Waveguide-integrated superconducting nanowire single-photon detectors

2.1 Detection efficiency

Detection efficiency is defined as the probability of electronically registering an event upon the arrival of a photon at the detector [45]. System detection efficiency is the product of three main contributions: coupling efficiency, absorption efficiency and internal quantum efficiency. Coupling efficiency considers all the coupling losses from the experiment’s optical output channel to the nanowire detector. Absorption efficiency describes the probability that a photon reaching the detector is actually absorbed in the superconducting nanowire material. Internal quantum efficiency is the probability that an absorbed photon is converted into a recordable electrical signal [20]. Superconducting nanowires only realize high detection efficiency if several conditions are satisfied. First, a proper optimization of the optical waveguide-to-nanowire coupling is fundamental to achieve high absorption efficiency, as discussed in Section 4.1. In addition, it is desirable to operate the device in the deterministic current-crowding regime, where the internal quantum efficiency saturates at its maximum value. Current-crowding detection is predominant in the presence of a large hot-spot radius in comparison with the nanowire width, as observed for small band-gap and long relaxation time superconductors [107] and for high depairing currents [32]. This can be achieved by working well below the critical temperature [108], [109] and by improving the superconducting film quality [110]. The latter aspect becomes more relevant also considering that, to observe current-crowding detection in the presence of a small hot-spot, narrow nanowires will be fabricated [111], [112]. Here inhomogeneities and defects limit the experimentally achievable switching current [113]. In Figure 2A, the characteristic bias current dependence of the OCDE is shown for a silicon nitride (SiN) waveguide-integrated niobium nitride (NbN) SNSPD. The measured detection efficiency saturates close to the critical current, indicating that the detector is operating in the deterministic detection regime. Saturation of the detection efficiency is a desirable feature because it allows for operating the detector in a regime in which small fluctuation of the bias current will hardly affect the detector response. Saturated detection efficiency at low bias currents allows for obtaining a high SNR of the detection system, as discussed in Section 2.2.

Figure 2:

Noise performance of SNSPDs.

(A) In blue (linear scale on the left) is reported the OCDE curve for an NbN SNSPD integrated on a SiN waveguide at different bias currents I_B. The x axis is normalized to the switching current I_SW. The efficiency is bias current dependent and reaches a saturation at 80% I_SW. In black (log scale on the right) is reported the bias current dependence of the dark count rate. At low bias, the electronic noise floor represents the main contribution, while near I_SW, intrinsic dark counts are predominant. In the intermediate range (green shaded area), it is possible to observe the contribution of stray light inside the cryostat sample chamber. (B) Inter-arrival time measurement of a waveguide-integrated SNSPD. For this detector, the dead time, i.t., the time after the detection event in which no other events are recorded is 10 ns, while the overall recovery time (time needed for the detector to recover full efficiency), starting from t=0, is 18 ns.

For typical stand-alone SNSPDs, system detection efficiency is the relevant parameter of interest, because these devices usually interface with the experiment via fiber or free-space links. In nanophotonic applications, where all the relevant photons are propagating optical waveguides, one often defines the OCDE, which does not consider the insertion losses of external light sources onto the chip. As most material systems that are employed for optical waveguides provide extremely low-loss interfaces between the detector region and the photonic integrated circuitry, which is realized in the experiment under study, only the absorption and internal quantum efficiencies contribute to the OCDE in a meaningful way [102]. The most common method to determine the efficiency of single photon detectors uses carefully calibrated light sources that emit a well-characterized number of photons [45], [114]. In this technique, calibration devices on the chip under test allow for determining the absolute number of incident photons that reach the nanowire detector by monitoring the transmission through a reference port of the device [105], [115]. A calibrated power meter [116] or an integrating sphere is used for precise optical power measurements, and separately calibrated attenuators [117] allow for determining the absolute number of photons reaching the detector. Alternative methods such as the correlated photon method [45], [118], [119] or calibration with synchrotron radiation [120] have also been adopted. The former can suffer from low photon conversion efficiency of the source, while the latter requires access to a suitable synchrotron radiation source, which is not readily available at most laboratories.

2.2 Dark count rate

Single-photon detectors occasionally register events even when none of the sought-after signal photons were incidental [17], [45]. Such detector noise is commonly referred to in terms of the dark count rate, which is made up of three main contributions [111]: electrical noise, background radiation and intrinsic dark counts, as depicted in Figure 2A. Electrical noise in the bias and readout circuitry can generate electrical pulses that will inadvertently be interpreted as photon absorption events. The presence of scattered or background light, e.g. blackbody radiation, in the vicinity of the nanowire detector can also lead to undesired detection events, which are unrelated to the optical signal under study. Thermal excitations in a nanowire that is biased close to its critical current can trigger switching from the superconducting to the normal state, thus resulting in electrical output pulses [38], [121]. The latter process leads to an exponential increase of the dark count rate with bias current, which further increases with temperature. This intrinsic behavior of superconducting nanowires has been observed, especially in the presence of defects or nanowire bends [113]. Other than shielding the system from background radiation [122] and reducing the electronic noise via appropriate filtering and low noise amplification, e.g. at cryogenic temperatures [123], it is highly beneficial to operate the detector at lower bias current. This helps to avoid a biasing regime where nanowire detectors are most sensitive to undesired superconducting fluctuations and thus result in minimal dark count rates. However, this preference for operating nanowire detectors at low bias current needs to be weighed against the desire for high detection efficiency, requiring high bias current. An optimal compromise in terms of noise equivalent power is typically achieved at the onset of the saturation regime (see Section 2.1), where low dark count rates and high detection efficiency are achieved simultaneously.

2.3 Recovery time and afterpulsing

After a detection event, the detector is temporarily not able to produce any electrical response. This time interval (dead time) is followed by a transient time needed for the detector to restore its full efficiency (reset time). The recovery time τ_r is the sum of these two time intervals and sets a limit to the effective maximum count rate a detector can support R_max=1/τ_r [21], [124]. To assess an SNSPD’s recovery time, it is instructive to consider the detectors decay time τ_d=L_K/R_L of the electrical output pulses, which is determined by the kinetic inductance of the device L_K and on the load resistance R_L of the electrical readout electronics (typically 50 Ω).

The kinetic inductance is directly proportional to the detector length and inversely proportional to the nanowire width [41]. Therefore, shorter detectors show lower kinetic inductance and therewith feature shorter pulse decay times resulting in faster detector recovery. While shorter detectors may be desirable for enabling high count rate devices, the shorter nanowire length will also lead to lower absorption efficiency and hence lower detection efficiency. However, embedding nanowires in optical resonant structures is one approach where bandwidth is traded off for simultaneously achieving fast detector response time and high detection efficiency in a nanophotonic device, as discussed in Section 4.2. Afterpulsing in SNSPDs is clustering of dark counts in the time domain and is mainly related to the presence of reflections in the electronic readout circuit [125], [126].

