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Abstract
High coincidence-to-accidental ratio (CAR) is crucial for photon-pair sources (PPSs) integrated with pump reject filters (PRFs) in silicon, but CAR values currently reported for integrated PPS/PRF chips still fall short of those achieved using stand-alone sources with external PRFs. Here we report measured and modelled CAR values for a micro-ring resonator PPS integrated with a PRF consisting of a three-stage, cascaded (via their through ports), contra-directional coupler (CDC) that compare favorably even with some stand-alone sources. CDC-based PRFs provide the benefits of compact area and wide reject bands without a need for tuning, in comparison to prior-art implementations.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Quantum computational advantage has been demonstrated recently using photons manipulated by bulk-optic components to implement large-scale Boson sampling [1]. As proposed in 2012 [2], further scaling and performance advantages should be possible by integrating the components on a single photonic chip. More generally, the integration of multiple single-photon sources, beam-splitters, phase shifters, and single-photon detectors will be required to realize fault-tolerant quantum computations based on linear optical quantum computing [3,4]. In addition to computing, heralded single photon sources can be used in practical secure quantum communications and key distribution protocols as explained in [5,6]. Quantum correlated photon-pair sources have several potential applications in quantum enhanced sensing such as optical target detection based on temporal correlations of photon-pairs [7] and protein concentration measurements [8].
On-chip, heralded, single-photon sources have been realized in silicon using photon pairs generated by spontaneous four-wave mixing (FWM) in long waveguides [9,10], micro-ring resonators (MRRs) [11–16], and photonic crystal structures [17]. These sources, based on degenerate or non-degenerate spontaneous FWM, require the use of high ($>90$dB) extinction ratio (ER) pump rejection filters (PRF) to achieve a high coincidence to accidental ratio (CAR) in photon-pair coincidence measurements [18]. While CAR values in excess of 12,000 have been achieved using optimized micro-ring resonator sources in silicon with external filters [19], the best results from sources with integrated PRFs report a CAR $< 100$. To be useful in sophisticated, fully-integrated information processing circuits, it is desirable to improve the performance of sources with integrated, small-footprint PRFs.
Previous works have reported integrated PRF based on cascaded MRRs [20–23], Bragg-grating filters [18,24], cascaded Mach-Zender Interferometers (MZIs) [25], and sub-wavelength waveguide filters [26]. All of these approaches have drawbacks: Cascaded MRR are narrow-band filters that require tuning elements; Bragg grating filters need to be millimeters long [18] and cascading Bragg gratings is complicated by resonances created in the reject band ; cascaded MZIs occupy several square millimeters [25] and they also require tuning elements to achieve high ER; and sub-wavelength waveguide filters share the same limitations as Bragg grating filters, while also suffering from larger fabrication variability.
In this work, we integrate an MRR photon-pair source with a PRF comprising a three-stage, contra-directional-coupler (CDC) in an SOI platform [27–30]. Advantages of cascaded, multi-stage, CDC filters include their compact areas (as small as 700x14.44 $\mu m^2$ [31]), their wide reject bands (that can span 6nm as in [31]), and the fact that they do not require tuning elements. Other potential advantages stem from the relative ease with which the rejected pump light can be accessed without the need for a circulator. These include redirecting it to pump another pair source, or off-chip to reduce heat load, and/or to on-chip power or spectral monitors (see Fig. 1(a), and Ref. [32]). We achieved a peak CAR of 125 (corrected for detector dark counts) [33], or 27 (uncorrected) for pump powers less than 1mW injected into the MRR, which represents a two fold improvement over previously reported values [18,21,22,25,34].
Fig. 1. (a) Schematic of a CDC unit cell where the ports and the physical parameters are labeled. (b) Dispersion curves for the coupled-waveguide (strip) structure without corrugations simulated in Lumerical-MODE solutions using the CDC parameters of $G=220$nm, $W_1=450$nm, $W_2=550$nm and $\Lambda =320$nm. (c) The solid blue and magenta lines are the measured spectra of the through-port and drop-port of the single-stage CDC whose parameters are listed in Table 1, respectively. The dotted green line is the through-port simulation result using the Eigen-mode expansion (EME) approach described in [35]. The solid red line is the plot of Eq. (1) using the same parameters listed in Table 1. (d) Simulation result of the three-stage cascaded CDC filter, shown as yellow dotted line obtained using the EME approach, is compared to the measurement result of an actual three-stage cascaded CDC filter shown in solid blue line. The solid red line is the plot of Eq. (2) using the same parameters listed in Table 1.
