Superconducting nanowire single-photon detectors (SNSPDs)^1,2, or also referred to as superconducting strip photon detectors (SSPDs), have played vital roles in many classical and quantum photonic applications^3-8. Different from most commonly used, meandering SNSPDs^9,10, fractal SNSPDs are featured with low polarization dependence of their detection efficiency^11-15. Up till now, all the fractal SNSPDs reported in literature were packaged and configured into single-channel systems^12-15. On the other hand, to our knowledge, multi-channel SNSPD systems, either reported in literature^16-19 or commercially available²⁰, are all polarization sensitive, and the multi-channel systems with SNSPDs that all feature low polarization sensitivity remain unexplored. Such a high-performance multi-channel system would be very useful for multi-photon coincidence counting that is often used in experimental quantum photonics to characterize non-classical light sources^17,21 and quantum computation^3,22,23.

In this paper, we report on an eight-channel fractal SNSPD system in the wavelength range of 930 to 940 nm. This spectral range overlaps with the emission spectra of a category of single-photon sources based on III-V semiconductor quantum dots (QDs)^24-27. In the system, we include 6 fractal SNSPDs¹² and 2 fractal superconducting nanowire avalanche photodetector (SNAPs)^14,15. The design and nanofabrication of the devices were carefully and strategically optimized; the highest system detection efficiency (SDE_max) for the SNSPDs and the SNAPs are $96_{-5}^{+4}$% and 95 ± 5%, respectively, at the base temperature of 2.2 K. The average SDE for eight channels for all states of polarization is estimated to be 90 ± 5%. While both types of detectors show high SDE, the SNSPDs exceed in low dark-count rates (DCRs) and, therefore, low noise-equivalent power (NEP), whereas the SNAPs exhibit higher operating speed and better timing resolution. As a direct application, two channels were used to measure the second-order correlation functions of light emission from a single-photon source based on a semiconductor QD and from a pulsed laser, and the results were compared with those measured by two silicon single-photon avalanche diodes (SPADs).

The detectors to the arced fractal geometry were designed similar to what have been reported previously¹⁵ but with several important improvements so as to pursue extremely high SDE in the wavelength range of 930 to 940 nm. (1) The photosensitive area of each detector was expanded to allow more tolerance of the misalignment between the fiber and the detector and to ensure close-to-100% coupling efficiency. To this end, the photosensitive areas of the SNSPDs and the SNAPs were designed to be 13.7 μm × 13.7 μm and 15.2 μm × 15.2 μm, respectively. Note that the fractal design of the SNAPs does not support an arbitrary size of the photosensitive area, hence the sizes of two types of detectors couldn't be made to be identical. (2) The thickness of the NbTiN film was still 9 nm¹⁴, but the width of the nanowire was increased from 40 to 50 nm so as to reduce the difficulty in patterning and therefore increase the yield. Our consideration is that, as the targeted wavelength is 930 to 940 nm, the energy of a single photon is larger than that of a photon in the telecommunication wavelength range of 1550 nm; a nanowire wider than what we used in the past^14,15 could probably yield saturated detection efficiency. Fig. 1a, c present the false-colored scanning-electron micrographs of the resulting fractal SNSPD and SNAP, respectively, and Fig. 1b, d present their equivalent circuitries. The process of nanofabrication is presented in METHODS. (3) For further enhancing optical absorptance, we increased the number of the pairs of the dielectric layers in the bottom of distributed Bragg reflector (DBR) from 6¹⁴ to 8 pairs. Fig. 1e presents the designed microcavity composed of SiO₂ and Ta₂O₅ dielectric layers. The thicknesses of each SiO₂ layer in the DBR, each Ta₂O₅ layer in the DBR, and the SiO₂ defect layer are 152 nm, 106 nm, and 296 nm, respectively. The simulated intensity distribution of the light intensity along the y_D direction, assuming no NbTiN nanowires, is shown as the red line in Fig. 1e. Each detector was fabricated into the keyhole shape for self-aligned packaging with optical fiber²⁸ for top illumination. The photosensitive regions of the two types of detectors were designed and fabricated to be larger than the optical spatial modes, giving some tolerance of misalignment to ensure efficient optical coupling.

All the measurements were performed by cooling the detectors to 2.2 K in a 0.1-W close-cycled Gifford-McMahon (G-M) cryocooler. For this particular cryocooler, we purchased the bare cryocooler and the compressor unit from Sumitomo, and designed and implemented the vacuum system with feedthroughs for optical fibers and electronic cables, the plate for mounting the chip packages, as well as the radiation shields. The cooling curves are presented in Fig. 2. During the cooling process, a power supply with the frequency of 60 Hz was used to increase the power of the compressor, and made the cooling process faster²⁹. Specifically, we presented the cooling curves of the system with a single channel and eight channels configured, as shown in Fig. 2a. Additionally, zoom-in views are presented in Fig. 2b. The cooling speed of the system configured with a single channel is much faster than that of the eight-channel system, and it also reaches a lower minimum temperature due to the lower heat load. The single-channel system reaches a minimum temperature of 2.0 K after 3 h of the cooling process, whereas the eight-channel system reaches a minimum temperature of 2.2 K after 6 h.

