Transfer-printed single photon sources coupled to wire waveguides

Photonic integrated circuits (PICs) are attractive platforms to perform large-scale quantum information processing. While highly-functional PICs (e.g. silicon based photonic-circuits) and high-performance single photon sources (SPSs, e.g. compound-semiconductor quantum dots (QDs)) have been independently demonstrated, their combination for single-photon-based applications has still been limited. This is largely due to the complexities of introducing SPSs into existing PIC platforms, which are generally realized with different materials and using distinct fabrication protocols. Here, we report a novel approach to combine SPSs and PICs prepared independently. We employ transfer printing, by which multiple desired SPSs can be integrated in a simple pick-and-place manner with a theoretical waveguide coupling efficiency>99%, fulfilling the demanding requirements of large-scale quantum applications. Experimentally, we demonstrated QD-based SPSs with high waveguide coupling efficiencies, together with the integration of two SPSs into a waveguide. Our approach will accelerate scalable fusion between modern PICs and cutting-edge quantum technologies.

made printing g S1(a). The d an optical holds a glass ed. The stamp rd184, Dow bumps with a The pillar-like reducing the contact area with the sample substrate, resulting in an improved positioning accuracy during the transfer process. The position of the stamp can be controlled with fine adjusters in the three axes.
With the top stage, the pitch and roll of the stamp can also be controlled. The right stage (blue) holds SPS and waveguide samples on the top, the positions of which can be finely tuned by the combinations of fine adjusters and piezo actuators. The sample rotation can also be corrected using an incorporated rotational stage. The sample image was obtained by the microscope, the magnification of which can be switched by rotating the turret equipping objective lenses. For the transfer printing, first, we attached a PDMS stamp to an appropriate airbridge nanobeam cavity under the microscope, as shown in Fig. S1(b). Then, we quickly peeled the stamp off by moving an actuator in the vertical direction ( Fig. S1(c)). The peeling speed is roughly 3 mm/s. The success probability of this picking up process is about 70~80% in the current setup and condition. Then, we brought the lifted nanobeam cavity onto to a target waveguide. Subsequently, the cavity was carefully loaded above the waveguide manually using the piezo actuators (Fig. S1(d)). During the loading process, we paid attention to the cross markers patterned in both the coupons respectively containing the cavity and the waveguide. The same cross markers are patterned to both the sides of the waveguide: a part of one of them can be seen in Fig. 3(a) in the main text (see also Fig. S1(f)). The top cross markers on the cavity coupon are slightly enlarged compared to that on the waveguide coupon and thus the image contrast formed between the two elements served as a guide for sample positioning. Figure S1(e) shows a picture during the nanocavity release by slowly peeling the stamp off. We succeeded in this release step almost without fail in the current transfer condition. A microscope image of a completed sample is shown in Fig. 3(a) in the main text. The transferred SPS is bonded tightly on the waveguide wafer via van der Waals force [3]. When integrating two nanocavities into a waveguide as shown in Fig. 5(a), we did not see significant disturbance on the printing process by the prelocated nanocavity. This suggests the possibility for dense integration of a larger number of SPSs by transfer printing, which would be required for realizing large-scale quantum PICs. In this regard, the parallel transfer of multiple photonic structures by transfer printing [4] will also be of importance for scalable integration.
In order to evaluate the printing accuracy, we fabricated 8 different printed nanocavities with the same design and measured them with a high resolution optical microscope. A photograph of a typical completed sample is shown in Fig. S1(g). After the digital edge enhancement of the picture, we deduced the perimeter of each element, which was employed to determine the center positions of the cavity and waveguide. The absolute positioning error between the two elements in the y direction (normal to the waveguide) was estimated to be ~60 nm on average. The standard deviation of the error was evaluated to be ~40 nm. Also from the pictures, unwanted sample rotations are found to be less than 1 degree.
In the current work, we did not pre-select a suitable nanobeam cavity. Therefore, only one out of three to four samples contain QDs resonating with the cavity mode. The sample discussed in the main text is one of such samples. For the sample with two SPSs on the single waveguide, we prepared 8 pairs of such structure. One of them have QDs in each cavity and has been used for the discussion in the main text. This randomness in the SPS fabrication can be easily avoided by pre-selecting suitable QD SPSs by optical experiments prior to the transfer processes.
We used transfer printing for the fabrication of glass-cladded wire waveguides. For this purpose, first, we prepared airbridge wire waveguides with grating exit ports [5] into a 130 nm-thick GaAs. The waveguide width was chosen to be 220 nm as discussed in the supplementary section 4. We placed the waveguides on a glass substrate by transfer printing. We then formed an upper clad on the waveguide by a spin-on-glass process (FOX15, Dow Corning). The clad surface above the waveguide was evaluated using an atomic force microscope and was found to be smooth with a root-mean-square roughness of only 0.4 nm. The thickness of the glass above the waveguide (= d) was precisely controlled to be 300 nm for the first sample shown in Fig. 3(a) by tuning the amount of solvent in the liquid glass material and the spin speed.
For the experiments in Fig. 5(a), d = 270 nm was used.