In Section 2, we describe the design of our CDC-based, three-stage PRF and compare the measured performance of stand-alone devices with simulations. In Section 3, we show experimental results for our PRF integrated with an MRR photon-pair source, including coincidence measurements of the resulting photon pairs, and compare these with model predictions. Finally, in Section 4, we discuss the implications of the experimental and theoretical results obtained, toward scaling photonics-based quantum computing and communication systems.
2. Stand-alone, multi-stage, cascaded CDC filters
In this section, we explain the design flow of our multi-stage, CDC, pump-reject filter, and compare the simulation results to the measurement results obtained from stand-alone filter devices fabricated by electron-beam (E-beam) lithography.
2.1 Design
As shown in Fig. 1(a), the CDC unit cell consists of two parallel $SiO_2$-clad strip silicon waveguides with average widths, $W_1$ and $W_2$, separated by an average distance $G$. Each is square-wave-corrugated with amplitudes $\Delta W_1$ and $\Delta W_2$. The definitions of these parameters, chosen for demonstration purposes (as explained below), are summarized in Table 1.
Table 1. Definitions of the physical parameters of the CDC unit cell shown in Fig. 1(a).
The relevant optical parameters of this CDC, that are accessible in a published compact model compatible with Ansys/Lumerical Interconnect [37], are defined in Table 2. The target operating parameters, $\lambda _{CDC}$ and $\Delta \lambda _{null}$, for this application are determined by the MRR mode spectrum. Specifically, $\lambda _{CDC}$ should coincide with the pump mode wavelength and $\Delta \lambda _{null}$ should be approximately the free spectral range (FSR) of the MRR. The target $ER$ is $\geq 90dB$. These requirements are essential to reject the pump power, needed for the photon-pair generation, and to achieve a high CAR value for the photon-pairs detected at the single photon detectors [18]. The un-corrugated waveguide parameters $W_1, W_2$ and $G$ were chosen based on previous work [32] that showed these provide an appropriate baseline for fine-tuning the other physical parameters to realize high-quality CDC at operating wavelengths near $1.5 \mu m$ with bandwidths $\sim 5 nm$, using the available E-beam process. The design starts by plotting the dispersion curves of the two relevant coupled modes characteristic of the un-textured ($\Delta W_1=0$, $\Delta W_2=0$, $G\ne 0$) strip waveguides, $n_{eff1}$ and $n_{eff2}$, as shown in Fig. 1(b). Together with the average dispersion, $n_{eff,avg}$, the desired center wavelength of the CDC, $\lambda _{CDC}$, then determines $\Lambda$. The CDC filter first-nulls bandwidth, $\Delta \lambda _{null}$, and the maximum extinction ratio $ER$ are each related to both $\kappa$, and the total number of unit-cells in the CDC, $N$, as described in Refs. [30,36]. Generally, large ER requires large $N$ but the maximum value of $N$ is limited by the slight, gradual non-uniformity of $n_{eff}$ over the length of the fabricated devices, which is process specific. For the process used here, reliable CDC are obtained for overall lengths $\le \sim 400 \mu m$, which sets a value of $N=1200$. The final optical parameter that needs to be determined is therefore $\kappa$, which is controlled by the remaining physical parameters $\Delta W_1$ and $\Delta W_2$. With the target $\Delta \lambda _{null} \sim 5 nm$, the appropriate value of $\Delta W_1$, set equal to $\Delta W_2$ for simplicity, is $60 nm$. This results in an estimated $ER \sim 45dB$ for $N=1200$, based on the coupled mode theory (CMT) estimate for the transfer function, $T_{through}$, of this single-stage, CDC, pump-reject filter [28,30].
where $s^2=\kappa ^2-(\frac {\Delta \beta }{2})^2$, and $\Delta \beta = \beta _1 + \beta _2 -2\pi /\Lambda$, which reflects the phase-matching condition of the CDC grating. $\beta _{1,2}$ are related to the effective indices $n_{eff_{1,2}}$ as $\beta = 2\pi n_{eff}/\lambda$.Table 2. Optical parameter definitions of the CDC unit cell.
