1. INTRODUCTION

In the ongoing development of quantum optical technologies, devices will need to be easier to use, more compact, robust, and scalable, making them available to a broader community. These technologies include applications in quantum communication [1–4], optical quantum metrology [5–8], and optical quantum computation and simulation [9–12]. For example, a true single-photon source on-chip as a turnkey device would open up quantum technologies to an unprecedented user group.

Quantum dot (QD) excitonic states are excellent quantum emitters, showing bright emission of single photons [13–17] and excellent suppression of multi-photon states [16,18,19]. These properties are achieved due to the level structure and radiative efficiency of the optically allowed lowest-level exciton states.

While single QD exciton emission is inherently bright with a low multi-photon contribution, the emitted light can be further enhanced and directed into a Gaussian mode by coupling the QD to an optical cavity [14,20,21]. In the weak coupling regime between emitter and cavity, this is known as the Purcell effect [22]. For a cavity with quality factor $ Q $ and mode volume $ V $, the Purcell effect is characterized by $ {F_p} = \frac{3}{{4{\pi ^2}}}{(\frac{\lambda }{n})^3}\frac{Q}{V} $ for a dipole emitter in resonance with the cavity, placed at the maximum of the electric field, and with proper aligned polarization. $ \lambda $ is the wavelength of the fundamental mode resonance, and $ n $ is the material’s index of refraction. With the emitter and cavity in resonance, this shortens the radiative lifetime. While various optical cavities can be used [17], a particularly useful cavity is the pillar microcavity [23], because the single-photon emission is in a well-defined Gaussian mode. Since weak cavity coupling reduces the radiative lifetime, decoherence contributions to the emission linewidth are reduced, leading to bandwidths that can approach the spontaneous-emission lifetime limit, and near-unity photon indistinguishability [17,24].

Because of the single-mode nature of the micropillar cavities, the resonant excitation pump and resonance fluorescence signal are in the same spatial mode. Separating the pump laser from the signal is often achieved through pump–probe cross polarization, leading to a signal reduction that is at best 50 % [16,25–28]. This reduction in efficiency eliminates quantum applications that require high efficiency (as opposed to brightness) [9].

It has previously been shown that orthogonal pumping of QDs embedded in planar cavities suppresses scattered laser light [18,28–31]. Nevertheless, this was limited to planar structures with moderate [32] or no Purcell enhancement of the emitter lifetime. Micropillar cavities, on the other hand, have much better Purcell enhancement [14,21] due to their high $Q$ with a relatively small mode volume, but resonant excitation is limited to cross-polarized excitation [16,26,27]. Current approaches for orthogonal pumping of micropillar cavities are free-space and require cross polarization, and cannot couple to multiple cavities [33].

Alternative approaches to in-plane excitation that also remove the 50% photon loss associated with cross polarization have recently been demonstrated. They include using the polarization splitting induced by elliptical cavities shown earlier in [34], demonstrating efficiency when accounting for the detector efficiency [35], and an alternative approach using a coherent two-color pump source [36].

In this paper, we demonstrate a ridge-waveguide-coupled optical cavity architecture where the resonant laser pump and the collected resonance fluorescence are spatially orthogonal. This combines orthogonal waveguide pumping with micropillar cavities, allowing for the filter-free off-chip coupling of single photons without the 50% penalty in source brightness and efficiency present in most current device designs. The device design combines the advantages of waveguides [37–39] with the advantages of cavity quantum electrodynamics [12,17]. The waveguide enables us to excite several micropillar cavities simultaneously, while it significantly reduces laser scattering. We verify our experimental results through simulation, and discuss the limitations of the current design. We show that the presented device structure allows for confined cavity modes with a Purcell factor of about 2.5, in-plane guided waveguide modes for excitation, and suppression of unwanted pump laser scattering, leading to a filter-free autocorrelation value of $ {g^{(2)}}{(0)_{{\rm fit}}} = 0_{ - 0}^{ + 0.043} $, where by “filter-free” we mean no spectral, temporal, or polarization filtering.