Device design
We optimized the SPS based on the PhC nanobeam cavity on a glass-cladded wire waveguide [6] so as to maximize the single photon coupling efficiency into the waveguide. Here after, we conducted all the electromagnetic simulations by using the three dimensional finite difference time domain (FDTD) method. First, we designed the PhC nanobeam cavity on a flat glass substrate [7]. We considered a GaAs nanobeam with a width of 370 nm and a thickness of 130 nm. The air holes were patterned with a period (a) of 230 nm and radii of 53 nm. The lattice period was modulated near the cavity center so as to support a very high Qfactor of over 5 million for the fundamental cavity mode at the normalized frequency (a/λ) of 0.249. The polarization of the fundamental mode is mainly transverse electric (electric field parallel to the substrate). Details of the nanocavity design are described in the supplementary section 3. Then, we simulated light coupling into the glass-cladded waveguide placed directly below the cavity with separation d. We set the waveguide width and thickness to be 220 nm and 130 nm, respectively. These parameters were chosen so as to maximize the cavity-waveguide coupling strength for a given d (see the supplementary section 4): this optimization is essential to increase the maximum possible cavity-waveguide coupling efficiency (η) in design. The calculation of η starts with the simulation of the investigated cavity mode until reaching to its steady state by FDTD method. Then, we measured all the light leakage from the simulator, together with that from the waveguide. In this way, we can deduce η by the ratio of waveguide light leakage to that from the whole domain.
In an analytical fashion, we can describe η by the following equation: where Q0 and Qwg are the design cavity Q without and with the waveguide, respectively. 1/Qscatter expresses the additional photon loss into free space due to the introduction of the waveguide. From the equation, for realizing a high η, it is vital to design a very high Q0 and a low Qwg, while suppressing 1/Qscatter. The high Q0 (>5 million) of our PhC nanobeam cavity is highly suitable for increasing η. The reduction of 1/Qscatter is possible by taking a large enough d, which in turn exponentially increases Qwg. We overcame this difficulty by optimizing the waveguide parameters so as to minimize Qwg to 1,300 for d = 300 nm (see the supplementary section 4). In this design, 1/ Qscatter becomes negligible and η reaches to be 99.4%. In contrast, for ds much smaller than 300 nm, the above discussion based on the perturbation theory (coupled mode theory) does not hold anymore, since the index modulation by the waveguide becomes too strong to treat as a perturbation for the cavity mode. In this case, the significant cavity-to-free space leakage is turned  Figure S6(c) ith θ from 0 to 1 ven under the ex 00 nm and θ = ssuming the exp han 100 nm and ear-unity η ove ansfer printing ver 50,000.

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ement setup
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Experimental estimation of η and β.
The estimation of experimental cavity-waveguide coupling efficiencies (ηexp) was done based on the measured cavity Qfactors. First, we measured 9 nanobeam cavities that were placed on flat glass and did not coupled to the waveguide. By fitting the measured PL peaks with Lorentzian function, we deduced an average cavity Q-factor on flat glass (Qave) to be 13,000. The standard deviation of the Q values was estimated to be ~ 1,000. In addition, the emission spectrum measured for the cavity mode coupled to the waveguide was fitted to deduce the experimental Qfactor (Qexp) of 3,600. The larger Qexp than the designed Q of 1,300 for d = 300 nm can be explained by the deviation of the structural parameters in the fabricated device: in particular, the change in the cavity resonance wavelength disturbs the phase matching between the cavity and waveguide and degrades their coupling strength. Using the measured cavity Q-factors, we deduced an ηexp of 72% based on the following equation: This equation assumes that the observed reduction of the Qfactor when introducing the waveguide is dominated by the leakage of photons into the waveguide. This assumption is fairly reasonable in the current situation where d is large enough to suppress the additional cavity photon leakage into free space, as confirmed in the numerical simulations (see the supplementary section 2). Even with fabrication imperfections, we can expect the dominance of the waveguide loss: from the view point of the cavity, the largest index perturbation inducing its photon leakage is provided by the waveguide itself. Indeed, we have experimentally confirmed that the significantly-suppressed free space radiation from the cavity after coupling to the waveguide, as discussed using the measured spectra in Fig. 3(c) in the main text.
For the case when loading the two cavities to the single waveguide, we measured a Q-factor of 1,000 (950) for the left (right) cavity, resulting in ηexp of 92% (93%). In this case, ηexp improved due to the slight reduction of d to 270 nm, which reduces the cavity Q-factors and increases the coupling between the cavities and the waveguide. We note that a more direct measurement of ηexp will be possible by measuring the transmission spectra of the waveguide after coupling to the cavity [6].
Regarding the estimation of the experimental β (βexp), we performed time-resolved PL measurements. First, we measured emission decay rates of several single QDs that were embedded in PhC nanobeams on plane glass and decoupled from any cavity modes. The average decay rate was measured to be 0.5 GHz (= γother), which is roughly half of that for QDs in an unprocessed region of the sample. This reduction of the decay rate stems from partial photonic bandgap effect in the PhC nanobeam [2]. Then, we measured emission decay rates of the investigated QD emission peaks coupled to the cavity mode (γexp). For deducing γexp , we performed fitting for the measured PL decay curves using a model consisting of a 3-level QD [11]. We fit the whole decay curve including the initial intensity rise for better lifetime estimation. In the model, the QD characteristic is described with two decay time constants, composed of carrier relaxation time from the upmost level to the middle radiative state and spontaneous emission time to the lowest level. An important note here is that, in this fitting model, the two time constants equally impact on the shape of PL decay curve in essence. There, slower time constant always determines the slope of the PL decay irrespective of the assignment of the two time constants to the actual physical processes. As such, one should keep in mind that there is a possibility that the decay slope is determined by the carrier injection process [11]. Whereas, we know that our similar QD exhibits a very fast carrier decay within a time less than 50 ps [12]. Given this previous observation, we treated the slower time constant in the deduced values as the spontaneous emission rate in the following discussion. With the decay rate values for spontaneous emission, we deduced βexp by the following equation [13]: For the QD discussed in Fig. 4(b) in the main text, γexp was measured to be 3.9 GHz at the resonance, resulting in βexp of 87%. For the QD in the left (right) cavity in Fig. 5(d)((e)) in the main text, γexp was measured to be 2.2 (1.2) GHz at 3 K, at which the QD is detuned from the cavity resonance by 2.0 (1.8) nm. The resulting βexp was 77% (58%). The experimental single photon coupling efficiencies into the waveguide were simply obtained by multiplying the two efficiencies, that is ηexpβexp. It is noteworthy that the estimation of βexp by the lifetime measurements can exclude the contribution of photon emission from the other QDs. This is important since our QD SPSs exhibit certain levels of background cavity emission that is probably supplied by other QDs present in the cavity (~2 QDs on average with a rough estimation).