From Eq. (1) it is clear that the maximum $ER_{max}$ occurs at $\lambda _{CDC}$, where $\Delta \beta = 0$, and is given by $ER_{max}=sech^{2}(\kappa N\Lambda )$. The overall theoretical ER can be further increased by cascading several identical CDC stages via their through-ports. For $M$, cascaded, identical stages with the same $N$ and $\kappa$ values, the net transfer function becomes
The transfer functions for the single and three stage CDC filters were calculated using Eq. (1) and Eq. (2), as shown as red curves in Fig. 1(c) and Fig. 1(d) respectively. The $n_{eff}$ values for this calculation were obtained using Ansys/Lumerical’s MODE solutions to find the dispersion of the coupled modes of the un-corrugated waveguides separated by a distance G, and the $\kappa$ value was estimated from a finite difference time domain (FDTD) bandstructure simulation of the full corrugated structure defined by the parameters in Table 1. The transfer functions were also estimated using the Ansys/Lumerical eigen-mode expansion solver, with the results shown as green-dashed lines in the corresponding plots. The blue solid lines in Figs. 1(c) and 1(d) show the measured data.
It is clear that while the coupled mode model replicates the reject bandwidth quite well, the center wavelength and maximum ER are significantly different than the measured values. The center wavelength $\sim 1552.3$nm, the first null bandwidth $\sim 4.8$nm, and the maximum ER $\sim 45$dB of the measured single-stage CDC filter are in much closer agreement with the model results from the eigen-mode solver. The center wavelength and bandwidth of the three-stage CDC filter are also in quite good agreement, but the measured maximum ER of $\sim 60$dB in this case is far below the model prediction of $\sim 157$dB. Our ability to accurately assess the true extinction ratio of the cascaded CDC filter bank is currently limited by the scattered light reaching the output coupler from the input GC region, as shown in Fig. 3 [25].
Concluding this CDC design section, it is to be noted that we chose uniform CDCs, i.e., without apodization, in order to maximize our through-port ERs for given bandwidth and length constraints. Higher drop-port efficiencies can be achieved using apodization [31] but this comes at the expense of the through-port ER.
2.2 Fabrication
Stand-alone single and triple stage CDC were fabricated using the target physical parameters listed in Table 1. These devices were patterned in an HSQ resist on an SOI wafer consisting of 220nm silicon on top of a 2$\mu m$ buried oxide, using a JEOL JBX-8100FS, 100 keV E-beam writer. The chips were covered with 2.2$\mu m$ thick silica cladding layers. The lithography and subsequent plasma etching were done by Applied Nanotools Inc. [38,39]. The measured transfer functions are shown overlaid with the corresponding simulation results in Fig. 1(c) and (d).
While the experimental and simulated results are in reasonable agreement for the single stage device, only the bandwidth of the measured three-stage device agrees favorably with the simulations. The dynamic range of our detection apparatus, together with the combined insertion loss of 18 dB associated with the input and output grating couplers (GC), limited the measurable ER to approximately 60 dB. The dynamic range of our optical power meters is $\sim 70-80$dB, and the scattering light from the input GC that appears at the output GC as noise at the optical power meter further degrades the dynamic range. Both the input and output GCs were aligned to the same fiber array during testing of these standalone CDC filters. This limitation motivated us to redesign the layout of the three-stage CDC filter integrated with an MRR photon-pair source to isolate the input GC from the output port of the CDC filter, as shown in Fig. 2(ai).
Fig. 2. (ai) Schematic diagram of the layout of the MRR photon-pair source integrated with the three-stage CDC filter showing the input and output GCs and the output EC of the circuit. (aii) A microscope image showing the fabricated MRR photon-pair source, the directional coupler (DC), and three-stage CDC filter. (b) The power spectra of the MRR monitor output from the DC is shown in blue, the drop-port of the first stage of the three-stage CDC filter shown in yellow, and the through-port of the cascaded three-stage CDC filter is shown in green. (c) The through ports spectra of one-, two- and three-stage CDC filters cascaded via their through-ports, as well as the power measured from the calibration structure connecting a GC to an EC. (d) The stimulated FWM idler power (measured, solid lines; simulated from 3, dotted lines) versus the pump power at the input waveguide of the MRR for two different signal laser powers [$5 \mu W$ and $10 \mu W$] at the input of the MRR.
