Sources of single photons are one of the key building blocks for quantum photonic technologies such as quantum secure communication and powerful quantum computing. To bring the proof-of-principle demonstration of these technologies from the laboratory to the real world, complementary metal–oxide–semiconductor (CMOS)-compatible photonic chips are highly desirable for photon generation, manipulation, processing and even detection because of their compactness, scalability, robustness, and the potential for integration with electronics. In this paper, we review the development of photonic devices made from materials (e.g., silicon) and processes that are compatible with CMOS fabrication facilities for the generation of single photons.
Quantum technologies hold the promise that they will bring revolutions to many areas of our everyday life such as communication  and computing . More specifically, the no-cloning theorem, which states that an unknown quantum state cannot be copied without being measured and thus destroyed, guarantees the security of information in a quantum network; and a quantum bit (qbit) can be in a superposition of many quantum states, making it possible to process a large amount of states simultaneously and leading to exponentially faster computing. To implement these technologies, among various systems, those based on photons have drawn a lot of attention because: (i) photons provide easy access to extraordinary quantum properties such as superposition and entanglement, (ii) photons are a natural choice for long-distance quantum communications using the existing optical fiber network infrastructure, and (iii) photons are compatible with complementary metal–oxide–semiconductor (CMOS)-integrated photonic devices and thus have the potential to be generated and processed in a scalable way. Figure 1 shows a schematic quantum photonic chip that includes single-photon sources and processing circuits. Each single-photon source is a complete system consisting of photon generation devices, pump reflector, spectral filters, single-photon detectors (SPD), and electronics for photon multiplexing. In this paper, we review the progress of single photon sources based on photonic devices made using CMOS fabrication facilities and discuss the remaining challenges and possible solutions toward real-world applications.
This review begins with a brief clarification about the term “CMOS compatibility” used in this paper. Section 3 presents the popular strategies for developing single-photon sources, with a focus on various CMOS-compatible silicon-based devices including silicon nanowires, microring and microdisk resonantors, and slow-light structures. Section 4 addresses the remaining challenges and possible solutions. Section 5 summarizes and concludes the paper.
2 CMOS compatibility
CMOS is a technology for constructing electronic integrated circuits in traditional semiconductor industry. CMOS refers to both a particular style of digital circuitry design and the family of processes used to implement that circuitry on integrated chips. As millions of components can be printed as one unit using lithography (i.e., photolithography and electron beam lithography) on the same chip, the major advantages of CMOS are low cost, fast manufacturing, and volume production, which have revolutionized information technology and changed the life style of modern society.
As silicon is the dominant substrate material for CMOS fabrication and it exhibits excellent linear and nonlinear optical properties, silicon photonics has become a newly emerging field for on-chip optical signal processing and interconnects with the major argument of CMOS compatibility [3–5]. The term “CMOS compatibility” has been widely used in the silicon photonics community. Although there is not a strict definition of this term, it generally refers to both materials that can be prepared and processed by CMOS facilities, and fabrication processes such as photoresist spin coating, lithography, etching, and photoresist removing that do not contaminate the CMOS product line. As an example, Fig. 2 illustrates the flow of fabricating silicon photonic crystal (PhC) slow-light waveguides using silicon-on-insulator (SOI) wafers . With the above definition, devices based on materials beyond silicon, such as silicon nitride and Hydex also fall into the category of CMOS-compatible platforms [7, 8]. In this paper, we focus on silicon-based devices.
3 CMOS-compatible devices for single-photon generation
3.1 Two major strategies for single-photon sources
Single-photon sources are a crucial resource for the implementation of quantum enhanced technologies. The ideal single photon sources should emit single-photons on-demand, and indistinguishable in all relevant degrees of freedom–central frequency, bandwidth, spatial mode, and polarization. Two strategies have been proposed to develop the desired single-photon sources . One is to use “single-emitter” quantum systems [10, 11] such as semiconductor quantum dots or color centers in diamond. These systems emit single photons nearly on-demand, and there is a trend to integrate these systems on photonic chips [12, 13]; however, producing highly indistinguishable photons from distinct emitters remains challenging because of the difficulty in fabricating identical emitters at the nanoscale [14, 15]. The other approach is to generate correlated photon pairs via spontaneous nonlinear optical processes, such as spontaneous parametric down conversion (SPDC) or spontaneous four-wave mixing (SFWM) in suitable crystals or waveguides, where the detection of one photon in a pair “heralds” the existence of its partner.
In the approach based on SPDC or SFWM, photons are emitted at defined directions and thus easy to collect. As the nonlinear processes are ultrafast, the emission of photons are nearly instantaneous and so their temporal and spectral properties can be very well controlled. This leads to highly indistinguishable single-photon emission, either from one source based on wavelength degenerate photon-pair generation , or from separate sources . Therefore, the demonstration of photonic quantum protocols has been heavily reliant on SPDC or SFWM photon sources [16, 18–24]. However, there is one disadvantage of such photon sources: the photon emission is probabilistic, and the probabilities of generating one pair and multi-pairs are coupled to each other. It is nontrivial to simultaneously increase the probability of single pair generation while suppressing that of multipair generation. We will address this challenge later in Section 4. In Section 3.2, we focus on one particular CMOS-compatible platform, silicon-based devices, for on-chip single-photon generation.
3.2 Silicon devices for single photon generation
Since the first demonstration of on-chip quantum photonic circuits , it has become a holy grail to integrate optical components on a photonic chip for quantum information processing [18–23]. Nevertheless, most of these demonstrations only have the photon processing circuits on-chip, leaving single-photon sources with bulk optics, and only in  single-photon generation and processing take place simultaneously in a nonlinear lithium niobate waveguide array. There is an urge to develop CMOS-compatible on-chip single-photon sources.
As a CMOS-compatible material, silicon is the most widely used platform for developing chip-based single-photon sources via optical nonlinear wave mixing processes. As silicon is centrosymmetric, the second-order nonlinearity vanishes and the third-order nonlinearity dominates, and therefore, SFWM in silicon devices is the key process for single-photon generation. There are two forms of silicon, amorphous and crystalline silicon, both exhibiting about 1000 times higher nonlinearity than silica glass. In the following sections, we focus on crystalline silicon unless stated otherwise.