Afterpulsing and recovery time are typically characterized by acquiring the inter-arrival time distribution of detection events from which the second-order correlation function can be calculated [82], [127], as depicted in Figure 2B. This technique consists of illuminating the detector using a continuous wave (CW) laser and collecting the recorded counts with a fast oscilloscope or a field programmable gate array (FPGA) acquisition board to generate a histogram of the time delay between subsequent events. To properly model the detector response when operated near the maximum count rate, the contribution of more than one prior detection events shall be considered. To account for these nonlinearities, a higher order correlation model between time-tagged detection events has been proposed [128]. The purpose of this model, experimentally validated on semiconducting single-photon detectors, not only is restricted on the characterization of the timing response of the detector but also allows to obtain a more general detector calibration, which includes detection efficiency and dark count rate and can be applied for any binary detector, such as SNSPDs.

2.4 Timing uncertainty (jitter)

In addition to being able to operate a single-photon detector at high counting rate, it is also desirable to register events with low timing uncertainty, especially for timing correlation experiments. The relevant quantity, the timing jitter, describes the uncertainty in the time domain with which an electrical signal is registered after a photon was absorbed in the nanowire [22]. The timing jitter can be determined by using a pulsed laser source and collecting a histogram of the time delay between a trigger signal from the laser and the electronic readout signal of the detector [111], [129]. Trigger signals synchronous with the emitted laser pulses can, for example, be generated from high-speed photodiodes, which allow for taking full advantage of the high timing accuracy in the generation of ultrafast pulse trains with mode-locked lasers (typically <1 ps). The jitter performance of an SNSPD fundamentally depends on three main contributions. The first one is an intrinsic contribution, which has been evidenced for bulk SNSPDs and has been associated to the superconducting fluctuations in the thermalization processes that take place from the initial photon absorption until an electrical output pulse is generated [22]. Evidence for such fluctuations was found with SNSPDs made from amorphous superconductors, where this contribution appears to play a significant role when the detector is operated at low bias currents (probabilistic regime), while it is less prominent when the detector is operated in the regime of saturated detection efficiency (deterministic regime) [130]. A second contribution, referred to as geometric jitter, is related to the variation in the position where a photon is absorbed, which results in an arrival time fluctuation of the nanowires voltage response at the counting electronics [22], [131]. Longer detectors experience higher geometric jitter, and it was observed that uniform illumination of a detector will reduce this contribution to the overall jitter value [131]. In waveguide integrated SNSPDs, the geometric jitter contribution is expected to be rather small due to the uniform illumination of the nanowire in the evanescent field of a nanophotonic waveguide, as well as the nanowire’s short length as compared to meander-type SNSPDs. The third contribution to the overall detector jitter is associated with the SNR of the detector voltage pulse, which improves at high bias currents, where the corresponding output voltage is also higher, further depending on the readout electronics [129]. Typical jitter values <50 ps have been achieved with Nb-based detectors. Employing low-temperature amplifiers and readout electronics, low jitter values of 2.7-ps jitter at 400-nm wavelength and 4.6 ps in NIR wavelength have been recently demonstrated with 5-μm-long, 7-nm nominal thickness, NbN nanowires, with respective widths of 120 and 80 nm [94]. Interestingly, these performance values were shown to still be limited by the readout scheme. Hence, superconducting electronics could be designed to improve impedance matching between the detector and the RF readout circuit, thus allowing for further reducing overall device jitter. While current sub-10-ps jitter SNSPDs already offer exciting perspectives for practical applications, any further improvement of the detectors’ timing accuracy will eventually allow for studying the intrinsic detector behavior and better understanding and exploiting the physics underlying the detection mechanism.

2.5 Spectral range

Superconducting nanowire single photon detectors provide high detection efficiency from UV to mid-infrared wavelengths [19], [112], [132]. As discussed in the Introduction, a cloud of quasiparticles is generated upon photon absorption in the nanowire, which in turn switches to a resistive state triggering a detection event. The quasiparticle concentration during the initial stages of the detection process depends on the ratio between the incident photon energy and the superconducting energy gap [35]. The higher the photon energy (i.e. shorter wavelengths), the more quasiparticles are generated, and it will be more likely to operate the detector in the deterministic regime. The detection efficiency will further depend on the relation between quasiparticle cloud size and nanowire geometry as current crowding and quasiparticle diffusion affect the performance [19]. Considering only the superconducting material specific properties, there is no lower limit for the shortest detectable wavelength. On the other hand, the longest detectable wavelength is determined by the superconducting gap and by the nanowire width. NbN and WSi nanowires have shown saturated spectral response up to 5.5 μm [112], evidently limited by the capability to fabricate (narrow) nanowires with higher uniformity. For waveguide-integrated SNSPDs, the spectral range of the detector is determined not only by material properties and geometry of the superconducting strip but also by the waveguiding material. Several material systems that are well suited for fabricating photonic integrated circuits have limited transparency windows. Silicon, for example, is a very popular choice for many integrated optics applications due to its high refractive index, which guarantees strong mode confinement inside a waveguide. However, silicon is only transparent for wavelength in the NIR spectral region and can therefore not take advantage of the full spectral bandwidth of waveguide-integrated SNSPDs. Alternative photonic integrated circuit material systems such as aluminum nitride (AlN) [133], silicon nitride (SiN) [111] and the more exotic polycrystalline diamond [115], however, feature extremely large optical transparency windows and have been demonstrated to be suitable for realizing high-performance SNSPDs, as discussed in Section 3.1. Among these materials, diamond is particularly attractive because it provides optical transparency from the UV to the mid-infrared. Beyond the material platform, an additional bandwidth limitation of waveguide-integrated SNSPDs arises from the waveguide geometry required for low-loss propagation of transverse electric and magnetic field modes (e.g. the waveguide cross-sections determine the maximum wavelength for which a propagating mode is still supported). Lastly, the mechanism for coupling light into an optical waveguide on a chip may underlie further bandwidth constraints, as it is, for example, the case when using optical grating couplers [134].

2.6 Photon number resolution

Superconducting nanowire single photon detectors are generally treated as binary threshold detectors for which PNR is not intrinsically possible, unless additional elements are introduced, for example, arrays of interconnected detectors [135], [136], [137], [138] or by an opportune engineering of the electronic readout scheme [139]. However, at low bias current and under specific illumination conditions, a detector response can be observed only if several photons are absorbed simultaneously [30], [140], [141], [142]. In such a situation, the working point can be tuned to distinguish between the absorption of n photons or more, and less than n photons. When characterizing and using SNSPDs in this particular modus operandi, it is essential to choose suitable bias current and illumination conditions. This threshold detection regime is attractive to perform quantum detector tomography of the device under testing [143], [144], [145], [146] or, for applications with faint lasers, adopting coherent tomography [16], [140].