3. Integration of a CDC filter with a MRR photon-pair source
In this section, we show the experimental results for a three-stage CDC filter integrated with an MRR photon-pair source. A chip containing several circuits, each consisting of MRR photon-pair sources connected to three-stage CDC filters with the layout shown in Fig. 2(ai), was fabricated using the same process described in the previous section. The input pump beam, the tapped MRR monitor output channel, and the drop-port output from the first CDC stage were all coupled on or off chip via GC. The outputs of the CDC filters, i.e., the through-ports of the three cascaded filters were coupled out of the chip using edge couplers (ECs) [38]. All of the remaining ports of the three-stage CDC filters were terminated to avoid reflections.
3.1 Passive measurements
Detailed measurement results were obtained from the specific device shown in Fig. 2(aii). This MRR is an all-pass MRR which has a radius of $18 \mu m$, a waveguide width of 425nm chosen to minimize the dispersion at 1550nm, and a gap between the bus and the ring of 240nm. These dimensions are layout dimensions, not the fabricated dimensions. The tap directional coupler (DC) routed $8 \%$ of the MRR through port to the monitor GC. The tap coupler before the CDC filter was included merely for convenience, so that a single-port measurement yields all three relevant resonances of the MRR. Each of the CDC filter stages has the nominal physical parameters given in Table 1.
All the waveguides used for routing, from the input GC to the MRR and from the tap DC to the output GC, are 500nm wide. The output of the cascaded three-stage CDC filter is connected to an EC via a 3 $\mu m$ wide, 2.4mm long waveguide to reduce the loss of MRR-generated photon-pairs between the CDC filter and the output EC. The input GC, connected to the MRR, has a coupling loss of 11.5dB. The measured FSR of the MRR is 5nm, as shown in Fig. 2(b). A single-mode lensed-fiber is used to collect the light out of the chip, via the EC, with a combined measured coupling loss of 5dB at 1550nm which is outside the reject band of the CDC filter. The measured CDC filter reject band is $\sim$3.8nm and its center wavelength is 1558.7nm, as shown in Fig. 2(b). The blue curve in Fig. 2(b) shows the three resonance wavelengths of the MRR that were used in the stimulated FWM setup, where the signal, pump, and idler wavelengths are 1553.48nm, 1558.45nm, and 1563.465nm, respectively. The green curve is the output spectrum of the three-stage CDC measured using a lensed fiber.
The ER of a single-stage CDC filter is measured from Fig. 2(c) to be $\ge 31$dB within $+/-1.8$nm at 1555.95nm. This is less than that ER measured for the standalone devices, which were nominally of the same design. The two chips were fabricated a year apart, and we attribute this reduced performance to changes in the nano-fabrication process between the two runs. The measured ERs for the two-stage and the three-stage CDCs are 45dB and 59dB, respectively, the latter again being limited in part by the dynamic ranges of our detectors, but also possibly by stray scattered pump light that appeared at the output ECs without passing through the CDC chain [25]. This latter contribution was minimized, but not eliminated in our layout (Fig. 2(ai)) by introducing large lateral ($\sim 2 mm$) and longitudinal ($\sim 3.6 mm$) offsets of the input GC from the output EC. This large L-shaped offset of input and outputs reduced the stray light detected at the EC output by a factor of $\sim 10 dB$ in comparison to a long but inline geometry when comparison tests were done on the structures shown in Fig. 3(a). The data shown in Fig. 3(b) was obtained by injecting laser light into GC1 of both the straight and the L-shape filters, where the output waveguides of those bypassed the CDC chain and were routed directly to ECs (un-monitored) adjacent to the monitored ECs at the outputs of the CDC filters. In this experiment the signals from the monitored ECs were measured within the rejection bands of the CDCs using one of the single photon detectors described in the next section.
