The top concave cavity mirror is mounted on a stack of three piezo nanopositioners. The bottom part—including the 30-pairs DBR and QD layers—is mounted on a stack of three nanopositioners (XYZ) and two tilt stages (Θ, Φ). The λ-thick GaAs layer containing an InAs QD layer is grown on top of the 30-pairs AlAs/GaAs DBR. The centre wavelength of the bottom DBR is 890 nm. The top surface of the QD layer is coated with 50-nm-thick Au/Ti grids, which facilitates the location of the selected QDs with high quantum efficiency. This set-up provides the in situ ability to align the cavity with selected QDs. The inset shows a numerical simulation of the radiation from a dipole in an open-cavity structure. The numerically simulated Q-factor is ~9,000 and the Purcell factor is 18. The probability that single photons can transmit through the top of the cavity is η_top = 0.939.

The QD–open microcavity system is cooled down to 4 K in a closed-cycle cryostat. Note that although the open cavity provides the key advantage of full tunability, maintaining high stability with it presents an extreme technical challenge because even a 1 nm drift of the cavity length would cause a ~40 GHz shift of the cavity’s resonance frequency and a drop of 78% of the maximum Purcell factor. We made various efforts to overcome the environmental vibrations (refer to Supplementary Section 4 for more detailed information on the vibration isolation method and stability of the QD–open microcavity system).

To maximize the brightness of the single-photon emitters, we first pre-select QDs with high quantum efficiencies by removing the top concave cavity and comparing the π-pulse resonance fluorescence of hundreds of bare QDs. The positions of the brightest candidates are recorded. Then, the top mirror returns, forming a fully tunable open microcavity that allows in situ coupling of the cavity spatially and spectrally.

The basic excitation protocol follows the resonant excitation of a QD in a mode-splitting cavity^19,21. The mode-splitting here is induced by the birefringence of the GaAs material, and the magnitude of mode-splitting can be manipulated by applying strains in the GaAs material²². Compared with geometrically asymmetric cavities, birefringence-induced mode-splitting does not induce far-field optical mode deformation, which is favourable for higher single-mode fibre collection efficiency. Figure 2a shows the experimental excitation scheme used in practice. The measured Q-factor of each mode is ~8,400 and splitting between two modes is ~83 GHz, which gives a cavity splitting (Δω) to cavity linewidth (δω) ratio of 2.07. A singly negatively charged QD emitting at a wavelength of 884.5 nm with high quantum efficiency η_qd is coupled to the cavity’s H-polarized mode. We then can excite the QD with a V-polarized laser pulse and collect the H-polarized single photons.

Fig. 2: High-efficiency single-photon source under shape-optimized pulse excitation.

a, Excitation scheme of a polarized single-photon source in a mode-splitting cavity. b, Deterministic generation of polarized single photons under a series of pulse excitations with different pulse widths. c, The corresponding single-photon purity under different pulse width excitations. d, The resonance fluorescence photon counts as a function of the square root of excitation laser power when the pulse width is 69 GHz. At the π pulse, the end-to-end single-photon counts per second reach a maximum of (14.28 ± 0.01) million under laser excitation with a repitition rate of 25.38 MHz, which corresponds to a system efficiency of 0.712(18). The red dotted line indicates the loss-tolerant threshold value of two-thirds.

In a previous experiment¹⁹, the frequency mismatch between the V-polarized excitation laser and the H-polarized cavity mode meant that only a small fraction of the laser could actually be used to excite the QD. The frequency of the partial excitation laser may be far detuned with the QD, leading to a reduction of the π pulse single-photon counts. Compared with low-Q resonator structures such as the bullseye cavity, this problem is more severe in high-Q resonators such as micropillar and open-cavities.