2. DEVICE AND SIMULATION

The device fabrication begins with a distributive-Bragg reflector (DBR) planar microcavity with QDs at the center of a ${4}\;\lambda $ cavity [see Appendix A and Fig. 2(a)]. Our device design minimizes scattering between the waveguide modes, but it also maintains confinement in the out-of-plane micropillar cavity mode. Simulations indicate that the best results are pillar diameters between 2 and 3 µm and waveguide widths between 0.55 and 1.25 µm, where smaller waveguides increase the cavity confinement and decrease the polarization mode splitting, but also increase the scattering at the waveguide–cavity interface. A finite-difference time-domain (FDTD) simulation of the confined micropillar cavity modes, split by the presence of the waveguide, is shown in Fig. 1(a). The top (bottom) mode has major $x$ ($y$) electric component, resulting an $x$ ($y$)-polarized out-of-plane emission. The waveguide and cavity modes have orthogonal Poynting vectors, respectively in-plane and out-of plane, and thus do not couple. Waveguided light therefore excites the QD in the micropillar directly, rather than coupling to the cavity modes. To emphasize this point, in Fig. 1(b) we show an FDTD simulation of the far-field intensity from the cavity when pumped from the waveguide $ {E_y} $ mode. Whereas the cavity mode far field features a Gaussian mode profile with an angular spread of $ {\lt} 30 \,\,{\rm deg}$ to collect the full mode, the scattered field has very little intensity at angles $ {\lt} 20 \,\,{\rm deg}$. The small amplitude of the scattered light far field provides further evidence (the full integrated intensity of the scattered light to the top is $ {\lt} 10^{ - 4} $). In Figs. 1(c) and 1(d) we show simulation intensity results for the two waveguide modes ($ {E_y} $, ${E_z}$). While there is scattering in both cases due to topology changes in the waveguide, there is no apparent coupling to cavity modes.

 

Fig. 1. Simulation of the confined modes in the device for a 2.5 µm diameter cavity and a 0.95 µm waveguide. (a) Intensity of the $x$ ($y$) electric field component for the $x(y)$-polarized confined cavity mode. The two modes, split by 0.05 nm and overlapping by 92%, have different strengths but similar spatial extent. (b) Far-field image of the device with the cavity in the center when pumped from the side, as illustrated in (c) and (d). The far field is on a half-sphere calculated at 1 m distance from the device and is plotted in polar coordinates. The intensity does not match the common intensity scale on the right. The intensity of the total scattered light to the top is less than $ {10^{ - 4}} $. (c), (d) Electric field propagating in the waveguide at the height of the quantum dots, injected on the left into the fundamental eigenmodes of the waveguide; (c) is polarized along the $y$ and (d) along $z$ direction.

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Fig. 2. Scanning electron microscopy images of the sample. (a) Cleaved edge of the sample, which is used to couple the laser into the waveguide. The waveguide at the sample edge is 5.5 µm wide and adiabatically tapers down to the design width. (b) The waveguide is connecting micropillar cavities, which are used for out-of-plane enhancement of the emission of quantum dots; (c) zoom on a single micropillar cavity. The cavity shown is 2.8 µm in diameter, and the waveguide is 1.25 µm wide.

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To suppress residual scattering, we planarize the sample with a polymer and cover it with gold, opening circular apertures over the micropillars and allowing outcoupling of the QD emission [40] (see Appendix A for the details of the fabrication). The device before planarizing and gold coating is shown in Fig. 2. Figure 2(a) shows the cleaved edge of the device, which is used for coupling of a free-space beam. The width of the waveguide then adiabatically tapers down to its design width. The current chip design combines eight different waveguide widths and pillar diameters. Figure 2(b) shows the waveguide connecting five micropillar cavities. However, each waveguide connects 25 micropillar cavities of the same size along one waveguide; the cavities differ in size for different waveguides. The cavity diameters increase from 2.1 to 2.8 µm, and the waveguide width changes from 0.55 to 1.25 µm, both in 0.1 µm steps. Figure 2(c) shows a single micropillar cavity.

 

Fig. 3. (a), (b) Cavity quality ($ Q $) factors and Purcell factors, respectively, measured before planarization of the sample. Blue dots are the mean of the measured $ Q $ factors, blue triangles are the best single measured values for a given cavity diameter, and purple lines show the fit of the $ Q $ factors, with sidewall scattering as a free parameter, and the expected Purcell factor from this fit and a calculated mode volume. (c) Variation of normal cavity mode wavelength and (d) the normal mode cavity splitting with cavity diameter, where blue dots are again mean values. The waveguide width changes with the cavity diameter; see main text for details. The orange lines are numerical simulations. Error bars represent one standard deviation.