The following discussion focuses on the case that all photons are co-polarized, because this is generally preferable in silicon devices. Depending on the pump configuration, there are two types of SFWM processes. As shown in Fig. 3, when there is only one pump, the generated photons are at two different frequencies 𝜔s and 𝜔i, satisfying energy conversion 𝜔s + 𝜔i = 2𝜔p and phase matching ks + ki + 2𝛾P − 2kp = 0; while when there are two pump waves at different frequencies 𝜔p1 and 𝜔p2, the generated photons are frequency degenerate at 𝜔s,i, also meeting the requirement of energy conversion 2𝜔s,i = 𝜔p1 + 𝜔p2 and phase matching 2ks,i + 𝛾 (P1 + P2) − kp1 − kp2 = 0 . The former process can be used for heralded single-photon generation [26–37], and the latter can be used for indistinguishable photon-pair generation [38–40]. Phase matching is achieved by engineering the dispersion profile of the device through designing the device geometry and tailoring the waveguide core-cladding index contrast by the use of different cladding materials.
Generally speaking, a single-photon source based on SFWM is a complete system consisting of a pump laser, a nonlinear optical waveguide, spectral filters, SPDs, and electronics for photon statistics analysis [Fig. 1, Fig. 3(c)]. So the performance of a photon source is not solely determined by the nonlinear waveguide, but by the whole system. In this paper, we do not intend to compare the performance of photon sources based on different silicon devices in detail, but rather present the advantages and disadvantages introduced by fabrication constrains and physics behind different devices. We begin with silion nanowires.
3.2.1 Silicon nanowires
Amongst various silicon photonic devices, silicon nanowires have the simplest structure. The cross section of a typical nanowire is shown in Fig. 4. The 450 nm wide and 220 nm high silicon core is surrounded by SiO2 cladding (the top cladding can also be polymer or air). Such a small area and high index contrast result in an extremely high nonlinearity and anomalous dispersion in the telecommunication 1,550-nm band for TE poloarized pump. This enables efficient SFWM for photon generation over a broad bandwidth in only a few millimeters long nanowires [26–29]. More importantly, CMOS fabrication techniques allow the addition of inverse tapers at both input and output ends of a nanowire [Fig. 4(b)] for fiber pigtailing, which significantly improves the photon collection efficiency and system stability [28, 41].
The advantages of the nanowire platform are that it can tolerate higher fabrication-introduced size inaccuracy, and the broad SFWM bandwidth provides the flexibility of selecting desired photon wavelengths and pump wavelengths. The side effect of the broad SFWM bandwidth is that we have to use narrow bandpass filters to block all other unwanted photons, resulting in large photon collection losses. Compared with the resonant and slow-light devices discussed later, to achieve the required SFWM efficiency, nanowires need to be several orders of magnitude longer and pumped by a pulsed laser with high peak power.
As a typical example of silicon-nanowire-based photon sources, in Ref. , a 1.15 cm long, 200 nm wide, 460 nm thick, and silica-cladded nanowire was pumped by 90 ps pulses to generate correlated photon pairs. The bandwidth for pair generation was measured to be at least 2.8 THz and the pairs were filtered by 25 GHz filters. At a coupled peak power of 20 mW, the maximum coincidence-to-accidental ratio (CAR) of 320 was achieved and the corresponding photon-pair generation rate was approximately 130 kHz.
3.2.2 Silicon microrings and microdisks
To make a nonlinear device for single-photon generation more compact, using resonant and slow-light structures is a promising solution. These structures include microrings [29–31], microdisks , PhC slow-light waveguides [33–35], and microring- and PhC-cavity-based coupled resonator optical waveguides (CROW) [36, 37].
Figure 4(c) and (d) shows the diagrams for a typical microring and microdisk, respectively. A microring has a closed loop waveguide and a bus waveguide that couples the light in and out of the loop; while a microdisk has a bus waveguide to couple light in and out of a disk that guides light through whispering gallery modes. In both structures, photons can travel for many orbits and thus the nonlinear interaction between photons and the device can be enhanced. This requires all photon wavelengths satisfy the resonance condition niL = m𝜆i, where ni is the effective mode index of the microring or microdisk at vacuum wavelength 𝜆i, L is the device circumference, c is the speed of light in vacuum, and m is a positive integer, which is different for photons at different wavelengths. A microring can be either a perfect circle [30, 31] as shown in Fig. 4(c) or a racetrack cavity . Both the bus and loop waveguides have a cross-section similar to that shown in Fig. 4(a). The gap between the bus and loop waveguides can be optimized so that maximum pump power is stored in the loop, enhancing the nonlinear interaction. This optimized gap is the critical coupling distance, at which the resonant bandwidth 𝛿v is very narrow and thus the Q-factor Q = v/𝛿v can be very large. For example, if the resonant wavelength is 1,550 nm and the resonant bandwidth is 100 MHz, Q = 1.9 million. It is the cross-section dimension that determines the basic SFWM properties such as phase matching bandwidth and the loop circumference together with the bus-loop gap that determine the enhancement.
Despite the fact that a microdisk enhances the SFWM efficiency in a very similar way to a microring, there are several differences. First, unlike a silicon ring that sits on a SiO2 substrate, a silicon disk sits on a SiO2 pedestal. This means that the cladding is fixed as air. Therefore, the dispersion is determined largely by the disk thickness. For a disk thickness of 260 nm, the zero-dispersion wavelength is shifted to the telecommunication band around 1,550 nm . Second, unlike a microring in which both the loop and bus waveguides are integrated on one chip, a microdisk is usually accessed through a tapered optical fiber as the bus waveguide [Fig. 4(d)]. As both ends of a tapered fiber are just single-mode fibers, the input and output coupling efficiencies are very high, resulting in unprecedented single-photon spectral brightness . However, the side effect of such a coupling system is that it is difficult to package and thus lacks stability.
The features of microrings and microdisks are summarized as follows (i) Taking the advantage of the massive enhancement from resonant effects, the required pump power for photon generation [30, 32] is five orders of magnitude lower than that required for nanowires [26, 27] and the device area is two orders of magnitude smaller than nanowires. (ii) The resonance bandwidth is extremely narrow, so the generated photons do not need to be filtered using narrow band filters and thus experience much less losses. (iii) Owing to the narrow resonance bandwidth, they are usually pumped by narrow linewidth continuous wave (CW) lasers, which is not good for the multiplexing schemes discussed later in Section 4 because of the lack of a clock for the generated photons. (iv) The resonant wavelengths are extremely sensitive to environmental temperature and fabrication fluctuations, and so tunable elements such as micro-heaters are required to make two devices emit indistinguishable photons for high-visibility quantum interference . (v) Once a microring or microdisk is fabricated, both pump and the generated photons can only be at the resonant wavelengths and thus lack flexibility. (vi) Because of the fabrication-introduced side wall roughness, light scattering occurs in a microring or a microdisk. Pump and generated photons travel along the ring in both clockwise and anticlockwise directions. This results in a detrimental coherent backscattering. The signature of this effect is that the single resonance dip splits to a doublet in the transmission spectrum [29, 32, 43]. The back scattering can introduce large losses to the generated photons.