To overcome this problem, we use a 4f optical pulse shaping system²³ to shape the laser pulse. The shaping system consists of two reflective diffraction gratings, two identical lenses and one slit. The first grating is used to transform frequency components into spatial ones, whereas the second grating is for an inverse process. According to Supplementary Section 6, a narrower excitation pulse width in the frequency domain allows the intra-cavity pulse to resonantly excite the QD more effectively. We therefore set a width-tunable slit at the Fourier plane to filter out unwanted frequency components. As shown in Fig. 2b, a set of clear Rabi oscillations are observed by resonantly exciting the selected QDs with different pulse widths from ~96 GHz to ~46 GHz. These oscillations illustrate an improvement in the π pulse single-photon counts, as well as a reduction in the power required for their excitation when utilizing narrower pulse widths.

It should also be noted that narrowing the pulse width in frequency will broaden the pulse length in the time domain, which can cause re-excitation of the QD and reduce the single-photon purity. In Fig. 2c we show the measured second-order correlations of the single photons under different excitation pulse widths. By optimizing the balance between single-photon purity and brightness under various excitation pulse widths, we determined that 69 GHz represents the optimal excitation pulse width for exciting our selected QD in the open cavity. Under this shape-optimized pulse excitation, a single-photon source with minimum excitation power, near-unity single-photon purity and maximum single-photon counts can be achieved simultaneously. The shaped pulse excitation generates 13% more single photons at the π pulse, in comparison to the unmodified pulse excitation with a pulse width of 96 GHz.

Having optimized the shaping system, we proceeded to measure the efficiency of our single-photon system. To avoid the dead time zone (30 ns) of the superconducting nanowire single-photon detector (SNSPD), we utilized an amplitude electro-optic modulator to decrease the repetition rate of the excitation laser to 25.38 MHz, which is one-third of the original frequency of 76.13 MHz. The single photons collected at the single-mode fibre end are directly connected with the SNSPD, whose detection efficiency is 0.79(2). In Figure 2d we present the corrected resonance fluorescence photon counts plotted against the square root of the excitation laser power. Using a π pulse power of 10.24 nW, we observed a π pulse single-photon count rate of approximately 14.28 million counts per second, resulting in a system efficiency of 0.712(18). This is the highest achieved single-photon source’s system efficiency of all reported physical systems.

An important feature of high-efficiency single-photon source can be manifested by intensity squeezing²⁴, that is, the reduction of intensity fluctuation. Such an observation was only possible very recently^25,26, after 20 years development of QD single photons, highlighting the importance of improving the system efficiency of single-photon sources. The standard deviation of counts in a single-photon source is reduced by an intensity squeezing factor of (1−?) compared with the shot-noise, so the value of intensity squeezing is a natural benchmark to characterize the overall efficiency of single-photon sources. Here, ρ is the overall efficiency, including both the collection efficiency and the detection efficiency. A time-correlated single-photon counting system is used to record the arrival time of each photon for further analysis. Figure 3a shows the real-time detected single photons at π pulse with a time bin of 1.0 μs; the corresponding histogram is shown in Fig. 3b. The standard deviation of single-photon counts (blue) in Fig. 3b is 2.43(8), which shows sub-shot-noise intensity fluctuation with an intensity squeezing of 1.89(14) dB.

Fig. 3: System efficiency characterization of the single-photon source.

a, The single-photon stream with a time bin of 1.0 μs; 1,000 bins of single-photon counts are recorded. b, The corresponding normalized histogram. The intensity fluctuation of single photons is represented by the dark blue dots and fitted with a binomial function. The green shading shows the shot-noise-limited source with the same photon count rate. The directly measured intensity squeezing of the single-photon source compared with the shot-noise limit is σ_SPS/σ_SN = 0.65(2) under π pulse excitation. The grey shading shows that the corrected intensity squeezing value at the first lens is 3.92 ± 0.18 dB. c, Statistics of consecutive n-photon events within 10 min. Up to 40 photons in a row can be acquired; the line indicates an exponential decay fit. The error bars represent 1 s.d., deduced from propagated Poissonian counting statistics of the raw detection events.