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3. EXPERIMENTAL RESULTS

The $Q$ values of the cavities were measured in photoluminescence, using the QDs as a gain medium. The cavity $Q$ values are low enough to not be significantly affected by any QD absorption. Here, the QDs were pumped above-band with a cw Ti:sapphire laser at 780 nm using a high excitation power density of $ {P_{{\rm pump}}} \approx 3 \times {10^3}\;{{\rm Wcm}^{ - {2}}} $. The mean of the measured $ Q $ factors is plotted in Fig. 3(a). The large error bar comes from the distribution of measured $ Q $ factors. We assume that this is due to the moderate QD density, where the QD spontaneous emission does not uniformly fill the cavity mode. To fit the size dependence of the $ Q $ factors, we used $ \frac{1}{Q} = \frac{1}{{{Q_{\rm planar}}}} + \frac{1}{{{Q_{\rm scatt}}}} $ [41], where $ {Q_{\rm planar}} = 8350(50) $ is the calculated fundamental mode $ Q $ factor of the planar microcavity prior to the etching of the micropillars, and $ \frac{1}{{{Q_{\rm scatt}}}} = \frac{{\kappa J_0^2({k_t}R)}}{R} $ is an explicit function for the scattering loss of a micropillar of radius $ R $ with the Bessel function of the first kind $ {J_0}({k_t}R) $, where $ {k_t} = {n^2}{k^2} - {\beta ^2} $, with the core refractive index $ n $, the mode propagation constant $ \beta $, and the sidewall loss parameter $ \kappa $. The only free parameter for fitting is $ \kappa $, and the fit estimates $ \kappa = 3.8(2) \times {10^{ - 10}}\;{\rm m} $, which is comparable to results by others [42,43]. The expected Purcell factors are in the range of 2–3 for the measured $ Q $ factors, with the mode volume from the electric field distribution from the FDTD simulations; see Fig. 3(b). Since the $Q$ values are determined from Fig. 3(a), the discrepancy between the data and simulation is likely due to uncertainty in the FDTD simulations of the electric field distribution originating from finite mesh size. The normal-mode cavity wavelength shifts to a shorter wavelength with small cavity diameters, as shown in Fig. 3(c), reflecting the increased electric field confinement with smaller cavity diameters. The cavity normal-mode splitting before planarization, shown in Fig. 3(d), is roughly a factor of three larger than the simulations, which either is due to uniform process variations because of the consistency of the offset or is, again, related to the FDTD simulations of the electric field distribution. One of the modes is linearly polarized along the waveguide, whereas the other mode is orthogonal linearly polarized.

 

Fig. 4. Red shows the exciton lifetime out-of-resonance with the cavity mode, and blue shows the exciton lifetime on-resonance with the cavity mode. The quantum dot was excited above-band using a 2 ps Ti:sapphire laser at 820 nm with a 76 MHz repetition rate. The emission was collected synchronized to the emission laser to extract the lifetime. The excitation power for the red curve was slightly higher than for the blue curve, to measure with comparable count rates. This led to a different rise time for the two curves, probably due to excitation of biexciton–exciton cascades in the off-resonant case. Nevertheless, this did not affect the measured exciton lifetimes. Uncertainties in the lifetime fit are one standard deviation.

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Although the QDs have random emission energy within a broad Gaussian distribution and position, we measure a single-photon lifetime enhancement above 2 for about 10 out of 100 devices at 5 K without tuning. An example lifetime measurement is shown in Fig. 4, where we compare the lifetime of an exciton on resonance with the cavity with an exciton that is not located in the cavity. The exciton used for comparison is from a QD elsewhere on the sample with the same energy as the cavity-coupled one, to get a reference lifetime of emission into bulk. The Purcell factor is calculated as the ratio of the decay times of an emitter in a cavity and an emitter in bulk, here approximated by the emitter decay time in the waveguide at the same cavity resonance wavelength. Based on the measured lifetimes, the Purcell factor is $ {F_P} = 2.44(6) $.

We measure the second-order correlation statistics by exciting a QD state resonantly through the waveguide mode using a tunable cw semiconductor laser. One expects a flat second-order autocorrelation function with $ {g^{(2)}}(0) $ close to 1 for a Poissonian source, such as an attenuated laser signal, and a dip in the autocorrelation function with $ {g^{(2)}}(0) = 0 $ for a perfect single-photon source. The measured autocorrelation is shown in Fig. 5. With no filtering in the resonance fluorescence and with a Rabi frequency of $ \Omega \approx 1\;{\rm GHz }$, we find $ {g^{(2)}}(0) = 0.00_{ - 0}^{ + 0.04} $, where the error is calculated from the fit uncertainty. This value of the uncertainty of $ {g^{(2)}}(0) $ is comparable to or better than those previously published, where cross polarization and filters were used [16,25–28]. The fit function is a convolution of the known detector response and an exponential function. The single-photon avalanche detectors (SPADs) have a measured detector response of 289(5) ps. Another approach to obtain a $ {g^{(2)}}(0) $ value without deconvolution is through pulsed excitation. However, due to a combination of QDs being present throughout the cavity–waveguide device and the QD density, we cannot use pulsed excitation to only excite single-QD states. This could be remedied in the future through control of the QD density and deterministic QD positioning only in the cavity regions. To estimate the Rabi frequency, we performed a series of $ {g^{(2)}}(0) $ measurements and fit the correlation function following Muller et al. [28].