To investigate the backscattering effect in microrings on single photon generation, we design an experiment as shown in Fig. 5(a). The bus and loop waveguides of the ring have the cross section similar to that shown in Fig. 4(a) with air as the top cladding. The ring radius is 21 µm, and the bus-loop waveguide gap is 155 nm to achieve critical coupling, resulting in a Q = 400, 000. We pump the ring through a circulator so that we can collect both forward and backward-propagating photons. We measure the coincidences between signal (blue) and idler (red) photons from different output ports of the wavelength division multiplexers (WDMs). There are four combinations: SPD1 and SPD2 (both photons forward), SPD3 and SPD4 (both photons backscattered), SPD1 and SPD4 (idler forward but signal backscattered), and SPD2 and SPD3 (signal forward but idler backscattered). The results are plotted in Fig. 5(b), showing that a significant amount of photons are backscattered. When we reduce the Q-factor of the ring to 40,000 by dropping index-matching fluid on top of the ring, the backscattering is reduced and most photons travel in the forward direction. Our demonstration indicates that because of fabrication constraints, a high-Q microring is not necessarily better than a low-Q one; and to make full use of the potential of high-Q microrings, we have to reduce the wall roughness (i.e., surface roughness).
3.2.3 Silicon slow-light waveguides
Besides the resonant structures described earlier, slow-light structures can also be used to enhance the SFWM efficiency and thus significantly reduce the footprint of the device. Three slow-light structures have been exploited for single-photon generation via SFWM in the literature: photonic crystal waveguides (PhCWs) [33–35], microring CROWs , and PhC cavity CROWs . Our group mainly contributes to the PhC slow-light waveguides. First, we use PhC slow-light waveguides as an example to explain how slow-light propagation can enhance single-photon generation.
A PhCW has a triangular lattice of air holes etched in a suspended silicon membrane with a row of holes missing along the K direction, as shown in Fig. 6(a). The row without holes acts as the waveguide core and the air-hole lattice as the cladding. The photonic crystal cladding forms a photonic bandgap for guiding light. Near the bandgap edge, the dispersion can be very large and the group index ng can be much greater than the native material refractive index n0. The ratio S = ng/n0 is defined as the slowdown factor. As illustrated in Fig. 6(a), the enhancement to single-photon generation from slow-light propagation is twofold. First, when a pulse of light enters the PhCW region, the falling edge of the pulse travels more slowly than the rising edge and the pulse gets spatially compressed, so the peak intensity of the pulse increases. Second, the entire pulse travels more slowly in the PhCW than in a nanowire. These two effects increase the nonlinear coefficient 𝛾 (i.e., the nonlinear interaction per unit length per unit power) by approximately two orders of magnitude, and in turn the SFWM efficiency, which is proportional to 𝛾2, by four orders of magnitude .
Note that a large group index at one particular wavelength is not sufficient for efficient SFWM, the group index ng should be nearly constant across a broad bandwidth for phase matching. This is realized by laterally shifting the first row of holes on both sides of the waveguide core away from the core by tens of nanometres . By adjusting the lattice period, hole diameter and the shift of the first row of holes, both ng and the slow-light bandwidth can be varied [44, 45]. Figure 6(b) shows the measured group index and transmission for a 96 µm long PhCW with a lattice period of 404 nm, hole radius of 115 nm and first row shift of 50 nm . The wavelength window (between dotted lines, about 15 nm bandwidth) with a flat group index of around 30 and slightly increased loss defines the slow-light regime. Low loss coupling to the PhCW is achieved by silicon nanowire access waveguides with inverse tapers terminated by wide polymer waveguides at both the input and output of the PhCW region [Fig. 6(c)].
Next we consider CROW structures for single-photon generation. A CROW consists of a sequence of coupled resonators with high Q-factors . Each individual resonator forms a unit cell of the CROW and can be a microring [Fig. 4(f)]  or a PhC cavity [Fig. 4(g)] . Light propagates through a CROW via evanescent coupling between adjacent units . In both structures, the separation between two adjacent resonators is sufficiently large that they are weakly coupled. Consequently, the eigen-mode of the electromagnetic field in these structures is a linear combination of the high-Q modes of each individual resonator and forms a supermode.
There are several differences between a CROW and a single microring or PhC cavity. First, a CROW exhibits much larger group index and thus has the slow-light effect. Second, a microring CROW has much broader resonances than a single microring, which makes experimental alignment easier and offers better thermal stability. Third, a PhC CROW shows a broadband transmission rather than multiple narrow band resonances. The transmission band is similar to the slow-light band in a standard PhCW shown in Fig. 6(b). The nonlinear coefficient of a PhC CROW can be as high as 13,000 W−1m−1, which can significantly enhance the SFWM efficiency. The major limiting factor of a PhC CROW is that the slow-light bandwidth (5 nm) is narrower than a standard PhCW, making the isolation of generated photons from the pump challenging. Finally, a CROW has a much bigger footprint than a single microring and a standard PhCW because it has many microring or PhC cavity units.
Compared with nanowires, microrings, and microdisks, slow-light devices have much more complicated structures. The optical properties of slow-light devices are very sensitive to fabrication deviations. For example, if the air hole shape in a PhCW is elliptic rather than circular, or the hole sizes or the shift of the first row of holes close to the core deviate by a few nanometers, the slow-light bandwidth and central wavelength and the shape of the group index curve shown in Fig. 6(b) will change significantly . Because of this complexity, we usually need to make a series of waveguides with slightly different fabrication parameters so that at least one device meets the specific design. Besides the fabrication complexity, PhCWs and PhC CROWs have limited slow-light bandwidth, and thus there is not much flexibility to choose the wavelengths of generated photons.
3.2.4 Frequency-degenerate photon pair generation
In principle, the devices discussed in Sections 3.2.1–3.2.3 can be used for both frequency-nondegenerate and frequency-degenerate photon-pair generation. However, as shown in Fig. 3(a) and (b), there are two major differences in experimental implementations. (i) Frequency-degenerate photon-pair generation requires two different pump wavelengths. In the case of pulsed pumps, we have to be able to synchronize the pump pulses at two wavelengths; (ii) The generated photons are indistinguishable in all degrees of freedom such as wavelength, spatial mode, and temporal mode. We cannot separate them deterministically as easily as using a WDM in the frequency-nondegenerate photon-pair generation case. Splitting these photons probabilistically with a 50:50 directional coupler means that they are no longer useful for some tasks. For example, a Hong–Ou–Mandel (HOM) dip  with probabilistically split photons is limited to a visibility of 50%.