2.7 Yield and scalability

A key advantage of integrated technologies is that they allow for realizing large numbers of devices on a single chip. Semiconductor industry development has demonstrated continued miniaturization of integrated electronic circuits while preserving their functionality, which has resulted in today’s highly integrated electronic components. Photonic integrated circuits have been developed following similar technology and fabrication strategies. In this case, however, scalability (rather than scaling) is often referred to as the possibility to easily replicate photonic circuit elements in large numbers on the same chip. The minimal feature size of a photonic circuit is determined by the wavelength of the guided light, which constrains the minimal waveguide dimensions for which low-loss mode propagation in the material of choice (refractive index) is still guaranteed. Superconducting nanowire single photon detectors obey similar constraints but can be manufactured in reproducible fashion. Hundreds of waveguide-integrated devices are routinely fabricated on the same chip [147], and devices with up to 11 simultaneously working tungsten silicide (WSi) detectors have been reported [148]. In terms of device yield, amorphous materials such as WSi are more robust with respect to structural defects [82]. To the best of our knowledge, no systematic studies on degradation of detector performance parameters with time have been reported thus far. However, NbN nanowire detectors on SiN waveguides capped with a passivation layer of hydrogen silsesquioxane (HSQ) showed no change in critical current and detection efficiency over the course of 3 years. For NbN nanowire detectors on silicon-on-insulator (SOI) waveguides, a 97% fabrication yield was inferred from room-temperature measurements of more than 600 SNSPDs across two chips [149]. As these studies were performed in a research environment, it may be expected that fabrication yield of hybrid superconducting-photonic circuits will not be a limiting factor when resorting to state-of-the-art semiconductor industry fabrication routines.

2.8 Comparison with other waveguide-integrated detectors

To summarize the previous sections and put waveguide-integrated SNSPDs in perspective, we presented a comparison of crucial detector performance parameters in Table 2. We compared fundamental DARPA key metrics with the state-of-the-art for on-chip detector technology. As the detector output consists of electric signals, we also included information on state-of-the-art commercial time-correlated single-photon counting electronics because it may ultimately limit some of the performance characteristics of an overall photon counting system.

3.1 Integrated photonic platforms

In analogy with electronics, integrated optics has been acknowledged to be one of the most promising enablers for successfully implementing optical quantum technologies [4], [5]. A vast range of material platforms has been explored for integrated photonics [174]. To date, for a variety of them, the successful integration of superconducting nanowire single-photon detectors has been shown. In Figure 3A, we showed an atomic force microscope (AFM) scan of the nanowire detector pattern atop of different material substrates. The superconducting film is typically a few nanometers thick and the AFM measurement has been performed on the exposed e-beam resist. The difference between the materials is mainly given by the refractive index, which determines mode confinement and the transparency window that, in turn, defines the optical bandwidth. In fact, as also depicted in Figure 3B, each material shows a specific transparency window, in which light can be guided without being absorbed. Absorption in the cladding material influences also the optical bandwidth; therefore, the transparency window of SiO₂ and MgO are reported as well.

Figure 3:

Material platforms for waveguide integrated SNSPDs.

(A) AFM scan of NbN waveguide-integrated SNSPDs on different platforms. The scan has been made on an area of 1×1 μm on the E-beam resist (hydrogen silsesquioxane) used for the nanowire pattern exposure, before etching the nanowires. For each micrograph, the rms surface roughness of the waveguiding material is reported. The final resist height depends on the chemical concentration, the spincoating parameters and the dose used for the exposure. (B) Transparency window for different substrates adopted in integrated optic technology.

3.2 Superconducting materials for integrated SNSPDs

NbN, traditionally employed in radiation detection bolometers [206], was the first superconducting material used for single-photon detection in both free-space [30] and waveguide-integrated approaches [101], [102]. To enhance some of the functionalities of SNSPDs, during the last few years, many other materials have been investigated. In this section, we will review the most promising materials adopted for on-chip application.

4.1 Efficiency absorption engineering

A photonic waveguide consists of a ridge structure made of a dielectric material with refractive index higher than the surroundings refractive index [231]. Light is two-dimensionally confined in this structure and free to propagate along a third direction. The intensity of the travelling electric field does not abruptly vanish at the waveguide boundaries but decreases exponentially with distance. This evanescent coupling depends on the refractive index contrast between the waveguiding material and the surrounding environment. It is therefore possible to let the evanescent field interacting with external objects for sensing applications [202], [232] and by controlling the evanescent coupling between nanowires and waveguides the absorption probability can be optimized. As mentioned in the Introduction, in fiber-coupled detectors, light falls under normal incidence onto the nanowire detector and the absorption occurs only in the few-nanometer-thick superconducting material. Although optical stacks have been used to overcome this limitation [79], in general, for sufficient absorption efficiency, long meanders must be used [82], thus increasing the detector recovery time [21]. On integrated photon platforms instead, the evanescent coupling occurs longitudinally with respect to the electric field propagation direction, as depicted in Figure 4A. This is one of the major advantages of the waveguide-integrated architecture, as the absorption probability density can be higher than in the fiber-coupled configuration and shorter nanowires can be used, guaranteeing the combination of high detection efficiency, fast response and small footprint. In Figure 4B, C, we report a comparison of the absorption coefficient per unit length for different waveguide and detector geometries. Simulation results of Figure 4B show that fully etched structures exhibit a higher absorption compared with half-etched structures. This can be explained considering that, in the latter case, the propagating field is more confined towards the substrate and therefore the overlap integral between propagating mode and nanowires placed atop the waveguide is smaller. Besides increasing the detector length, the absorption efficiency can be optimized also by adjusting the nanowire width. On the other hand, an excessive increase of the wire width might limit the internal quantum efficiency of the device [111] or lead to a strong reduction of the device kinetic inductance, thus increasing the probability of observing latching [42]. In Figure 4C, the polarization dependence of the absorption efficiency is also shown. When the nanowire is placed atop the waveguide, transverse magnetic TM-like modes couple more strongly to the nanowire. Better absorption for transverse electric TE-like modes can be achieved by using longer detectors in a compact W-shape double meander geometry or, alternatively, by placing the nanowire at the side of the waveguide. In analogy to fiber-coupled detectors [79], [233], enhancement of the absorption efficiency has been obtained by embedding the detector in a photonic cavity or a resonant circuit [104], [106], [155]. As discussed in the next section, the cost of this improvement is a limited optical detection bandwidth.

Figure 4:

Absorption engineering.

(A) Simulation of the transmission of TE-like mode propagating into an SOI waveguide in the presence of a U-shape nanowire detector. The green inset shows the mode profile in the absence of the detector and the red inset shows the mode profile in the presence of an NbN nanowire. The FEM simulation has been performed using COMSOL Multiphysics considering a 100-nm-wide U-shape nanowire atop a fully etched Si 220-nm waveguide. (B) Simulated absorption per unit length at different nanowire width for a 340-nm-thick SiN on SiO₂ waveguide. Because of the better mode profile overlap with the nanowires, fully etched (FE, blue curve) waveguide exhibited a better absorption characteristic than half-etched (HE, red curve) waveguides did. (C) Comparison of the absorption coefficient for single meander (U-shape, green) detectors and double meander (W-shape, black) detectors on diamond on SiO₂ platform. In this configuration, because of their better coupling with the nanowire, TM-like modes (dashed lines) are better absorbed than TE-like modes (solid lines). For TE-like modes, experimental results using a balance splitter technique [103] are also reported (circles), following [171].

