than 90%. The curve is a fit to Eq. (2) with a maximum indistinguishability value of $V(0)=96.6\%$, ${\tau}_{c}=54.4\text{\hspace{0.17em}}\mathrm{ns}$, and $\delta {\omega}_{r}=17.8\%$. The reproducibility of our results, thanks to a deterministic fabrication, is evidenced by similar indistinguishability values obtained on *Device* 3: ${V}_{12.2\text{\hspace{0.17em}}\mathrm{ns}}^{\pi}=(96.1\pm 0.8)\%$ at a short temporal delay and ${V}_{463\text{\hspace{0.17em}}\mathrm{ns}}^{\pi}=(87.8\pm 1.6)\%$ for a first and thirty-ninth photon separated by 463 ns. These values of indistinguishability are corrected for the measured background noise arising from detector dark counts: the experimental setup used for these resonant-excitation measurements presents a low collection efficiency. Thus, an integration of detected raw counts that includes the background noise, which at zero delay is as large as nonvanishing counts due to photon dinstinguishability, would underestimate the intrinsic degrees of indistinguishability in our devices (see the Supplement 1 for details on this method). No correction for nonvanishing ${g}^{(2)}(0)$ was included.

Note that a high absolute brightness with this recently developed technology is yet to be achieved. However, since the mode profile of connected pillars is the same as isolated ones [27] and a photon extraction efficiency at the first lens of 65% has been reported on this sample [28], the same experimental methods as before should allow even higher absolute efficiencies than the 14% reported here.

## 4. DISCUSSION AND CONCLUSION

We provided here strong evidence that our sources emit long streams of indistinguishable photons. Under nonresonant excitation, even a first and a thirty-third consecutive photon, separated by 400 ns, display conclusive quantum interference. For a fixed pump power, photon indistinguishability decreases by only a few percents—about 8% at low powers and less than 4% at higher powers—before flattening to fixed values at longer timescales. This contrasts favorably to previous works, where photon indistinguishability has been observed to decrease by 40% in only 10 ns [29]. Moreover, under strictly resonant excitation, photon indistinguishability between a first and thirty-ninth photon remained at 88%. Interestingly, the observation of only small reductions in the temporal domain indicate that nonunity indistinguishability under nonresonant excitation is mainly caused by homogenous broadening of the spectral linewidth (governing coherence times at short temporal delays) and a limited inhomogeneous broadening (governing effective coherence times at longer temporal delays). The relative amplitude of the spectral diffusion at saturation is similar for both resonant and nonresonant excitation. However, *Device* 1 operates in a limited Purcell regime, whereas *Devices* 2 and 3 operate with a Purcell factor of around 7–10, leading to an increased radiative exciton linewidth. From this, we conclude that, although the application of an electrical bias in *p-i-n* diode structures allows a good control of the QD charge states, it does not lead to a significant decrease in the spectral wandering phenomena. The excellent indistinguishability observed in *Devices* 2 and 3 arises mainly from reduced pure dephasing of the exciton state, increased Purcell factor, and reduced time jitter in a resonant excitation scheme.

Our reported indistinguishability values correspond to the longest temporal delays here studied at a particular pump repetition rate of 80 MHz. This value only represents a lower bound on the number of photons we can generate—limited by radiative lifetimes in the order of a few hundred picoseconds—that can be further used in quantum information processing protocols with solid-state sources [39]. Previous works investigating noise spectra in resonance fluorescence have shown evidence of long streams of near transform-limited photons [40] in timescales potentially reaching seconds [41]. In fact, *Device* 2 has recently been shown to emit photons with near transform-limited linewidth on a millisecond timescale [42], in which case we would expect that our devices are producing at least hundreds of thousands of highly indistinguishable single photons.

Our findings are especially relevant in implementations with time-bin encoded degrees of freedom, such as some recently proposed schemes of linear-optics quantum computing with time-bin encoding [43,44], where the indistinguishability of temporally distant photons will directly determine quantum fidelities of the implemented protocols. Scaling solid-state multi-photon sources by combining multiple independent emitters remains challenging, as atomic growth accuracy or complex individual electric control over multiple devices is needed. These requirements can be circumvented by making use of a single photon source emitting a long temporal stream of highly indistinguishable photons that can be demultiplexed by fast active optics.

A high absolute brightness will be critical for successfully implementing multi-photon experiments with these sources, where their down-conversion counterparts currently require experimental runs of hundreds of hours [45,46]. The key role of high emission yields in these devices has been made explicit in the recent demonstration of a solid-state based multi-photon experiment [47], realized with *Device* 1, where integration times outperformed those in equivalent down-conversion implementations by two-orders of magnitude. Achieving high absolute efficiencies, and thus allowing the scaling of multi-photon experiments to larger photon numbers, becomes feasible due to the Purcell enhancement of *deterministically* coupled quantum dot-micropillar devices [9,27,28,37,48]. This necessary condition is unlikely to be found by chance with nondeterministic approaches, with reported [48] device yields of $\sim 0.01\%$ [26]. Thus, the deterministic fabrication, high absolute brightness, and long timescale indistinguishability of our devices will enable large-scale applications that have been heretofore impossible.

## Funding

Centre for Engineered Quantum Systems (CE110001013); Centre for Quantum Computation and Communication Technology (CE110001027); Asian Office of Aerospace Research and Development (FA2386-13-1-4070); ARC Discovery Early Career Research Award (DE120101899); ERC Starting Grant (277885 QD-CQED); French Agence Nationale pour la Recherche (ANR DELIGHT, ANR USSEPP); French RENATECH network Labex NanoSaclay; European Union’s Seventh Framework Programme FP7 (618078 WASPS).

## Acknowledgment

J. C. L. and A. G. W. thank the team from the Austrian Institute of Technology for kindly providing the time-tagging modules. M. P. A. thanks Halina Rubinsztein-Dunlop for the generous loan of equipment. The CNRS-LPN authors are very thankful to Anna Nowak for her help with the technology. A. G. W. acknowledges support from a UQ Vice Chancellor’s Research and Teaching Fellowship.

See Supplement 1 for supporting content.

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