Frequency-degenerate photon-pair generation via SFWM has been demonstrated in optical fibers previously [48, 49]. Very recently, several groups including us have reported the on-chip demonstrations based on silicon nanowires , PhC slow-light waveguides , and microrings [38, 40]. In Refs.  and , two CW lasers were used as the pump and thus did not have the challenge of pulse synchronization. In the demonstration using PhCWs , we used a single intensity modulator to modulate two CW lasers to generate the required pulses and thus the two pump pulses were automatically synchronized; while in Ref. , we spectrally sliced a broadband pulsed laser to get two pump pulses automatically synchronized. References [38, 39] did not deterministically split the degenerate photons. In both  and , photons were deterministically split using time-reversed two-photon HOM interference, as illustrated in Fig. 7. In the time-reversed HOM interference process, the two input two-photon states must have the same amplitude and phase. Reference  realized this through generating frequency-degenerate photons in two separate silicon nanowires with equal probability and adjusting the phases using micro-heaters [Fig. 7(c)]. In our recent demonstration , we used a single microring resonator in a Sagnac loop configuration to automatically match both the amplitude and phase [Fig. 7(d)], and thus the device area is only 207 µm × 54 µm = 0.011 mm2, 50 times smaller than that in .
Figure 8 shows how photon pairs generated via SFWM are used for HOM quantum interference. Photon pairs generated through the frequency-nondegenerate SFWM process are at different wavelengths, so they are distinguishable, meaning that two independent heralded photon sources are required to perform HOM interference [Fig. 8(a)]. This involves the measurements of four-photon coincidence events , which are much less likely to happen because each heralded photon source generates photons randomly. To make such a heralded single-photon source useful, we have to improve it to the nearly deterministic regime using the multiplexing schemes discussed later in Section 4.1. On the other hand, indistinguishable photons generated via the frequency-degenerate SFWM process can be used in traditional two-photon coincidence measurements shown in [Fig. 8(b)] and thus are immediately useful for many applications that require interfering two photons, such as a controlled-NOT quantum logic gate .
3.2.5 Summary of different structures
At the end of this section, we summarize the typical experimental results from the literature in Table 1. Note that some data are directly taken from the references and some of them are inferred from the experimental description. On the basis of these data, the advantages and disadvantages of different structures in terms of fabrication complexity, nonlinearity, footprint, stability, power consumption, package complexity, and tuning bandwidth (i.e., the frequency range photons can be generated over) are shown in Table 2. It can be seen that there is not a single structure that outperforms others. According to different applications, we should choose the most appropriate structures. For example, in the scenario that we care most about footprint and power consumption, we should choose resonators and then apply active control to achieve stability; while in the case we need photon wavelength flexibility and broad bandwidth, nanowires are the best option.
|Structures||Nanowires ||Microrings ||Microdisks ||PhC ||Microring CROW ||PhC CROW |
|Nonlinear coeflcient (W−1m−1)||300||-||-||4,000||4,100||9,000|
|Device footprint (mm2)||5.3 × 10−3||4.1 × 10−4||7.5 × 10−5||3.9 × 10−4||-||1.8 × 10−3|
|Coupled pump average power (mW)||0.18||0.019||0.079||0.055||16||0.03|
|Collected photon bandwidth (GHz)||25||5.2||2.2||50||62.5||25|
|Brightness (pairs s−1mW−2GHz−1)||1.6 × 105||4.4 × 108||6.2 × 107||1.5 × 106||4.6||8.8 × 107|
|Structures||Nanowires||Microrings||Microdisks||PhC||Microring CROW||PhC CROW|
|Fabrication||∘ ∘ ∘||∘||∘||∘||∘||∘|
|Nonlinearity||∘||∘ ∘ ∘||∘ ∘ ∘||∘ ∘ ∘||∘ ∘ ∘||∘ ∘ ∘|
|Footprint||∘||∘ ∘ ∘||∘ ∘ ∘||∘ ∘ ∘||∘||∘|
|Stability||∘ ∘ ∘||∘||∘||∘∘||∘||∘∘|
|Power||∘∘||∘ ∘ ∘||∘ ∘ ∘||∘ ∘ ∘||∘||∘ ∘ ∘|
|Package||∘ ∘ ∘||∘||∘||∘∘||∘∘||∘∘|
|Tuning bandwidth||∘ ∘ ∘||∘ ∘||∘ ∘||∘||∘ ∘||∘|
4 Remaining challenges and possible solutions
In the past decade, impressive progresses have been made in developing CMOS-compatible photonic devices for single-photon generation. For example, the advance of fabrication technology has brought the losses down. However, there are remaining fundamental and technological challenges toward useful on-chip single-photon sources in real-world applications. In this section, we discuss three challenges: (i) how to use multiplexing to overcome the intrinsic statistical limit of photon sources based on SFWM in silicon; (ii) nonlinear losses of silicon; and (iii) on-chip integration of spectral filters.
4.1 Multiplexing of heralded single photons
As we described in Section 3.1, we can get heralded single photons through correlated photon-pair generation through spontaneous nonlinear wave mixing. However, this process is probabilistic, making it very difficult to obtain single photons on-demand because we cannot increase the probability of getting one pair while simultaneously suppressing the probability of producing multiple pairs. More specifically, the probabilities of both single-(P1) and multi-pair (P>1) events are related to the mean number of pairs created per pump pulse µ. They both increase with µ, and P>1 increases more rapidly (to leading order it grows quadratically rather than linearly). Therefore, these sources must operate in the regime of µ ≪ 1 (and thus P1≪ 1) to minimize the multi-photon noise. This is a fundamental challenge in quantum optics. This non-deterministic nature of photon-pair generation limits the feasibility of next-generation quantum photonic technology that will require multiple simultaneous single-photon inputs.
With regard to the statistical nature, heralded single-photon sources do not seem to have a clear advantage over attenuated laser-based single-photon sources; however, the use of heralding, combined with active optical switching, does offer us an elegant solution to bring nondeterministic sources to the nearly deterministic regime. The idea is to use the knowledge of the heralding photons to deterministically combine the outputs of several probabilistic sources that are either spatially separated or are different from each other in temporal modes. These are known as the active spatial [50, 51] and temporal [52–54] multiplexing schemes. Through multiplexing, the probabilities of single- and multi-pair generation are decoupled, and thus both probabilities increase with the number of multiplexed modes linearly while the ratio between them remains the same. Consequently, the probability to get a single photon is enhanced and the quantum signal-to-noise ratio does not degrade.