4.2 Coherent perfect absorption (CPA) for near-unit absorption efficiency

In a travelling-wave configuration, the absorption efficiency depends on the coupling length between the detector and the travelling mode. Therefore, increased absorption efficiency requires long or wide detectors. While the latter case has negative impact on the internal quantum efficiency [111], long detectors result in larger footprint, longer recovery time and increased probability of imperfections, which could limit the detectors operation. In 2014, Akhlaghi et al. [106] proposed a CPA scheme to overcome the trade-off limitation between absorption efficiency and reset time of SNSPDs. As initially introduced by Chong et al. [234], CPA is an interference-assisted absorption effect, which, in a lossy system, allows complete dissipation of the input optical power of two counter-propagating beams illuminating a dissipative medium. In the configuration proposed by Akhlaghi et al. [106], destructive interference occurs between the directly reflected light at the front reflector and multiple reflections generated by a cavity. The cavity, depicted in Figure 5A, B, consists of two integrated photonic crystal elements acting as mirrors, realized by etching a series of holes into the Si waveguide. The back mirror is designed to be perfectly reflective; therefore, no light is transmitted through the cavity but can be either reflected or absorbed in the nanowire. The front mirror is designed such that, under resonant conditions, all incident light is dissipated inside the cavity. For negligible scattering losses, the nanowire represents the only dissipative medium and near-unit absorption efficiency at the detector can be achieved. In a real scenario, scattering losses are present inside the cavity and negatively impact the achievable absorption efficiency. The main sources of scattering losses are impedance mismatch between the Bloch and the guided modes at the interface between photonic crystal cavity and waveguide, and the propagation losses to the substrate. Optimized tapering of the input mirror and free-standing structures can therefore be respectively adopted to minimize these contributions. The simulated absorption in resonance is 98.4%, as depicted in Figure 5C (orange circles). The main limitation from obtaining unitary detection efficiency is due to losses to the substrate, which has been calculated as 1% lost contribution. The measurement data for the realized device are shown in Figure 5C. It is possible to observe that the best OCDE measures are 102±8% at 0.9I_SW resonance and at the temperature of 2.05 K (blue triangles). In the absence of CPA, the detector efficiency has been measured to be below 20% (red squares). As expected, the detectors’ functionality is limited in bandwidth, because of the presence of the cavity, but the filtering effect of the cavity helps to minimize the absorption of stray light, resulting in a reduced dark count rate. In addition, defect-induced dark counts are reduced by adopting compact size detectors. In this configuration, the dark count rate, with sealed optical windows, has been determined to be 0.1 cps. This almost-ideal detection efficiency performance is accompanied also by a strongly reduced reset time. For comparison, similar efficiencies in a standard configuration could be obtained only with a 160-μm-long U-shape detector with, consequently, 4.5 times slower recovery time. Fast detectors, with >Gcps count rate, would enable very sensitive time-resolved live imaging applications and high rate communication or cryptography. The CPA approach allows a break in the recovery time and absorption efficiency trade-off dilemma, allowing to design and fabricate very compact devices. Following a similar approach, by embedding a 1-μm-long NbN microbridge in a one-dimensional SOI photonic cavity, it has been possible to obtain recovery times below 500 ps, which could potentially enable detection rates on the order of the Gcps. Due to high scattering losses, the absorption enhancement was limited to an upper total OCDE of 30% [155]. A further improvement of the structure by adopting a 2D photonic cavity allowing a reduction of out-of-plane losses allows to reach almost 70% OCDE by maintaining high timing performances [157].

Figure 5:

Perfect absorber approach for SNSPDs.

(A) Model of the photonic crystal cavity for achieving near-perfect absorption as proposed in Ref. [106]. (B) SEM picture of the fabricated architecture. In the inset is presented the simulated profile of the electric field on the waveguide surface. (C) Measured OCDE at 0.9I_SW for two different devices (blue and green triangles). Orange circles represent the simulated absorption efficiency, and the red squares are the measured OCDE in the absence of the micro cavity. Figure adapted with permission from [106] © Springer Nature.

4.3 Flip-chip SNSPDs transfer technique for complex functionalities with high yield

Because of the need for complex architectures, which do not always require accessible high-end fabrication facilities, a recent trend in research is to refer to foundries for the fabrication of integrated photonic circuitry. It is therefore indispensable to develop deposition methods compatible with a back-end-of-the-line step. This is especially true for NbN, which for high-quality films, i.e. high internal quantum efficiency, requires high-temperature deposition. Najafi et al. [158] introduced a micrometer-scale flip-chip transferring process that enables the integration of SNSPDs into existing circuitry with high yield. NbN SNSPDs are, in a first step, realized on a thin (200–300 nm) SiN film on Si. After a pre-selection step in which the detectors are characterized to identify and select the best performing devices only, the Si substrate is etched, leaving only a thin flexible membrane with SNSPDs and electrical contact pads for their electrical connection. Subsequently, using a tungsten probe and PDMS as an adhesive, the selected detectors are transferred to the target waveguide. The contact pads of the detectors are connected to complementary gold pads on the hosting circuit with a final alignment precision, using an optical microscope, better than 1 μm. A sketch showing the transfer technique is reported in Figure 6A. To show the potentiality of this technique, an on-chip time-energy correlation measurement of entangled-photon pairs has been performed. For this experiment, 1560-nm photon pairs have been generated by an off-chip PP-KTP spontaneous parametric down conversion source, separated at a polarization beam splitter, collimated into two different fibers and coupled onto the photonic chip on a low-temperature stage (2.8–3 K). The photonic circuitry consists of two two-port directional couplers on which a total of four detectors have been integrated using the flip-chip process transferring technique, as depicted in Figure 6B. The pre-selected detectors exhibit an average OCDE of 52±6% and a FWHM jitter (using room temperature amplifiers) between 39 and 57 ps at 1550 nm. Time-resolved correlation measurements have been performed between the two input channels A and B. A final system timing uncertainty of 200 ps has been achieved, and as expected for a photon pair source, antibunching has been observed from A and B channels but not within the individual ones, as shown in Figure 6C. Using a classical light pulsed mode-locked laser source, instead, correlation between all the channels was observed (see Figure 6D). All the transferred devices showed the same performance as in the pre-selection stage, allowing to obtain a working photonic architecture, including detectors, with, in this case, 100% yield. The SiN membrane is flexible and can be potentially adopted to other surfaces. Successful integration on Al on sapphire waveguides has been demonstrated using this technique, which could also serve as a promising approach for transferring detectors on LiNbO3 substrates. The proposed method has been demonstrated to be an effective technique to pre-select working detectors and transfer them onto pre-existing photonic circuitry.

Figure 6:

Transfer protocol for hybrid detector devices.

(A) Sketch of the pick and place technique for transferring a detector onto a hosting chip with photonic waveguide and contact pads. (B) On-chip interferometer with four waveguide integrated detectors and two directional couplers. (C) Coincidence counts at different delay times for different channel combinations for the off-chip entangled-photon pair source and (D) for a mode-locked pulsed laser with similar output power that of the pairs source. Figure adapted with permission from [158].