We analysed consecutive single-photon events to reveal the overall efficiency. Figure 3c illustrates the number of consecutively detected n-photon streams. The integration time is 10 min, and a maximum of 40-photon events are observed at a count rate of 1.67 mHz. The event rate of consecutive n-photons should be ρⁿ × R_laser (where R_laser is the repetition rate of the pulse laser). By fitting the exponential decay, the overall efficiency ρ was determined to be 0.5652(7). Taking into account the detection efficiency of the used detector is 0.79(2), the system efficiency of the single-photon source is 0.715(18), which again confirms the efficiency measurement. If we combine with a detector with a system detection efficiency exceeding 93.7% and a full recovery time under 13 ns, the combined source and detection efficiency would exceed the two-thirds loss-tolerant threshold for scalable quantum computing. Such a detector seems promising given the rapid progress of SNSPD technology, which has already demonstrated near-unity detection efficiency at near-infrared wavelengths^27,28 and the capability for gigahertz detection rates^29,30.

In addition to measuring system efficiency, we conducted comprehensive characterizations of the single-photon source by evaluating its purity and indistinguishability. The single-photon purity is characterized using a Hanbury Brown–Twiss set-up³¹ and presented in Fig. 4a, with g⁽²⁾(0) = 0.0205(6). The data are directly measured without any further filtering. The excitation laser is found to be the primary source of residual multi-photon events. The indistinguishability of the photons is measured using an unbalanced Mach–Zehnder interferometer^32,33. Figure 4b shows the histograms of the normalized two-photon counts for cross and parallel polarization respectively. The raw two-photon quantum interference visibility is 0.928(1). After correction with the residual multi-photon probability of g⁽²⁾(0) = 0.0205(6) and an unbalanced beam splitter split ratio of 45:55, the corrected single-photon indistinguishability is 0.9856(13). The correction method is described in detail in Supplementary Section 10.

Fig. 4: Characterization of the pulsed resonance fluorescence single photons.

a, The intensity correlation histogram of the single photons under π pulse excitation measured using a Hanbury Brown–Twiss set-up. The second-order correlation at zero time delay is g⁽²⁾(0) = 0.0205(6). b, Quantum interference between two single photons. The input two photons are π pulse excited and prepared in cross and parallel polarization. The raw Hong–Ou–Mandel visibility is 0.928(1). c, Single-photon indistinguishability as a function of emission time separation. The corrected photon indistinguishability drops very slightly, from 0.9856(13) at 13.1 ns to 0.959(2) at ~2.67 μs. The error bars represent one s.d., deduced from propagated Poissonian counting statistics of the raw detection events (the count events for each point, from left to right, are 73,581, 20,052, 21,529 and 23,567).

To further prove that the single-photon source is ready for scale-up, it is imperative to verify that that the single photons are nearly transform-limited^34,35. Here we test the photon indistinguishability with different photon time delays using a delay line adjustable Mach–Zehnder interferometer³⁴. As shown in Fig. 4c, the corrected Hong–Ou–Mandel visibility is 0.9856(13), 0.985(1), 0.970(2) and 0.959(1) for the time delays of 13.1 ns, 670 ns, 1.31 μs and 2.67 μs, respectively. Compared with the 13.1 ns delay, the single-photon indistinguishability with 2.67 μs delay only drops less than 3%, indicating that the emitted single photons are close to the transform limit. Such high photon indistinguishability with long-time delay guarantees the performance in scalable photonic applications.

In conclusion, by resonant excitation of a QD embedded in an open-cavity, we have realized a deterministic single-photon source with a low multi-photon error of g⁽²⁾(0) = 0.0205(6), an indistinguishability of 0.9856(13) and system efficiency of 0.712(18), simultaneously, exceeding the required efficiency threshold for scalable photonic quantum computing¹⁰. Such a high-efficiency source can be immediately used for applications such as boson sampling, photonic cluster states generation, quantum communication and so on. Furthermore, this QD–open cavity system can be readily extended to the strong coupling regime by increasing the coupling rate and minimizing the cavity loss rate, thereby facilitating the implementation of photon–photon quantum gates. With its exceptional performance and considerable potential for various applications, our work marks a critical step towards scalable quantum technologies reliant on single photons.