The architecture of the active spatial and temporal multiplexing schemes is schematically shown in Fig. 9. In spatial multiplexing shown in Fig 9(a), pump pulses from a single laser are coupled to an array of nonlinear waveguides (e.g., PhCW here) for photon-pair generation via SFWM. This forms an array of heralded single-photon sources. After generation, photon pairs are spectrally separated using WDMs [e.g., arrayed waveguide gratings (AWG) here]. The heralding photons are detected by fast and low-noise superconducting single-photon detectors (SSPDs), and the detection signals trigger a fiber-coupled opto-ceramic electro-optic switch made from ultra-low-loss lead lanthanum zirconium titanate (PLZT) . The heralded photons go through a fiber delay line to compensate the electronic delay in the heralding arm. The selected heralded photons are then routed to the common output of the switch to form a more deterministic single-photon stream. The idea of spatial multiplexing was first proposed by Migdall et al. in 2002 , followed by a potentially lower-loss method using electro-optic polarization controllers and polarization beam splitters rather than Mach-Zehnder interferometric switches in 2007 . The first experimental demonstration by Ma et al. did not achieve practical enhancement because of the use of bulk and high-loss components . We achieved the first practical enhancement of 62.4% to the heralded single-photon output probability for a fixed signal-to-noise ratio using the integrated architecture shown in Fig. 9(a) and the low-loss ceramic switch to multiplex two PhCW sources . Later on we showed that we could multiplex two sources by pumping a single PhCW from both ends and achieve similar enhancement . The benefit is that the required number of PhCWs can be reduced to half. Nevertheless a recent theoretical investigation shows that the resources, such as nonlinear devices, filters, and detectors, required for spatial multiplexing may be overwhelming when we scale this up . The solution will probably be the use of temporal multiplexing or the combination of spatial and temporal multiplexing, because temporal multiplexing allows the repeated use of the same detectors and photon-generation components and thus is significantly more resource efficient and scalable.
Several temporal multiplexing schemes were proposed [52–54], and the one shown in Fig 9(b) was originally proposed by Mower and Englund  and implemented by our group . In this particular configuration, a nonlinear device is pumped by pulses separated in time by period T, each generating correlated photon pairs randomly. The two photons from each pair are separated by frequency (color), and the heralding photons (red) are detected, indicating the existence of the heralded photons (blue). Depending on the time bin in which a pair is generated, an appropriate optical delay is applied to the heralded photon through a switching network so that it always appears in time bin t1 with a nominal period NT (e.g., N = 4 in the figure). For example, if the photon pair is generated in time bin t2, a (N − 1)T delay is applied to the heralded photon; while if the photon pair is generated in time bin t1, no delay is applied. To avoid generating more than one pair in the period of NT, the probability of generating a pair per pulse should be kept below 1/N. The major challenges of this scheme are to maintain the temporal and polarization indistinguishability of the multiplexed photons and to reduce the losses of the switching network. We have recently achieved nearly 100% enhancement to the heralded single-photon output probability for fixed signal-to-noise ratios for N = 4. More importantly, we have shown that the multiplexed photons are highly indistinguishable because the HOM interference using these photons exhibits 91% visibility . Our results show that this scheme is definitely feasible to break the intrinsic statistical limit and maintain the photon quantum state simultaneously. Note that the PLZT switches in our demonstration are CMOS compatible and can be integrated on a silicon substrate . The remaining challenge will be to further reduce the losses of optical components.
4.2 Nonlinear losses of silicon
Another challenge associated with silicon is the well-known nonlinear losses at the telecommunication wavelength bands. As silicon’s energy bandgap is approximately twice as much as the energy of one photon at around 1,550 nm, it can absorb two photons when the incident light has a high intensity and introduce two-photon absorption (TPA) losses. As shown in , in single-photon generation experiments, TPA does not only occur between two pump photons but also happens between one pump photon and one generated photon, introducing extra losses to the generated photons. Furthermore, once silicon devices absorb some photons, some electrons will become free carries and these free carries can absorb additional photons, introducing free-carrier absorption (FCA) losses to both pump and generated photons.
To avoid these nonlinear losses, we should operate in the low pump power regime because these losses only kick in at relatively high power [33, 34]. While Ref.  has shown that using electrodes to apply a voltage bias to a silicon device can remove free carries and thus significantly improve the source quality, it is more difficult to reduce TPA. It is possible to use a different material such as GaInP that has a large bandgap to prevent TPA; however, it won’t replace silicon unless the fabrication becomes more mature to bring the linear losses down .
4.3 On-chip spectral filters
The ultimate goal of the field is to integrate all components shown in Fig. 3(c) on a monolithic photonic chip using CMOS fabrication facilities. On-chip integration of spectral filters is essential, because the photons must be separated on-chip before they can be independently processed on-chip. As it is very difficult to integrate interferometric bandpass filters on-chip, alternative solutions have to be found to provide spectral filtering. Matsuda et al. have demonstrated the integration of an AWG and a nanowire on the same silicon chip . As the AWG can only provide 30-dB isolation, off-chip bandpass filters and fiber Bragg gratings are still needed to achieve the overall > 100 dB isolation. The most encouraging progress is probably the monolithic integration of cascaded microrings and Bragg reflectors that show more than 95 dB isolation . This is the first example in the field to realize completely on-chip generation and filtering of single photons. The future challenge is to reduce the losses of these components.
In conclusion, we have presented the progress on a CMOS-compatible platform, silicon-based devices, for single photon generation in the past decade. Silicon can be made into various structures: nanowires, mircrorings and microdisk, PhCWs, and microring and PhC-cavity-based CROWs using mature CMOS technology. For single-photon generation, the overall advantage of these silicon devices is that the high-photon generation efficiency and ultra small footprint make them promising for next-generation quantum information processors. There are some remaining challenges though. We have discussed how to achieve deterministic single-photon sources from silion by multiplexing many non-deterministic sources, the concern about the nonlinear losses in silicon, and the possibility and issues of integrating spectral filters on-chip. We believe that with the advance of new technologies, photonic-chip-based on-demand single-photon sources will become a reality.