Fig. 3. (a) Schematic diagram of the layout for the comparison between the straight shape CDC filter and an L-shape CDC filter. (b) Crosstalk measurements for both the straight and L-shape three stage CDC filters at input power of 0dBm to GC1 in (a) and recording the power output from their respective edge couplers within the reject bands of both CDCs.
3.2 Stimulated four wave mixing measurements
Figure 4 shows the setup used for stimulated FWM measurements of the MRR photon-pair source filtered with CDCs. A high-power, Keysight-N7744A laser, with absolute maximum rating of $16 dBm$, is used as the pump laser, and an HP-81682A tunable laser is used as the signal laser. Both lasers are filtered using JDSU-TB9 tunable Bragg-grating, band-pass filters (OTF1 and OTF3) to filter out the spontaneous emission noise. These filters have 3-dB bandwidths of 0.27nm. Both lasers are combined together using a 3dB, polarization-maintaining, directional coupler (PM-DC) and injected into the SOI chip via a 21-degree, angle-polished, fiber array. An HP-81635A power meter was used to measure the optical spectra of the MRR and CDC filters, shown in Fig. 4 as the "Monitor PM." The output power at the idler wavelength is extracted from the CDC filter output and filtered by OTF2 (OTF2 is identical to OTF1 and OTF3). OTF2 gives a large adjacent channel isolation by filtering any noise coming from the pump and signal lasers that appears at the idler wavelength. The total signal path loss, from the signal laser to the input of the fiber array, is $8 dB$. The pump path loss, from the pump laser to the fiber array input, is $7 dB$. The idler power is measured using an IDQuantique-ID210 avalanche photodiode (APD), single-photon detector (SPD), operated in the free-running mode. Its dark count rate is about $7.3$kHz, detection efficiency is $10\%$, and dead time is $100 \mu s$.
Figure 2(d) shows the idler power, generated by stimulated FWM and detected by the SPD, as it varies with the pump power at the input waveguide of the MRR for two signal laser power levels, $P_{sig}=[ -3dBm, 0dBm]$, which correspond to $[5 \mu W$ and $10 \mu W]$ of signal power reaching the input waveguide of the MRR. Figure 2(d) resembles the normal quadratic dependence between the idler and the pump powers at a fixed signal power. At a fixed pump power, we observe a (nearly) linear relationship between the idler and the signal powers. The idler power can be estimated from the following equation [14]
Fig. 4. Experimental setup for stimulated FWM measurement of the MRR photon-pair source filtered with three-stage CDC filter. OTF1: Optical tunable filter centered at the pump resonance. OTF3: Optical tunable filter centered at the signal resonance, OTF2: Optical tunable filter centered at the idler resonance, PM-DC: Polarization-maintaining directional coupler, SPD: Single-photon detector, SOI: Silicon-on-Insulator, TEC: thermo-electric controller. Pol.C.1,2: Polarization controllers 1 and 2. Monitor PM: Monitor optical power meter.
From this, we estimate the rate of photon-pair generation per unit power of the pump laser to be around $R_{spont.}= (1.06 MHz/mW^2)P^2_{pump}$. The estimated $R_{spont.}$, for an input power of $13$ dBm from the pump laser to the whole setup, which corresponds to 0.56mW at the input waveguide of the MRR, would then be $\sim 335$kHz.