Achievable single photon coupling efficiency with current technology
In the current demonstration, βexp did not reach to the maximum possible value probably due to the deviation of the QD position from the cavity field maximum, which degrades the Purcell effect enhancement. If the QD position was optimum, the maximum βexp would reach to 99.7%. Moreover, by optimizing the waveguidecavity distance (d) to 250 nm, it could be possible to increase η up to 96.3%, with slight reduction of the maximum possible β to be 99.4%. Overall, it would be possible to achieve a total single photon coupling efficiency of ηβ = 95.7% even under the present quality of the nanocavity fabrication. Meanwhile, we have already demonstrated a cavity Q-factor over 50,000 for PhC nanocavities [14]. With this fabrication quality, it would be possible to achieve ηβ over 98.4% with d = 250 nm. Moreover, if the Q-factor reached to that of the state-of-the-art PhC nanobeam cavity (~ one million), the maximum possible ηβ would become 99.6% for d = 300 nm. These estimations imply that the near-unity coupling of single photons into the waveguide is already within reach of the current process technology. It is noteworthy that the optimum d for realizing the highest possible ηβ varies with the achievable cavity Q-factor when not coupled to the waveguide, since ηβ is determined between the waveguide coupling and the Purcell effect which increase or decrease depending on the total Qfactor. Figure S8 shows measured spontaneous emission rates plotted as a function of cavity-QD detuning for the SPS discussed in Fig.  4 Figure S9 show PS coupled to a rating output po he position of the y moving the sa nder the micros rected at the na m continuous w btained almost measurement por he cavity couple ork, we perfor measurements (w mission from a plitter added to t ur PL measurem mall area of det microscope acces cations of the si mission from b eparated by 24 μ n text. The fast emitter-cavity when detune ort our conclu riginates from solid line in the inewidth of the olution does not the expectation in cavity. We con e QD to acousti QDs is known t enhancement [1 rve with a full wi match with thos dependence of th g emission fro ws a comparison waveguide, resp orts. Each spect e PL detection at ample such that scope. For all d anocavity center wave laser with a the same emi rt, suggesting be es to the waveg rmed the seco which often req a single grating the detection pa ment setup. Ou tection are loca ssing the sample ngle photon det oth the exit po μm). test emission r resonance. Th d from the r usion that the the Purcell e e figure shows a e cavity mode t match with the n from the conve nsider that this d ic phonons. The to support a br 5]. Indeed, th idth half maxim se discussed in t he decay rates of om the two e n of two emissio pectively measu trum was measu t the spectromet the detection p detection positi r. The pump so an average pow ission spectra r eam splitting at guide. Meanwhi ond order inte quire a beam s g out-coupler a ath. This is due t r single photon ated far away ( e. As such, the fie tectors are too s orts at once (th rate of 3.8 ns -1 e emission rat resonance. The e emission ra effect within th a Lorentzian pe (Q = 3,600). Th e Lorentzian pea entional theory discrepancy is du e phonon-assist road range of th he widened ra mum of 1.5 nm (2 the literature.