This work was supported by the Centre of Excellence (CUDOS, Project No. CE110001018), the Laureate Fellowship (FL120100029), and the Discovery Early Career Researcher Award programs (DE120100226) of the Australian Research Council (ARC). The authors would like to thank Juntao Li, Xinlun Cai, William Whelan-Curtin (Liam O’Faolain) for discussion about the CMOS processes.
 N. Gisin and R. Thew, “Quantum communication”,Nature Photon.1,165–171 (2007).10.1364/SPPCOM.2018.SpM3G.5Search in Google Scholar
 P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits”,Rev. Mod. Phys. 79, 135–174 (2007).10.1103/RevModPhys.79.135Search in Google Scholar
 M. Hochberg and T. Baehr-Jones, “Towards fabless silicon photonics”,Nature Photon.4, 492–494 (2010).10.1038/nphoton.2010.172Search in Google Scholar
 J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics”,Nature Photon.4, 535–544 (2010).10.1038/nphoton.2010.185Search in Google Scholar
 T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics”,Nature Photon.6, 206–208 (2012).10.1038/nphoton.2012.66Search in Google Scholar
 J. Li, L. O’Faolain, I. H. Rey, and T. F. Krauss, “Four-wave mixing in photonic crystal waveguides: slow light enhancement and limitations”,Opt. Express19, 4458–4463 (2011).10.1364/OE.19.004458Search in Google Scholar PubMed
 D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics”,Nature Photon.7, 597–607 (2013).10.1038/nphoton.2013.183Search in Google Scholar
 K. Wörhoff, R. G. Heideman, A. Leinse, and M. Hoekman, “TriPleX: a versatile dielectric photonic platform”,Adv. Opt. Techn.4, 189–207 (2015).10.1515/aot-2015-0016Search in Google Scholar
 M. D. Eisaman, J. Fan, A. Migdall, and S. V. Polyakov, “Single-photon sources and detectors”,Review of Scientific Instruments82, 071101 (2011).10.1063/1.3610677Search in Google Scholar PubMed
 A. J. Shields, “Semiconductor quantum light sources”,Nature Photon.1, 215–223 (2007).10.1142/9789814287005_0023Search in Google Scholar
 N. Mizuochi, T. Makino, H. Kato, D. Takeuchi, M. Ogura, H. Okushi, M. Nothaft, P. Neumann, A. Gali, F. Jelezko, J. Wrachtrup, and S. Yamasaki, “Electrically driven single-photon source at room temperature in diamond”,Nature Photon.6, 299–303 (2012).10.1038/nphoton.2012.75Search in Google Scholar
 E. Murray, D. J. P. Ellis, T. Meany, F. F. Floether, J. P. Lee, J. P. Griflths, G. A. C. Jones, I. Farrer, D. A. Ritchie, A. J. Bennett, and A. J. Shields, “Quantum photonics hybrid integration platform”,Appl. Phys. Lett.107, 171108 (2015).10.1063/1.4935029Search in Google Scholar
 U. Rengstl, M. Schwartz, T. Herzog, F. Hargart, M. Paul, S. L. Portalupi, M. Jetter, and P. Michler, “On-chip beamsplitter operation on single photons from quasi-resonantly excited quantum dots embedded in GaAs rib waveguides”,Appl. Phys. Lett.107, 021101 (2015).10.1063/1.4926729Search in Google Scholar
 K. Konthasinghe, M. Peiris, Y. Yu, M. F. Li, J. F. He, L. J. Wang, H. Q. Ni, Z. C. Niu, C. K. Shih, and A. Muller, “Field-field and photon-photon correlations of light scattered by two remote two-level InAs quantum dots on the same substrate”,Phys. Rev. Lett.109, 267402 (2012).10.1103/PhysRevLett.109.267402Search in Google Scholar PubMed
 A. Sipahigil, K. D. Jahnke, L. J. Rogers, T. Teraji, J. Isoya, A. S. Zibrov, F. Jelezko, and M. D. Lukin, “Indistinguishable photons from separated silicon-vacancy centers in diamond”,Phys. Rev. Lett.113, 113602 (2014).10.1103/PhysRevLett.113.113602Search in Google Scholar PubMed
 A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits”,Science320, 646–649 (2008).10.1126/science.1155441Search in Google Scholar PubMed
 J. W. Silverstone, D. Bonneau, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, C. M. Natarajan, M. G. Tanner, R. H. Had-field, V. Zwiller, G. D. Marshall, J. G. Rarity, J. L. O’Brien, and M. G. Thompson, “On-chip quantum interference between silicon photon-pair sources,”Nature Photon.8, 104–108 (2014).10.1038/nphoton.2013.339Search in Google Scholar
 A. Politi, J. C. F. Matthews, and J. L. O’Brien, “Shor’s quantum factoring algorithm on a photonic chip”,Science325, 1221 (2009).10.1126/science.1173731Search in Google Scholar PubMed
 A. Crespi, R. Ramponi, R. Osellame, L. Sansoni, I. Bongioanni, F. Sciarrino, G. Vallone, and P. Mataloni, “Integrated photonic quantum gates for polarization qubits”,Nat. Commun.2, 566 (2011).10.1038/ncomms1570Search in Google Scholar PubMed PubMed Central
 J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer,X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Boson Sampling on a Photonic Chip”,Science339, 798–801 (2013).10.1126/science.1231692Search in Google Scholar PubMed
 B. J. Metcalf, J. B. Spring, P. C. Humphreys, N. Thomas-Peter, M. Barbieri, W. S. Kolthammer, X.-M. Jin, N. K. Langford, D. Kundys, J. C. Gates, B. J. Smith, P. G. R. Smith, and I. A. Walmsley, “Quantum teleportation on a photonic chip”,Nature Photon.8, 770–774 (2014).10.1038/nphoton.2014.217Search in Google Scholar
 A. Solntsev, F. Setzpfandt, A. S. Clark, C. W. Wu, M. J. Collins, C. Xiong, A. Schreiber, F. Katzschmann, F. Eilenberger, R. Schiek, W. Sohler, A. Mitchell, C. Silberhorn, B. J. Eggleton, T. Pertsch, A. A. Sukhorukov, D. N. Neshev, and Y. S. Kivshar, “Generation of nonclassical biphoton states through cascaded quantum walks on a nonlinear chip,”Phys. Rev. X4, 031007 (2014).10.1103/PhysRevX.4.031007Search in Google Scholar