Measurement on the SDE and DCR// FCR (false-count rate) of individual representative devices of the two types was firstly conducted. For measuring SDE, we used the method based on time-correlated single-photon counting³⁰ and used a SuperK with a monochromator as the light source (full width at half maxima [FWHM] spectral width: 2 nm). Low-noise radio-frequency (RF) amplifiers working at room temperature were used in this work. The schematic diagram of the experimental setup is presented in Fig. 3a.

Fig. 3b presents the SDE_max, SDE_min and DCR for the SNSPD (channel C2). The switching current, I_sw, was 13.2 μA, and when I_b > I_sat = 8.1 μA, the SDE-I_b curves show saturated plateaus. I_sat was determined by fitting the measured SDE_max-I_b with an error function, taking a derivative that yielded a bell-like function, and finding the smallest I_b on the right of the peak making the normalized derivative less than 0.01. This I_b was treated as I_sat. DCR drops swiftly as decreasing the bias current from I_sw. As shown in Fig. 3c, at the bias current of 9.4 μA, where NEP (calculated from SDE_max and DCR, NEP = $\frac{h v}{\mathrm{SDE}_{\max }} \sqrt{2 \mathrm{DCR}}$, where, hν is the photon energy^31,32) gets minimized, SDE_max = 95 ± 5%, SDE_min = 93 ± 5%, polarization sensitivity (PS) = 1.02, and DCR = 1.25 cps. The minimum NEP is 0.36 × 10⁻¹⁸ W⋅Hz^−1/2. The relative error of the SDE measurement was estimated to be 5.3%, following the detailed analysis of various sources of uncertainties as in refs.^15,33. The SDE has been corrected by taking into account of the optical reflection from the fiber facet when measuring optical power; the uncorrected values were SDE_max = 98% and SDE_min = 96%.

In comparison, Fig. 3d presents SDE_max, SDE_min and FCR for the SNAP (channel C4). The false counts include the dark counts and the afterpulses^14,34,35. The switching current was 25 μA, and when I_b > I_sat = 19.7 μA, the SDE-I_b curves show saturated plateaus. FCR decreased as the bias current was decreased from I_sw, but when 13.8 μA < I_b < 20.0 μA, and when I_b was further decreased, the detector operated in the unstable regime, and the FCR increased dramatically because of excessive afterpulses^14,34,35. Therefore, as shown in Fig. 3e, at the bias current of 20 μA, NEP (calculated from SDE_max and FCR, NEP = $\frac{h v}{\mathrm{SDE}_{\max }} \sqrt{2 \mathrm{FCR}}$) gets minimized, SDE_max = 94 ± 5%, SDE_min = 93 ± 5%, PS = 1.02, and FCR = 25.8 cps. The minimum NEP is 1.61 × 10⁻¹⁸ W⋅Hz^−1/2. Therefore, the lowest FCR of the SNAP is a bit higher than the DCR of the SNSPD at the appropriate operating bias current.

It is noted that recent studies illustrated that the constrictions and bends are prone to generating dark counts^36,37; however, here, the fractal SNSPD and the fractal SNAP containing a plethora of bends in their photosensitive regions did not show excessive dark or false counts even when fully biased. These observations indirectly evidenced the uniformity of the curved nanowires we patterned and fabricated. On the other hand, since the fractal geometry includes many U-turns and L-turns in the pattern of the nanowire, which is a key difference with the most commonly used meander SNSPDs, therefore it is thought that the mechanism of the dark and false counts of the fractal SNSPDs and SNAPs is still quite elusive and that it needs more detailed research.