 

Fig. 5. Second-order autocorrelation of photons from a single quantum dot state in the weak excitation resonance fluorescence regime. The fit function is a convolution of the known detector resolution and the expected signal. The blue solid curve is the fit function, and the red dashed line is the resulting autocorrelation function for an infinitely fast detector, which gives $ {g^{(2)}}(0) = 0.00_{ - 0}^{ + 0.04} $. The Rabi frequency is 1 GHz. Uncertainties are one standard deviation. Inset: Resonance fluorescence when the laser is on-resonance (orange) and residual laser scattering (blue) when the laser is detuned by 0.2 nm from the quantum dot resonance, with an equivalent Rabi frequency of 6 GHz. The residual scattering signal is displayed as a factor of 50 higher than measured, to make the signal visible.

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Beyond 1 GHz we cannot characterize the $ {g^{(2)}}(0) $ as we enter the strong light–matter interaction regime. To estimate the laser scattering at high Rabi frequencies, we detune the laser from the QD resonance (see the inset in Fig. 5). If we assume this is roughly the resonant value, the estimated laser contribution to the single-photon resonance fluorescence signal from this measurement is $ {\lt} 1 \% $ at a Rabi frequency of 6 GHz. For a Rabi frequency of 6 GHz we measured 4 Mcts/s on the SPAD detectors when the QD was in resonance with the cavity. With a detector quantum efficiency of approximately 0.22 at 930 nm, and considering a 10% counting error due to the detector dead time of 50 ns, the count rate corresponds to approximately 20 Mcts/s on the detector. We note that the high antibunching of the device is only present with the metal planarization. Without the metal planarization, the autocorrelation was at best close to 0.5, and in many cases it showed only a very small deviation from 1, as the laser scattering competes with the single-photon resonance fluorescence from the single-QD state.

4. DISCUSSION AND CONCLUSION

Four parameters are important in the characterization of single-photon sources: The source brightness, i.e., how many useful photons are collected; the source efficiency, i.e., the percentage of arbitrary time bins occupied by single photons; suppression of multi-photons, as measured by the second-order correlations ($ {g^{(2)}}(t) $); and the indistinguishability of the quantum light. In many emerging quantum optics experiments and applications, the brightness of the source is critically important to a successful outcome. For example, boson sampling was simulated using QD single photons [44]; the source produces 26 Mcts/s without normalizing out detector inefficiencies using cross polarization. With our approach this could be boosted by a factor of 2, yet in some cases, as in Ref. [44], where a single photon source is demultiplexed, other processes (for instance, Pockels cells) are the limiting factor to useful brightness. For some quantum communications protocols, such as BB84, single-photon brightness may provide an appealing advantage to attenuated lasers. For higher-order photon correlations, this reduces the measurement time by the correlation order squared [e.g.,  a factor of 4 for $ {g^{(2)}}(t) $], which allows for the expansion of the number of interacting nodes and photons. In other applications, such as linear optical quantum computing [9] and quantum metrology [5–8], the source efficiency above certain thresholds is critically important, while the source brightness is an added benefit. Single-photon sources require various degrees of multi-photon suppression, but while some applications require extremely high indistinguishability, others require none.

Our device design has a variety of flexible attributes. The device has partially overlapping cavity modes of orthogonal polarization; thus, the emission can be unpolarized for certain applications such as BB84, or polarized for other applications such as boson sampling. Furthermore, the cavity-mode splitting can be adjusted through processing. However, the device design is not without issues. These include the alignment of the in-plane QD dipole with the waveguide mode for optimum pump light efficiency and the alignment of the QD with the pillar cavity, which here is not optimized. Both of these issues relate to the classical efficiency of the device, for instance, the number of working devices and the pump efficiency, and can be overcome with further engineering.

While the waveguide coupling to the cavity provides efficient in-plane QD resonant excitation, a small component of the QD resonance fluorescence couples back into the waveguide and not into the cavity mode. From our simulations, we estimate this to be about 10%–15% of the total QD emission. Finally, while a count rate of 20 Mcts/s constitutes a bright source, the system is cw pumped and the radiative decay rate is 2.5 GHz. The large difference is due to spectral-diffusion-induced blinking of the emission. Adding a small amount of nonresonant light can markedly reduce this effect [45,46]; however, this was not implemented here, to avoid the need for spectral filters.

The presented device is a first step toward an all integrated single-photon source. A future device could divert a small fraction of the light on-chip for real-time metrology analysis (the 10%–15% discussed above), while sending most of the light off-chip to be used in an application. Such an approach would require low-loss waveguides [47], on-chip detectors [48], and schemes to measure on-chip indistinguishability and multi-photon suppression [30]. While each presents its own challenges, they are individually useful in various emerging quantum photonics applications.