 J. Carolan, C. Harrold, C. Sparrow, E. Martín-López, N. J. Russell, J. W. Silverstone, P. J. Shadbolt, N. Matsuda, M. Oguma, M. Itoh, G. D. Marshall, M. G. Thompson, J. C. F. Matthews, T. Hashimoto, J. L. O’Brien, and A. Laing, “Universal linear optics”, emphScience349, 711–716 (2015).10.1126/science.aab3642Search in Google Scholar PubMed
 B. A. Bell, D. A. Herrera-Martí, M. S. Tame, D. Markham, W. J. Wadsworth, and J. G. Rarity, “Experimental demonstration of a graph state quantum error-correction code”,Nat. Commun.5, 3658 (2014).10.1038/ncomms4658Search in Google Scholar PubMed
 G. P. Agrawal,Nonlinear Fiber Optics, 4th ed. (Academic, Elsevier, 2006).10.1016/B978-012369516-1/50011-XSearch in Google Scholar
 J. E. Sharping, K. F. Lee, M. A. Foster, A. C. Turner, B. S. Schmidt, M. Lipson, A. L. Gaeta, and P. Kumar, “Generation of correlated photons in nanoscale silicon waveguides”,Opt. Express14, 12388–12393 (2006).10.1364/OE.14.012388Search in Google Scholar
 K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watanabe, K. Yamada, Y. Tokura, and S. Itabashi, “Frequency and polarization characteristics of correlated photon-pair generation using a silicon wire waveguide”,IEEE J. Sel. Top. Quantum Electron.16, 325–331 (2010).10.1109/JSTQE.2009.2023338Search in Google Scholar
 K. Harada, H. Takesue, H. Fukuda, T. Tsuchizawa, T. Watananabe, K. Yamada, Y. Tokura, and S. Itabashi, “Indistinguishable photon pair generation using two independent silicon wire waveguides”,New J. Phys.13, 065005 (2011).10.1088/1367-2630/13/6/065005Search in Google Scholar
 S. Clemmen, K. Phan Huy, W. Bogaerts, R. G. Baets, Ph. Emplit, and S. Massar, “Continuous wave photon pair generation in silicon-on-insulator waveguides and ring resonators”,Opt. Express17, 16558–16570 (2009).10.1364/OE.17.016558Search in Google Scholar PubMed
 S. Azzini, D. Grassani, M. J. Strain, M. Sorel, L. G. Helt, J. E. Sipe, M. Liscidini, M. Galli, and D. Bajoni, “Ultra-low power generation of twin photons in a compact silicon ring resonator”,Opt. Express20, 23100–23107 (2012).10.1364/OE.20.023100Search in Google Scholar PubMed
 E. Engin, D. Bonneau, C. M. Natarajan, A. S. Clark, M. G. Tanner, R. H. Hadfield, S. N. Dorenbos, V. Zwiller, K. Ohira, N. Suzuki, H. Yoshida, N. Iizuka, M. Ezaki, J. L. O’Brien, and M. G. Thompson, “Photon pair generation in a silicon micro-ring resonator with reverse bias enhancement”,Opt. Express21, 27826–27834 (2013).10.1364/OE.21.027826Search in Google Scholar PubMed
 W. C. Jiang, X. Lu, J. Zhang, O. Painter, and Q. Lin, “Silicon-chip source of bright photon pairs”,Opt. Express23, 20884– 20904 (2015).10.21236/ADA584017Search in Google Scholar
 C. Xiong, C. Monat, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, J. G. Rarity, and B. J. Eggleton, “Slow-light enhanced correlated photon pair generation in a silicon photonic crystal waveguide”,Opt. Lett.36, 3413–3415 (2011).10.1364/OL.36.003413Search in Google Scholar PubMed
 C. Xiong, C. Monat, M. J. Collins, L. Tranchant, D. Petiteau, A. S. Clark, C. Grillet, G. D. Marshall, M. J. Steel, J. Li, L. O’Faolain, T. F. Krauss, and B. J. Eggleton, “Characteristics of correlated photon pairs generated in ultra-compact silicon slow-light photonic crystal waveguides”,IEEE J. Sel. Topics Quantum Electron.18, 1676–1683 (2012).10.1109/JSTQE.2012.2188995Search in Google Scholar
 C. Xiong, M. J. Collins, M. J. Steel, T. F. Krauss, B. J. Eggleton, and A. S. Clark, “Photonic crystal waveguide sources of photons for quantum communication applications”,IEEE J. Sel. Topics Quantum Electron. 21, 205–214 (2015).10.1109/JSTQE.2014.2375154Search in Google Scholar
 M. Davanco, J. R. Ong, A. B. Shehata, A. Tosi, I. Agha, S. Assefa, F. Xia, W. M. J. Green, S. Mookherjea, and K. Srinivasan, “Telecommunications-band heralded single photons from a silicon nanophotonic chip”,Appl. Phys. Lett.100, 261104 (2012).10.1063/1.4711253Search in Google Scholar
 N. Matsuda, H. Takesue, K. Shimizu, Y. Tokura, E. Kuramochi, and M. Notomi, “Slow light enhanced correlated photon pair generation in photonic-crystal coupled-resonator optical waveguides”,Opt. Express21, 8596–8604 (2013).10.1109/CLEOE-IQEC.2013.6801635Search in Google Scholar
 Y. Guo, W. Zhang, S. Dong, Y. Huang, and J. Peng, “Telecom-band degenerate-frequency photon pair generation in silicon microring cavities”,Opt. Lett.39, 2526–2529 (2014).10.1364/OL.39.002526Search in Google Scholar PubMed
 J. He, A. S. Clark, M. J. Collins, J. Li, T. F. Krauss, B. J. Eggleton, and C. Xiong, “Degenerate photon-pair generation in an ultra-compact silicon photonic crystal waveguide”,Opt. Lett.39, 3575–3578 (2014).10.1364/QIM.2014.QW4B.5Search in Google Scholar
 J. He, B. A. Bell, A. Casas-Bedoya, Y. Zhang, A. S. Clark, C. Xiong, and B. J. Eggleton, “Ultracompact quantum splitter of degenerate photon pairs”,Optica2, 779–782 (2015).10.1364/OPTICA.2.000779Search in Google Scholar
 T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, Jun-ichi Takahashi, M. Takahashi, T. Shoji, E. Tamechika, Sei-ichi Itabashi, and H. Morita, “Microphotonics devices based on silicon microfabrication technology,”IEEE J. Sel. Topics Quantum Electron.11, 232–240 (2005).10.1109/LEOS.2003.1252935Search in Google Scholar