3.3 Coincidence measurements
Figure 5 shows the setup used for coincidence measurements of the MRR photon-pair source filtered with the three-stage CDC filter. The input light, coming from the pump laser, is coupled to the MRR through the input GC from one side of the chip and the light from the CDC filter output is coupled out of the chip via the EC and the lensed SM-fiber. The polarization of the light emerging from the lensed fiber is adjusted by (Pol.C.2) then passed to a 3dB PM-DC. One output of the 3dB PM-DC is filtered with OTF3 aligned to the signal wavelength, and the other output is filtered with OTF2 aligned to the idler wavelength. The measured isolation of OTF2 at the center wavelength of OTF3 was $50$dB and the measured isolation of OTF3 at the center wavelength of OTF2 was also $50$dB. The function of the 3dB-PM fiber splitter combined with the tunable filters is wavelength division de-multiplexing of the idler and signal photons. This causes an unavoidable, additional 3dB loss due to the use of the PM splitter. The output of each of the filters, OTF2 and OTF3, is connected to an IDQuantique-ID210 APD-based SPD. Both SPDs (SPD1 and SPD2) have $10 \%$ detection efficiencies, and their dark count rates are approximately $7.3$kHz and $8.2$kHz, respectively. Both SPDs are operated in free-running mode, and their dead times are set to be $100 \mu$s. These SPDs convert the single-photon counts to electrical pulses that are counted by a time correlated single photon counting system (TCSPC), a PicoQuant-PicoHarp300. The timing resolutions of the two SPDs used in our setup, are 190$p$s and the timing resolution of the Picoharp300 was set to 128$p$s during the coincidence histogram measurements. The overall timing resolution of the coincidence detection system was $\sim 230p$s. The chip is mounted on an optical stage with a thermo-electric cooler (SRS-LDC501) to stabilize the chip temperature at a value of $20 ^{\circ }C$ with a temperature stability of $+/- 15m$K (worst case variation). The total measured loss from the pump laser to the input of the fiber array is $4$dB. The measured idler path loss from the lensed fiber output to SPD2 is $7.3$dB. The measured signal path loss from the chip output to SPD1 is $8.3$dB. Figs. 6(ai) and 6(aii) show the spontaneous FWM signals recorded by the SPDs with the OTFs tuned to the idler and signal wavelengths of 1563.465nm and 1553.48nm, respectively. Figure 6(b) shows the coincidence histograms for the photon-pairs generated by the MRR source, integrated over 1200s period with a timing resolution of 128 $p$s for power levels ranging from $0.28$mW to $0.84$mW. Figure 6(b) also shows the histogram generated from the dark counts of the SPDs. To estimate the coincidence counts (CC), we integrated the coincidence peak over a 256$p$s time window around the peak. The accidental counts (AC) were then obtained by doing the same integration over a 256$p$s time window shifted to large delays, far from the peak (see line included in the highest power curve in Fig. 6(b)). The dark counts (DC) were obtained using the same integration window with the pump laser turned off. Figure 6(c) shows the CC, AC, and DC so obtained as a function of the pump power at the input waveguide of the MRR. In Fig. 6(d) we show the coincidence to accidental (CAR) values obtained by removing the large dark count contribution [40],
along with the raw CAR obtained using $CAR = \frac {CC}{AC}$. The uncertainty bars in the top blue curve in Fig. 6(d) (corrected for dark counts) were obtained by averaging the denominator of Eq. (5) over a much wider range of time bins (71.68 ns). If the coincidence window of 256$p$s to integrate the CC, AC and DC values is increased to 768$p$s, the peak CAR value drops from 125 to $\sim$ 70, due to the increased accidental counts accumulated within the coincidence window [11]. Figure 7 shows the estimated on-chip (at the output of the MRR) pair generation rate from Eq. (4) as a red solid line with square markers. To compare with the externally measured coincidence data described above, we divided the measured coincidence counts by the total integration time of the histogram $T=1200s$ to convert it to rates, and normalized these by the collection efficiencies for the signal and idler photons ($\eta _1$) and ($\eta _2$), using $(CC-AC)/T=\eta _1 \eta _2 R_m P^2_{pump}$ [11]. Here $R_m$ is the pair generation rate on-chip at 1mW pump power $P_{pump}$. The collection efficiencies ($\eta _1=31dB, \eta _2=28dB$) included the losses of OTF2,3, Pol.C.2, the 3dB PM coupler and the losses from the edge coupling to the lensed fiber as well as the detection efficiencies of SPD1 and SPD2 for both the signal and idler channels. The estimated rate of on-chip pair generation is shown as open circles in Fig. 7 and the quadratic fitting function is shown in dotted blue line. The results estimated from the measured coincidence counts are very close to the estimate based on the stimulated FWM data using Eq. (4). This difference appears to be less than the uncertainty in the net losses used to arrive at the data in the lower curve. The estimated insertion loss of our three-stage CDC filter, based on standalone device measurements, is about 2.5dB measured outside the reject band of the CDC. This value is comparable to the filters reported in [25,34] and much less than the results reported in [18,21].Fig. 5. Experimental setup for coincidence measurements of the MRR photon-pair source followed by the three-CDC filter. OTF: Optical tunable filter, Pol.C.: Polarization controller, SPD: Single-photon detector, TEC: Thermo-electric cooler, Monitor PM: monitor power-meter, PC: Personal computer, TCSPC: Time correlated single photon counting module, PM-DC :Polarization-maintaining directional coupler. DUT: Device under test.