4.4 SNSPDs array for photon number resolving detection

PNR capability, i.e. the possibility of retrieving the information about the number of photons that have been absorbed after the detection of an event, would be of great advantage for many applications; photon number statistics [235], quantum communication [236] and cryptography [237] are only few examples. For true-photon number sensitivity, transition edge sensors (TES) are typically employed [238]. The response of a TES is directly dependent on the amount of absorbed energy and therefore to the number of incident photons. The main drawback of TES is that they are based on the thermal response and their recovery time is in the order of microseconds. Differing from TES, superconducting single-photon detectors are threshold detectors, meaning that they are only capable to distinguish the presence of a photon or not [30], [140], [142]. Therefore, even if the final response is binary, SNSPDs can discriminate in a threshold mode the presence of many photons. On the other hand, this multiphoton sensitivity is typically inefficient and not truly number-resolving. True PNR can therefore not be achieved intrinsically by SNSPDs. Yet, integration with photonic architectures can help to overcome this limitation by approaching almost-true PNR. As proposed by Sahin et al. [137], by creating a multiplexed array of integrated superconducting nanowire single-photon detectors atop the same waveguide, it is possible to probabilistically discriminate the number n of photons present in an incoming pulse. For an increased number N of detectors in the array, if N>n, there is a high probability that the absorption occurs in a sparse way, such that, with each detector, only one photon is absorbed [239]. This technique is not absolute, as it requires a priori estimation of the maximum number of photons present for each pulse to establish which would be a proper number of detectors in the array. Parallel and serial configurations [136], [239] can be adopted to achieve an output signal very similar to the more traditional TES response, with the main advantage of being two orders of magnitude faster than TES, because of the short SNSPDs’ recovery time. In Figure 7, a schematic of the integrated series array proposed by Sahin et al. [137] is depicted with an example of the output signal. For this proof-of-principle experiment, a PNR up to four photons has been achieved. Alternatively, time-multiplexing using long ring resonators and ultra-fast detectors can be employed for PNR [240]. In this case, the working principle is not based on the spatial distribution of the photons. Instead, the incident pulse is divided into N weak pulses separated by a time interval Δt, thus limiting the overall timing performances. For N>n and Δt bigger than the detector recovery time, it is possible to discriminate the number of incident photons. On-chip delay lines can be readily achieved using integrated ring or spiral structures [241].

Figure 7:

Photon number resolving SNSPDs.

(A) Waveguide-integrated photon number resolving detector with series configuration. (B) Persistence map of the detector output. Up to four-photon discrimination has been achieved. It can be observed that SNSPDs allow to improve the recovery time of few orders of magnitude with respect to TES. Figure adapted with permission from [137] ©AIP Publishing.

4.5 On-chip single-photon detection with spectral sensitivity

The attractive characteristics of SNSPDs can be of great interest in the life Sciences. Spectroscopy techniques, such as FRET [242] and FLIM [243], allow the lifetime monitoring of how molecules interact and communicate with each other, enabling the investigation of the functionality of the cells and their fundamental components. Solid-state detectors or photomultiplier tubes [244] are typically used for detecting weak emission of light in these experiments. For superior timing resolution and high speed, superconducting nanowire single-photon detectors would represent an attractive alternative suitable solution. Well-performing detectors are indeed a necessity but not a sufficient requirement. Life Science applications require also to resolve spectral information of the system under investigation. In this section, we review two different approaches that exploit the best performances of detectors, in terms of detection efficiency, speed, timing response to achieve energy resolution in very compact and well reproducible devices. The first approach consists of the integration of wavelength discriminating photonic circuitry with detectors [105], while the second approach combines the unknown weak signal with a local oscillator to achieve near quantum limited spectral sensitivity [245]. Thanks to its large transparency window, from the visible to the NIR, and low losses, silicon nitride is an attractive platform for spectroscopic applications; therefore, both experiments presented here have been realized using SiN on SiO₂. An on-chip single-photon spectrometer has been realized [105] by combining an arrayed waveguide grating (AWG) structure [246] with eight superconducting detectors at the output. A representation of the structure is shown in Figure 8A. AWGs are, nowadays, used for wavelength division multiplexing (WDM) in photonic networks and consist of two star couplers [247] connected by multiple waveguides of different length. Star couplers are devices capable of redistributing the optical power with low loss from one or more input waveguides to one or more output waveguides. The first coupler serves therefore as a low loss multiport splitter. The signal is injected to an array of waveguides with precisely designed length to guarantee a constant phase shift increment from one waveguide to the other. At the combining star coupler, the waveguides array is condensed to few output waveguides. Thanks to the phase shift occurring within the array grating, the travelling waves will interfere at the output coupler, leading to a spatial redistribution of the input spectrum so that, for each output channel, only a portion of the original bandwidth will be transmitted. By placing a detector at each output port, it is then possible to achieve spectral information of extremely weak light signals. One single-photon spectrometer at the NIR range (1550 nm) with 24-nm spectral bandwidth and resolution of 2.2 nm and one spectrometer in the visible range (738 nm) with 60-nm spectral bandwidth and a final resolution of 6.4 nm have been realized. In this experiment, the number of available channels in the measurement system was limited to eight; therefore, the spectrometer has been designed with eight output ports only. In principle, the number of output channel can be increased to achieve a higher resolution or bandwidth. For short wavelength applications, especially, the main limitation of the number of output channels is the fabrication resolution. In fact, to avoid signal leakage, output ports should not overlap. In Figure 8B, we show the response of the eight-channel SPS in the near-IR range. A comparison with the room-temperature characterization of the device, performed using output grating couplers, indicates a blue-shift of 1 nm. This shift is due to a thermal change of the refractive effective index of the structure after cool down. The on-chip efficiency of the device, which takes into account the AWG losses and the detectors OCDE, was determined to be at 18% for the NIR device and 20% for the visible spectrometer. Concerning the detector characterization, an average detection efficiency of 60% and a 3-ns recovery time were achieved. The system timing jitter, with room-temperature amplifiers, was determined to be of 50 ps close to the switching current for both wavelengths regimes. The functionality of this device has been successfully tested by characterizing silicon vacancy (SiV) color centers in diamond, which are promising candidates for labeling in biological tissue and for single-photon emission [248]. The zero photon line (ZPL) for this sample is at 738 nm, i.e. at the central wavelength of the visible range SPS. In Figure 8C, the fluorescence spectrum of several SiV centers embedded in a nanodiamond cluster was shown. The broad spectrum is related to the wide emission window at room temperature and is consistent with the spectrum recorded with a conventional spectrometer. The scanning capabilities for the confocal microscope allowed to realize a map of the nanocluster emission spectrum. The combination of the spectral resolution and the high scanning resolution allowed to realize a lifetime mapping of the diamond nanocluster, as depicted in Figure 8D. The integration for SNSPDs on a wavelength-discriminating on-chip circuitry allows to obtain a spectrally resolved single-photon detection with high timing precision in a single nanophotonic device.

Figure 8:

Integrated single photon spectrometer.