 J. W. Silverstone, R. Santagati, D. Bonneau, M. J. Strain, M. Sorel, J. L. O’Brien, and M. G. Thompson, “Qubit entanglement between ring-resonator photon-pair sources on a silicon chip”,Nat. Commun.6, 7948 (2015).10.1038/ncomms8948Search in Google Scholar PubMed PubMed Central
 M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,”Opt. Express13, 1515–1530 (2005).10.1364/OPEX.13.001515Search in Google Scholar
 J. Li, T.P. White, L. O’Faolain, A. Gomez-Iglesias, and T.F. Krauss, “Systematic design of flat band slowlight in photonic crystal waveguides,”Opt. Express16, 6227–6232 (2008).10.1364/OE.16.006227Search in Google Scholar PubMed
 T.F. Krauss, “Slow light in photonic crystal waveguides,”J. Phys. D: Appl. Phys.40, 2666–2670 (2007).10.1201/9781420061529.ch4Search in Google Scholar
 A. Yariv, Y. Xu, R.K. Lee, and A. Scherer, “Coupled-resonator optical waveguide, a proposal and analysis,”Opt. Lett.24, 711–713 (1999).10.1364/OL.24.000711Search in Google Scholar PubMed
 C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of sub-picosecond time intervals between two photons by interference,”Phys. Rev. Lett.59, 2044–2046 (1987).10.1103/PhysRevLett.59.2044Search in Google Scholar PubMed
 J. Chen, K. Lee, C. Liang, and P. Kumar, “Fiber-based telecom-band degenerate-frequency source of entangled photon pairs,”Opt. Lett.31, 2798–2800 (2006).10.1364/OL.31.002798Search in Google Scholar PubMed
 J. Chen, K. Lee, and P. Kumar, “Deterministic quantum splitter based on time-reversed Hong-Ou-Mandel interference,”Phys. Rev. A76, 031804 (2007).10.1103/PhysRevA.76.031804Search in Google Scholar
 A. L. Migdall, D. Branning, and S. Castelletto, “Tailoring single-photon and multiphoton probabilities of a single photon on-demand source,”Phys. Rev. A66, 053805 (2002).10.1103/PhysRevA.66.053805Search in Google Scholar
 J. H. Shapiro, and F. N. C. Wong, “On-demand single-photon generation using a modular array of parametric downconverters with electro-optic polarization controls,”Opt. Lett.32, 2698–2700 (2007).10.1364/OL.32.002698Search in Google Scholar
 T. Pittman, B. Jacobs, and J. Franson, “Single photons on pseudodemand from stored parametric down-conversion,”Phys. Rev. A66, 042303 (2002).10.1103/PhysRevA.66.042303Search in Google Scholar
 E. Jeffrey, N. A. Peters, and P. G. Kwiat, “Towards a periodic deterministic source of arbitrary single-photons,” New J. Phys.6, 100 (2004).10.1088/1367-2630/6/1/100Search in Google Scholar
 J. Mower, and D. Englund, “Eflcient generation of single and entangled photons on a silicon photonic integrated chip,” Phys. Rev. A84, 052326 (2011).10.1103/PhysRevA.84.052326Search in Google Scholar
 H. Jiang, Y. K. Zou, Q. Chen, K. K. Li, R. Zhang, Y. Wang, H. Ming, and Z. Zheng, “Transparent electro-optic ceramics and devices,”Proc. SPIE5644,Optoelectronic Devices and Integration, 380 (2005).10.1117/12.582105Search in Google Scholar
 X.-S. Ma, S. Zotter, J. Kofler, T. Jennewein, and A. Zeilinger, “Experimental generation of single photons via active multiplexing,”Phys. Rev. A83, 043814 (2011).10.1103/PhysRevA.83.043814Search in Google Scholar
 M. J. Collins, C. Xiong, I. H. Rey, T. D. Vo, J. He, S. Shahnia, C. Reardon, M. J. Steel, T. F. Krauss, A. S. Clark, and B. J. Eggleton, “Integrated spatial multiplexing of heralded single photon sources,”Nat. Commun.4, 2582 (2013).10.1038/ncomms3582Search in Google Scholar PubMed PubMed Central
 C. Xiong, T. D. Vo, M. J. Collins, J. Li, T. F. Krauss, M. J. Steel, A. S. Clark, and B. J. Eggleton, “Bi-directional multiplexing of heralded single photons from a silicon chip”,Opt. Lett.38, 5176–5179 (2013).10.1364/OL.38.005176Search in Google Scholar PubMed
 D. Bonneau, G. J. Mendoza, J. L. O’Brien, and M. G. Thompson, “Effect of loss on multiplexed single-photon sources,”New J. Phys.17, 043057 (2015).10.1088/1367-2630/17/4/043057Search in Google Scholar
 C. Xiong, X. Zhang, Z. Liu, M. J. Collins, A. Mahendra, L. G. Helt, M. J. Steel, D.-Y. Choi, C. J. Chae, P. H. W. Leong, and B. J. Eggleton, “Active temporal multiplexing of indistinguishable heralded single photons”,Nat. Commun.7:10853, DOI:10.1038/ncomms10853, (2016).10.1038/ncomms10853Search in Google Scholar PubMed PubMed Central
 T. Shimizu, M. Nakada, H. Tsuda, H. Miyazaki, J. Akedo, and K. Ohashi, “10-GHz operation of a PLZT electro-optic modulator with a ring resonator formed on a silicon substrate”,International Conference on Solid State Devices and Materials, Hongo Campus, The University of Tokyo, Japan, (2010).10.7567/SSDM.2010.D-9-6Search in Google Scholar
 C. A. Husko, A. S. Clark, M. J. Collins, A. De Rossi, S. Combrié, G. Lehoucq, I. H. Rey, T. F. Krauss, C. Xiong, and B. J. Eggleton, “Multi-photon absorption limits to heralded single photon sources,”Sci. Rep.3, 3087 (2013).10.1038/srep03087Search in Google Scholar PubMed PubMed Central
 N. Matsuda, P. Karkus, H. Nishi, T. Tsuchizawa, W. J. Munro, H. Takesue, and K. Yamada, “On-chip generation and demultiplexing of quantum correlated photons using a silicon-silica monolithic photonic integration platform,”Opt. Express22, 22831–22840 (2014).10.1364/OE.22.022831Search in Google Scholar PubMed
 N. C. Harris, D. Grassani, A. Simbula, M. Pant, M. Galli, T. Baehr-Jones, M. Hochberg, D. Englund, D. Bajoni, and C. Gal-land, “Integrated source of spectrally filtered correlated photons for large-scale quantum photonic systems,” Phys. Rev. X4, 041047 (2014).10.1103/PhysRevX.4.041047Search in Google Scholar
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