Fig. 4 presents the time-domain properties of the SNSPD and the SNAP. Fig. 4a presents the oscilloscope traces of the output voltage pulses. The exponential-decay fittings show e⁻¹ time constants of 18.0 and 7.9 ns for the SNSPD and the SNAP, respectively. Fig. 4b presents the traces simulated by thermoelectrical simulation, without taking the RF amplifier (See METHODS) into consideration. The simulation reproduced the voltages pulses in terms of the relative amplitudes and the shapes. The simulated e⁻¹ time constants were 14.5 and 4.4 ns for the SNSPD and the SNAP, respectively. The differences between the simulated and measured results are mainly due to the fact that the electronic filtering effect of the RF amplifier was not taken into account in the simulation, and the value of kinetic inductivity taken from ref.³⁸ might be slightly different from that of the actual superconducting film used in our experiment. Fig. 4c presents the timing jitter (FWHM of the time-delay histogram) as functions of I_b for the SNSPD and the SNAP. Timing jitter was measured with a low-noise RF amplifier working at room temperature and an oscilloscope with a real-time bandwidth of 4 GHz. Note that the measurements were conducted at 1560-nm wavelength employing a femtosecond pulse laser and a high-speed photodetector with a bandwidth of 40 GHz. For the measurement of timing jitter, all the detectors were pigtailed with SMF-28e optical fibers. The lowest timing jitter for the SNSPD and the SNAP were 63 and 41 ps, respectively.

Eight detectors were installed in the cryocooler and complete characterization was performed. Fig. 5a presents a photograph of the cold head with eight fiber-coupled packages installed on the self-designed stage. Measurement on the SDE_max and SDE_min of the eight detectors was conducted. Fig. 5b presents the measured SDE_max as functions of the wavelength of the incident light, with all the detectors biased at 97% of each I_sw. SDE_max of C3 peaked at 930 nm, and SDE_max of the remaining channels peaked at 940 nm. After determining the peak wavelength of each channel, we measured the SDE_max as functions of the I_b normalized to each I_sw at their peak wavelengths, as shown in Fig. 5c. All the channels show saturated plateaus, and C4 and C8 are SNAPs, and the plateaus show relatively small bias region due to the unstable regime at low I_b. Fig. 5d summarizes the measured SDE_max and SDE_min of each channel. SDE_max of five channels exceed 90%, and SDE_max of all the channels exceed 80%. Each error bar represents 5.3% relative error. The average SDE for all states of polarization of the eight channels is estimated to be 90 ± 5%, which is the average of the 16 values of SDE_max and SDE_min. Fig. 5e presents the measured DCR or FCR at the I_b corresponding to the lowest NEP of each channel. Fig. 5f presents the e⁻¹ time constant of the falling edges of output pulses. The SNAPs exhibit lower kinetic inductance due to the parallel configuration of the nanowires, which resulted in smaller e⁻¹ time constants. Fig. 5g presents the measured timing jitter of each channel at 99% of its switching current. Among eight detectors, SNAPs showed better timing resolution (lower timing jitter) than SNSPDs.

A demonstration of applications, two channels (C1 and C4) were adopted to measure the second-order correlation functions, g²(τ), of the emission from a In(Ga)As/GaAs QD and from a pulsed laser. Fig. 6 presents the experimental setup. The sample containing the QDs was cooled down to 3.7 K in another close-cycled cryostat. An individual QD was selected and excited by a picosecond pulsed laser and by longitudinal-acoustic phonon-assisted excitation scheme^39,40. The emission wavelength was centered at 887.1 nm, and the excitation laser was blocked by a home-made grating-based spectral filter.

Fig. 7 presents g²(τ) measured by two SNSPDs and two silicon SPADs (purchased from Excelitas). For the emission from the QD, as presented in Fig. 7a, b, clear anti-bunching was observed, and g²(0) = 0.0587 was measured by the SNSPDs. In comparison, g²(0) = 0.0609 was measured by the SPADs. For the pulsed laser, as presented in Fig. 7c, d, g²(0) = 0.968 was measured by the SNSPDs and g²(0) = 0.996 measured by the SPADs. While the measured g²(τ) were quite consistent by using the SNSPDs and the SPADs, from Fig. 7d, it can be clearly seen that the timing resolution of SNSPDs is better than that of the SPADs. In Fig. 7d, the FWHMs of the g²(τ) peaks centered at τ = 0 are 125 and 500 ps measured by the SNSPDs and the SPADs, respectively.

In conclusion, an eight-channel system installed with fractal SNSPDs in the wavelength range of 930 to 940 nm that all feature low PS has been demonstrated in the current work. The highest SDE is $96_{-5}^{+4}$%, with 13 cps DCR. While both of the SNSPDs and the SNAPs achieved high SDE, the comparisons between them illustrate the strengths of each type—the former exhibits lower DCR and, therefore, lower noises, and the latter shows better properties in the time domain. Further improvement in the nanofabrication process can further enhance the yield of devices with high SDE and, therefore, the comprehensive performances of the system. A better understanding of the dark and false counts of the fractal SNSPDs and SNAPs is also needed. It is believed that such a system would be useful in many quantum photonic applications involving multi-photon coincidence detection.

Funding This work was supported by National Natural Science Foundation of China (62071322).

Acknowledgments Portions of this work were submitted to OFC conference 2024 and were accepted as an oral presentation.

Declaration of competing interest The authors declare no competing interests.