(A) Sketch of the on-chip single-photon spectrometer using an AWG connected to eight SNSPDs detectors. (B) On-chip device efficiency as a function of the wavelength. The detectors were biased at 0.9I_SW. (C) Emission spectrum of SiV color centers in diamond as recorded by the eight-channel visible-range on-chip spectrometer (blue bars). Yellow represented the emission spectrum obtained with a conventional spectrometer. (D) Map of the fluorescence lifetime of the SiV centers cluster. In the inset is shown an optical micrograph of the cluster under test. In green is indicated the area scanned for the lifetime map. Figure adapted with permission from [105] © OSA Publishing.

The major limitations of AWG spectrometers are a limited number of channels and the need of very high yield for detectors and photonic circuitry components. Another solution is to use coherent detection techniques [249]. This method, successfully adopted for LiDAR and space applications, allows to obtain extremely high spectral resolution by using only one detector. The working principle, depicted in Figure 9A, B, consists of combining the signal of interest (S) with a weak local oscillator (LO). The two signals start beating at an intermediate frequency (IF), which correspond to the signal and local oscillator frequency difference. By detecting the intermediate frequency and subtracting it from the known local oscillator frequency, it is possible to retrieve spectral information of the signal under investigation. This technique has been widely adopted in the past using hot electron bolometers [250]. The drawback of hot electron bolometers is that they exploit a thermal effect, which is slower, thus limiting the detection bandwidth. Solid-state single-photon detectors have been therefore introduced [251]. In this case, the response signal corresponds to a train of detection pulses, which repeat at the signals intermediate frequency. By adapting this technique with integrated SNSPDs, it is possible to exploit their extremely high speed to access a wider spectral bandwidth and their superior detection efficiency in the infrared range for an increased sensitivity. Coherent detection has been demonstrated using an 86% efficient waveguide-integrated SNSPD, with dark count rate of <100 cps at 80% of the switching current. To fully characterize the performance of this approach, two different experiments have been performed. The smallest detectable signal has been determined using a single CW laser source connected to a two-port fiber splitter, one of which was connected to an acousto-optic modulator for generating a local oscillator signal and test signal with a constant frequency shift of 400 MHz. The response signal of the detector has been amplified and analyzed using a spectrum analyzer (SA) to determine frequency and power of the beating signal. The minimal detectable power is limited by the SNR of the IF spectrum registered with the SA, which in turn depends on the detector efficiency (higher detection efficiency would allow to obtain a better SNR), dark count, electrical noise of the amplifiers and the dynamic range of the SNA. By controlling the local oscillator power, the SA resolution bandwidth and the acquisition time, an ultimate sensitivity limit of roughly two times the photon energy has been obtained. In Figure 9C, we showed a comparison of the minimal detectable signal at different signal photon fluxes in comparison with the MDS for a shot-noise limited system (unitary detection efficiency and no dark counts). Quantum sensitivity can be potentially achieved with better efficient detectors and with improved low noise electronics. To determine the detection bandwidth, two different attenuated lasers, one acting a signal and a second, as local oscillator, were adopted. The measurement results are depicted in Figure 9D. The detection bandwidth is defined as the intermediate frequency value at which the SNR is reduced by 3 dB. The detection bandwidth was mainly limited by the bandwidth of the readout scheme, in particular, by the adopted room-temperature amplifiers. Spectral resolution at the single-photon level is of great interest for both classical and quantum optics. Coherent detection with integrated SNSPDs allows to achieve extremely sensitive spectroscopy with high resolution (Δf/f>10¹¹). This technique can find interesting application for characterizing the emission spectra of on-chip sources, for communication multiplexing and for the investigation of extremely narrow fluorescence lines, also in the infrared region.

Figure 9:

Heterodyne mixing with SNSPDs.

(A) (I) Time-domain beating of the EM field generated by the overlapping of the LO and the S fields with a slight frequency shift. (II) Power oscillation at the intermediate frequency. (III) Voltage response of the SNSPD in the presence of beating. (IV) Count rate as recorded by a frequency counter. (V) Detection response in the frequency domain. (B) Schematic view of the W-shape SNSPDs. (C) SNR at different signal photon flux. The red curve represents the response for an ideal shot-noise-limited photodetector, with unitary efficiency and no noise. The arrows indicate the minimum detectable signal for SNR=0 dB. (D) Noise bandwidth for two different detectors geometries. The arrows indicate the −3 dB threshold used for the bandwidth determination. Figure adapted with permission from Ref. [245].

5.1 On-chip time resolved detection of quantum dot emission

Solid-state emitters, such as in GaAs quantum dots (QDs), have been proposed as reliable and potentially scalable sources of single photon. These devices can be integrated with state-of-art GaAs photonic platform, which is compatible with the integration of superconducting nanowire single-photon detectors, as described in Section 3.1.3. Although electrically driven emission has been demonstrated [252], [253], optical excitation still represents the most effective method for single-photon generation using QDs. The main drawback of this technique is the need for filtering the excitation laser light, which is scattered through the substrate or coupled into the waveguide, thus reducing the SNR at the SNSPDs. Reithmaier et al. [166] overcame this limitation by temporally filtering the detector signal to recover the emission of self-assembled InGaAs quantum dots embedded in GaAs on AlGaAs waveguide with in situ detection, using a waveguide-integrated NbN SNSPD. As depicted in Figure 10A, a pulsed laser diode was used to excite the QD emission, which propagates through the GaAs waveguide and is detected by SNSPDs at a distance of 1040±1 μm. QDs with sharp emission line were pre-selected using a confocal microscopy technique. In this experiment, the excitation laser was not filtered. An amorphous Si absorber layer has been deposited on the back surface of the chip to reduce the contribution of the stray light, and the luminescence signal has been retrieved by deconvolving the detector response signal and the excitation laser signal, using temporal filtering of the SNSPD response. The experimental results are reported in Figure 10B. In the absence of QDs, the time-resolved SNSPDs signal response function shows a Gaussian profile with FWHM of 290±70 ps, reproducing the pulsed emission of the excitation laser. In the presence of a quantum dot, instead, an exponential decay of the response function is clearly visible. The decay rate has been determined to be τ_QD=(0.80±0.07) ns and is compatible with the InGaAs lifetime [254], [255]. An important advance using this technique is the characterization of the emission lifetime with SNSPDs without any filtering of the excitation light. An off-chip confocal characterization of the source’s second order correlation function g(2)=0.36 simultaneous to the on-chip fluorescence characterization confirms the single-photon Nature of the QDs photoluminescent signal characterized using the on-chip detectors. The high timing resolution of SNSPDs allows to characterize the emission lifetime of single-photon sources integrated onto an optical waveguide using a time-filtering technique, which does not require any kind of off-chip filter stage, which would inevitably reduce the emitted signal intensity. The main limitation is the system jitter and the time duration of the excitation pulse, which could, for short-lifetime sources, affect the discrimination of the source fluorescence decaying signal. These limitations could be overcome with an improvement of the readout electronics and, where possible, a reduction of the excitation pulse duration.

Figure 10:

Integrated characterization of QD single photon emitters.