Fig. 6. a(i) The spontaneous FWM measured by the SPD2 at the idler resonance (1563.465nm) of the MRR at pump power of 0.845mW in blue, and the dark count rate (DCR) of the SPD in orange . a(ii) The spontaneous FWM measured by SPD1 at the signal resonance (1553.48nm) of the MRR at pump power of 0.845mW, and the dark count rate (DCR) of the SPD in orange . (b) Coincidence histograms accumulated in 1200s recorded for five power levels (from 0.2818mW to 0.845mW) injected into the MRR and a histogram (orange) for the dark accidental counts collected by the TCSPC (Picoharp300) with a resolution of 128ps. (c) Coincidence (blue circles), accidental (orange dash line), dark (green squares) counts integrated in a time window of 256ps from the histogram shown in (b), and plotted versus the input pump power at the MRR input waveguide. (d) The CAR versus pump power evaluated after removing the dark counts of the SPDs in an integration window of 256ps.
Fig. 7. The on-chip measured pair generation rate (green circles) versus pump power in the input waveguide of the MRR calibrated by dividing by the coupling losses $\eta _1$&$\eta _2$. The quadratic fit of the measured pair generation rate and the analytical estimate using Eq. (4) are shown in dashed blue and solid red lines, respectively.
Table 3 provides a comparison of maximum CAR values and associated pair generation rates (PGR) reported by others who have characterized chips with integrated pair generation sources and pump reject filters. The raw $CAR = \frac {CC}{AC}$ values are known to depend strongly on both extrinsic (detector efficiency, detector dark counts, black-body background counts, scattered pump light, etc.) and intrinsic (multi-pair generation and uncorrelated pair overlap) factors. Our peak raw CAR value of 27 at a PGR of 0.6 MHz compares favorably with, but is less than those reported in Refs. [18] and [34], despite the fact that much higher quality superconducting nano-wire single photon detectors were used in those studies. The use of $CAR=\frac {CC-AC}{AC-DC}$ serves as an attempt to compensate for the relatively poor quality of the avalanche diodes used herein, and suggests that measurements of our device with better detectors would yield raw CAR values in excess of others reported in Table 3.
Table 3. Summary of the performance comparison between previous results in the literature where an MRR photon-pair source was integrated on the same chip with a pump reject filter, including the results of our CDC pump-reject filters. SCSPDs are superconducting single photon detectors. The IL(dB) column refers to the idler and signal IL of the integrated PRFs. *Limited by the measurement setup.
To provide a more satisfying estimate of the anticipated impact of using higher quality single photon detectors, and to also address the issue of CAR versus PGR tradeoffs, we used the detailed CAR model reported in [41] to fit our raw CAR data as a function of PGR. The results, shown as the dashed red curve superimposed on our raw CAR data in Fig. 8, were obtained using the parameters summarized in Table 4. The maroon colored dashed line is the model prediction for the raw CAR value with only the dark count rate reduced by a factor of five times, and the black dashed line has both the dark count rate reduced by a factor of five times, and the detector efficiencies increased to 80%. Also shown in this figure, as red and yellow solid circles, are the maximum raw CAR values from the integrated source/filter chip references included in Table 3, along with a series of raw CAR values (purple circles) reported in Ref. [42] where a microdisk pair generation source was coupled to via a tapered optical fibre (all pump rejection done off-chip). The final set of data shown as open blue circles in this figure are our $CAR=\frac {CC-AC}{AC-DC}$ values, along with the model prediction (dashed green line) for this result using the exact same parameters as in Table 4.