(A) Schematic of the on-chip structure consisting of a 2-mm-long GaAs ridge waveguide containing a single layer of InGaAs QDs. The QDs are excited by a free-space pulsed laser diode, and their emission coupled to the waveguide and propagated to the NbN detector. The inset reports an AFM scan of the QD. (B) Photoluminescence signal detected by the SNSPD. Units are in counts per detected laser photon (cts/l). In the absence of the quantum dot (red curve), the instrument response function (IRS) of the excitation laser is recorded. In the presence of the QDs (blue data points), an asymmetric behavior is observed. By subtracting the IRF, the QD emission lifetime can be determined. The yellow-shaded area indicates the integration window in which the QD lifetime has been extracted. Figure adapted with permission from [166] © American Chemical Society.

5.2 Integrated autocorrelator

One key functionality for the advancement of integrated quantum photonics is the ability of characterizing the classical and quantum Nature of on-chip light sources. Superconducting detectors represent an ideal solution to realize on-chip measurement of sources’ second-order correlation with very low timing uncertainty. A very compact integrated autocorrelator has been proposed by Sahin et al. [256]. The scheme, depicted in the inset of Figure 11A, consists of two NbN SNSPDs (D1 and D2) integrated on top of the same GaAs waveguide. The main requirement for this design is symmetrical arrangement of the nanowires on the same waveguide to ensure equal coupling with the propagating evanescent field. The waveguide structure made of 300-nm GaAs on AlGaAs 1.85-μm wide was able to support both TE and TM modes, thus making the correlator polarization independent. Despite a calculated high absorption efficiency (>93%), the practical limitation of the system was low OCDE, related to a non-optimized film thickness, which compromised the internal quantum efficiency of the devices. This limitation can be overcome by improving the quality of the superconducting film. Importantly, the two detectors showed almost no crosstalk, resulting in a low noise system. Static cross-talk has been tested by measuring the variation of the switching current of one detector at different biasing conditions of the second detector (Figure 11B). In addition, a negligible contribution of the dark counts of one detector at different biasing to the second detector, as depicted in Figure 11C, has been shown. Better heat transport due to high thermal conductivity of GaAs could explain the reason for such low static cross-talk when compared with sapphire. The dynamic cross-talk, defined as the temporal variation of the detection probability of one detector due to switching of the second detector, has been tested by measuring the second-order autocorrelation function of a CW coherent light source (laser) and of a pulsed laser. As shown in Figure 11D, no artifacts in the coincidence counting signal have been found, confirming the absence of dynamic cross-talk. Uncertainty in propagation demonstrated a 4% experimental accuracy. Thicker superconducting film ensured high critical currents (22 μA), which are beneficial for a lower electronic SNR. The overall system jitter, using room-temperature amplifiers, has been determined to be 125 ps, near the switching current, which is sufficient for characterizing quantum dot single-photon emission. This very compact autocorrelator is a ready tool that can be adopted for the characterization of on-chip sources. A full architecture combining this autocorrelator with photoluminescent quantum dot sources and a photonic crystal cavity for on-chip filtering of the pump light is shown in Figure 11A. This structure has been successfully used to perform a TRPL characterization. The low extinction ratio of the pump light filtering block represents the main limiting factor. By placing the excitation spot far enough from the detector (500 μm or more), most of the signal was suppressed and only the QD emission was measured [167]. Evaluating the cross-talk for other substrates than GaAs would allow to adopt such a geometry also for different platforms. With an improved pump suppression, the proposed method is a convincing scheme, which could become a universal tool for fully integrated second-order autocorrelation measurement.

Figure 11:

Integrated HBT measurement with SNSPDs.

(A) Schematic of the on-chip HBT experiment as proposed in Ref. [167]. The sketch in the inset represents the waveguide-integrated autocorrelator using two nanowires onto a photonic waveguide. (B) Influence of the bias voltage applied on the detector D1 on the critical current of the detector D2. Within the experimental accuracy, no cross-influence between the two structures has been observed. (C) Dark count rate of the detector D1 versus D2 bias current. Also, when D2 was in normal state (starred points), no influence on the DCR of the first detector has been observed. (D) Intensity autocorrelation for a CW laser measured with the integrated autocorrelator. The absence of artifacts within the measurement uncertainty allows to exclude dynamic cross talk between the two detectors. Figure adapted with permission from [167], [256] © OSA Publishing.

5.3 Fully integrated quantum photonic circuit with an electrically driven light source

Substantial research efforts are today dedicated on finding reliable and fast sources that can be easily integrated on a wafer scale and can be coupled to waveguiding structures [257]. High brightness, reproducibility and no blinking are not the only requirements for on-chip light sources. Two major challenges must be faced: efficient coupling to photonic waveguides and the possibility of directly exploiting the emitted light on chip. Different solutions like quantum dots [166], [258], color centers [203] and parametric down conversion in nonlinear materials [162] have been proposed. External light can be easily coupled to waveguides or, in the case of nonlinear effects, can be directly generated inside the waveguiding material. On the other hand, a major bottleneck in the application of these sources for a full on-chip architecture is that these sources require optical excitation with light, which needs to be filtered on chip with very high extinction ratio. The pump light is typically orders of magnitude more intense than the emitted light, and on-chip filters capable of fully suppressing this undesired contribution are challenging to implement. Furthermore, integrated filters are generally based on waveguiding structures generating thermal effects and reflection, negatively influencing the functionality of the routing and detection components of the system. Therefore, in many of the experiments, light is filtered off-chip with a subsequent degradation of the original signal. A desirable solution is offered by adopting electrically driven single-photon sources, which do not need of any kind of external optical excitation. As proof of principle of a full on-chip source characterization experiment, a second-order correlation measurement of a carbon nanotube-based electrically driven single-photon source was performed [160]. Single-walled semiconducting carbon nanotubes (sc-SWCNTs) can operate at low temperatures and can also be deposited on a large scale using dielectrophoresis [259]. The nanotubes emission wavelength can be chosen by chirality and diameter and can span from the visible to the NIR wavelengths [260]. Furthermore, high emission rates on the order of Gcps have been reported [261], with would enable ultra-fast on-chip quantum optic processing. To characterize the quantum Nature of the waveguide-coupled light source, a fully integrated architecture for Hanbury-Brown-Twiss experiment has been realized. The system geometry, depicted in Figure 12A, consists of two waveguides integrated SNSPDs symmetrically located at the opposite side of a SiN waveguide on which a sc-SWCNT has been deposited. The whole characterization has been performed at exchange gas temperature of 1.6 K, using a liquid-helium cryostat. The emitted light evanescently couples to the waveguide and propagates towards the nanowire. Because of the symmetric position of the detectors with respect to the emission point, the waveguide acts as a beam splitter. By correlating the count rates of the detectors for different electrical excitation powers, antibunching characteristics of the source shown in Figure 12B could be observed. A limitation of this experiment was the short lifetime of the source (~72 ps), which is close to the system timing uncertainty. The system jitter was in fact limited by the readout electronics. By improving the electronics, using, for instance, cryogenic amplifier, better performance can be reached. In addition, it is important to consider that the whole experiment has been performed by driving the source with continuous current. The visibility could be improved by adjusting the excitation electronics for pulsed excitation. The experiment represents a successful demonstration of the integration of superconducting nanowire single-photon detectors for a full on-chip characterization of single-photon sources. The same architecture can be potentially adopted for any waveguide coupled source that does not need optical excitation. As a further improvement, a very interesting architecture for the simultaneous, full characterization of a single-photon state has been recently proposed by Thomay et al. [262]. Although demonstrated for stand-alone sources and detectors, this method can be adopted for a fully integrated on-chip cross correlation measurement using four single-photon detectors. This would represent a very fast and accurate way to fully characterize a single-photon source, with existing integrated technology and detectors.

Figure 12:

On-chip characterization of CNT single photon emitters.

(A) Schematic view of the on-chip device. The electrically stimulated emission from a sc-SWCNT couples and propagates inside the waveguide and reaches the integrated detectors. Due to the chirality properties of the emitter, the symmetric configuration allows 50:50 splitting of the emitted photons among the two detectors. (B) Coincidence histogram of non-classical light emission from the electrically driven nanotube obtained with the integrated correlator. (C) Zero-delay correlation function for different electrical power applied to the carbon nanotube. Figure adapted with permission from [160] © Springer Nature.

6.1 On-chip quantum interference

Quantum interference is of fundamental importance for exploring the quantum Nature of light and for quantum processing. This effect has been experimentally observed by Hong, Ou and Mandel (HOM) in 1987 [263]. When two indistinguishable single-photon reach a beam splitter simultaneously, they will interfere non-classically. They will be both reflected or transmitted through the beam splitter; therefore, the probability that the two photons will leave the beam splitter separately is zero. By modifying the path difference between the two photons and collecting the coincidence of the arrival of the photons at the two branches of the beam splitter with two single-photon detectors, it is possible to observe a dip in the coincidence probability at the zero-delay arrival time. This is the so-called HOM dip and is a clear sign of single photon’s indistinguishability. The width of the dip is given by the photons coherence time, while the depth indicates the level suppression of the photons coincidence probability, which is called visibility and expresses the purity of the single-photon state. Linear optics quantum computation is based on quantum interference of multiple photons [46], [48], [49], [264]. Integrated optics offers a complete set of ready-to-use building blocks such as beam splitters, interferometers and phase shifters for implementing quantum operators. The basic architecture for HOM interference consists of a single-photon source, a tunable delay line, a beam splitter and two single-photon detectors. On-chip quantum interference has been realized on SiN on SiO₂ substrate using a directional coupler device, acting as a beam splitter, and two NbTiN superconducting nanowire single-photon detectors, as depicted in Figure 13A [149]. An important advantage of this on-chip application is that the spatial overlap between the input modes of the directional coupler is guaranteed by the high lithographic control over the waveguide dimensions. For this experiment, an off-chip spontaneous parametric down conversion source (SPDC), a periodically poled potassium titanyl phosphate (ppKTP) crystal waveguide, has been used. The source was excited with a 775-nm pump laser to generate photon pairs at 1550 nm. The pump signal has been suppressed by using a 1064-nm long pass and a 1550-nm band pass filter. After adjusting the polarization of the emitted photons and the temporal delay between the two photons by the mean of an optical delay line, the photon pair has been transmitted into an on-chip interferometer at a temperature of 1.7 K. The coupling between the source and the on-chip interferometer has been performed using different conversion stages from free space, to fiber to grating couplers resulting in high coupling losses. Thanks to the extremely high SNR of superconducting nanowire single-photon detectors, by scanning the delay line around the zero-path difference, it has been possible to observe HOM interference with 97% visibility, as shown in Figure 13B. In Figure 13C, the dependence of the interfering single-photon state purity on the pump laser wavelength was presented. A degradation of the visibility by detuning the pump laser out of the quasi phase matching condition can be observed. More compact photonic structures, such as multimode interference (MMI) devices, can be adopted for the realization of an on-chip interferometer [265]. These structures do not only provide smaller footprint but also allow a more robust control in fabrication, allowing to maximize the spatial overlap between the interacting modes.

Figure 13:

On-chip quantum interference.

(A) Schematic of the on-chip interferometer. Two input focusing grating couplers are used to inject the photon pairs in the circuit. An external delay line is used to scan the arrival time of the photons at the beam splitter. Two reference ports (Ref₁, Ref₂) are used to control the input photon flux. The beam splitter consists of a directional coupler, which length has been optimized to maximize the photon pair mode overlap. SNSPDs are allocated at each output of the beam splitter for the coincidence measurement made with external coincidence electronics. (B) Coincidence detection rate between the two SNSPDs as function of the optical delay line position. The nominal pump power of the SPDC was set to 10.5 mW. (C) HOM interference visibility as a function of the SPDC pump wavelength (colored symbols). Black symbols represent the SHG efficiency as a function of the pump wavelength for the ppKTP crystal. Figure adapted with permission from [149].

6.2 Quantum interference in plasmonic circuits

When many functional devices on a single chip are needed, small footprint becomes very important. Dielectric waveguides are diffraction-limited systems, and the device size is still very large when compared with integrated electronics. Exploiting surface plasmon polaritons, which can propagate in extremely confined structures, allows to beat the diffraction limitation. SNSPDs have been demonstrated to be suitable also for the detection of single surface plasmon polaritons [266]. Single-photon impinging on a plasmonic waveguide has been used to excite plasmons, which propagate through a 7.5-μm waveguide equipped with NbN nanowires. A correlation measurement between off-chip APDs used to characterize the single-photon source emission and the on-chip detectors employed to count the plasmons propagating within the on-chip plasmonic waveguide allowed to confirm the original photons counting statistics, thus confirming single plasmon sensitivity of the system. In addition, Heeres et al. [267] showed quantum interference between indistinguishable plasmons using plasmonic-waveguide integrated NbN SNSPDs. This representative experiment paves the way for a smaller sized integrated platform for quantum information processing. Single photon generated by a type II SPDC source has been separated into two channels and coupled to different inputs of a two-port plasmonic beam splitter. The polarization of the two channels has been optimized to maximize the plasmon excitation. The beam splitter output was directed to two NbN superconducting meander-shaped nanowires made of a 5-nm-thick and 100-nm-wide NbN strip. By adjusting the time delay between the excitation photons and thus the arrival time of the two polaritons at the beam splitter, it was possible to observe the Hong-Ou-Mandel (HOM) dip at zero-time delay with a best-case visibility of 0.43±0.02. Further analysis and simulation allowed the authors to confirm that the reduced visibility compared to the one observed with the generated photon pairs of 0.92±0.01 can be associated with the excitation of long-range surface plasmons, which are not strongly confined. Supplementary simulation hinted an imperfect mode overlap in the beam splitter, which resulted in a reduction of visibility by 8%. An analysis of the time-resolved correlation allowed to determine a coherence time of 2.49±0.08 ps, very similar to the coherence time of the single-photon pair (2.51±0.03 ps), confirming that the plasmonic mode propagation does not degrade the wave-packed temporal resolution. This first experiment of quantum interference between surface plasmon polaritons on a chip opens new possibilities for compact quantum optics not limited by the conventional diffraction size, with potential to push towards the length scale of electronic components.