Fig. 8. The CAR values are plotted versus the pair generation rate on-chip comparing our results in blue circles for (CC-AC/AC-DC) and the red diamonds for the (CC/AC) to other results reported in the literature. The magenta dots are the results obtained from Ref. [42], the orange dot is the result of [18], and the yellow dot is the result from [34]. All the dashed lines were obtained by substituting the parameters of our coincidence setup in the model presented in [41] assuming a total pump rejection of 105dB. The green and red dashed lines are obtained using the actual system parameters listed in Table 4 to calculate (CC-AC/AC-DC), and (CC/AC) respectively. The dashed brown line is the same model calculation of (CC/AC) but with DCR1 and DCR2 values changed to 1440Hz, and 1640 Hz, respectively, at a detection efficiency of $10\%$. By improving the detection efficiency of the SPD from $10\%$ to $80\%$ at DCRs of 1440Hz and 1640 Hz, we obtain the estimated CAR in the black dashed line for the (CC/AC) formula.
Table 4. Summary of the fitting parameters used to obtain the results shown in the dotted green and red lines in Fig. 8. $\eta _d$ is the detector efficiency and $T_{win}$ is the coincidence window used in the modeling results in presented in Fig. 8. $\eta _1$ and $\eta _2$ are the channel detection efficiencies as defined previously in section 3.3. The rest of the parameters are defined in [41].
The analysis summarized in Fig. 8 strongly suggests that raw CAR values that could be measured using higher quality single photon detectors in our experiment would compare very favorably with both integrated and stand-alone pair generation sources reported in the literature, over a wide range of pair generation rates. It also suggests that using the formula $CAR=\frac {CC-AC}{AC-DC}$ to approximately compensate for this poor detector performance results in "corrected" CAR values lower than the raw CAR values that would actually be measured using better detectors, at least at high pair generation rates of interest.
4. Conclusions and future directions
On-chip integration of CDC pump reject filters with a MRR photon pair source yielded a peak CAR value of 27 when coincidences were measured off-chip using APD single photon detectors and inline signal/idler de-multiplexing filters with $\sim 50$dB ER. The corresponding on-chip pair generation rate obtained with 0.82 mW of pump power incident on the MRR source is estimated to be 600 kHz. The whole circuit area (three-stage CDC filter plus MRR) is $0.6 \times 0.125mm^2$ which is compact enough for scaling to large numbers of single-photon sources on a single SOI chip. By accurately modelling the measured dependence of the CAR on the pair generation rate, the estimated CAR values that would be obtained from this chip using high quality superconducting single photon detectors was estimated by changing only the detector dark count rates and efficiencies in the model. These results suggest that this integrated pair generation source/pump reject filter design offers the potential to achieve CAR values that exceed those of other integrated solutions, and even standalone sources, over a wide range of pair generation rates.
A fully-integrated heralded single photon source solution in silicon will require coupling the source/PRF circuit demonstrated here, with on-chip signal and idler filters, the output of which could be directly coupled to single photon detectors. The signal and idler filters could be implemented using the drop ports of narrow-band CDCs [29,31], or tunable MRRs [18]. The PRFs and the signal and idler filters could be monolithically integrated, or implemented on separate chips connected by low-loss photonic wire bonds (PWBs) [39]. Even if fully monolithic, PWBs may be useful for interconnecting the two filter stages across deep isolation trenches to minimize the impact of scattered pump photons that might be propagating in the substrate. The substrate scattering might also be substantially reduced by replacing the input GCs with PWBs or low-loss mode size converters to connect the circuit waveguides with V-groove-mounted optical fiber arrays [43,44]. Ultimately, several such sources will have to be multiplexed in time and space to improve the net on-chip photon-pair generation rate required for practical quantum communication [45] and computation tasks [3,4]. The four-port nature of the CDCs reported here would then offer a means of efficient pump-reuse [32] and/or extraction for better thermal management.
Funding
CMC Microsystems; Faculty of Graduate Studies, University of British Columbia; Natural Sciences and Engineering Research Council of Canada.
Acknowledgments
We appreciate the financial support received from the Natural Sciences and Engineering Research Council of Canada and Keysight technologies. We would like to acknowledge the support from Canada Micro-systems (CMC) to access the foundry services at AMF, our fabrication partners Applied Nanotools Inc., and funding provided from SiEPIC fab members.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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