Currently, there is no doubt that superconducting nanostrip single-photon detectors (SNSPDs) (formerly called superconducting nanowire single-photon detectors or superconducting single-photon detectors, and recently defined as above by IEC 61788-22-1 [1]) are innovative tools for a variety of advanced technologies because they can offer high sensitivity in a wide wavelength region ranging from ultraviolet to mid-infrared, low dark count rate, and low timing jitter [2–9]. In addition, if high-speed operation can be realized while maintaining the aforementioned excellent characteristics, it will have a great impact on various important applications such as pulse-position modulated (PPM) optical communications [10], characterization of high-speed single-photon sources [11], high-speed Hong–Ou–Mandel (HOM) observations [12], and so on. Generally, the operating speed of an SNSPD is restricted by the kinetic inductance (${{\rm{L}}_k}$) owing to the long superconducting nanostrip [13]; hence, the reduction in ${{\rm{L}}_k}$ while maintaining the photosensitive area is key to obtaining both high-speed operation and high detection efficiency (DE). The multi-element SNSPD array is a promising approach to improve the operation speed of the detector, because dividing the active area into multiple elements can not only reduce ${{\rm{L}}_k}$ but also distribute the incident photon flux into each element [14]. Furthermore, the multi-element SNSPD array can detect single photons even when several elements are responding, making it possible to detect photons incoming with shorter time intervals than the dead time of SNSPD. Because the SNSPD element in response cannot detect photons, the DE decreases during the dead time of the SNSPD element. However, the degree of decrease can be suppressed by increasing the number of elements. Significant efforts have been made to develop multi-element SNSPD arrays as single detectors.

One of the main concerns in building an SNSPD array system is how to process the output signals from multiple elements that determine the speed of the system. Reading the signals from all the elements independently is a promising approach that can eliminate the restrictions of the dead time of the SNSPD. However, this requires as many readout cables and reading modules as there are elements; this can make the entire system complicated and costly. In contrast, multiplexing the signals from all the elements into a single output line with a power combiner can simplify the system; with this approach, the system may even be able to resolve the number of photons [15]. However, because this approach superimposes the waveforms on a single output line, the response speed is still limited by the output pulse width of each SNSPD element. To take advantage of the high-speed characteristics of the SNSPD array with multiplexing architecture, it is effective to shorten the output pulse width. The superconducting single flux quantum (SFQ) circuit [16] is a good candidate to perform this task because it can reshape the output pulses from the SNSPD array into pulses with durations shorter than 1 ns and multiplex these pulses into a single output line [17]. In addition, the SFQ circuit operates in a cryogenic environment and can be implemented close to the SNSPD array in a cryocooler. Therefore, only a single output line and several bias lines are required to operate the system, which is advantageous for realizing a simple implementation even if the number of elements in the SNSPD array is increased. In this paper, we report the development and performance evaluation of a 16-element SNSPD array system implemented with a 16-input SFQ multiplexer, which can produce output pulses through a coaxial cable. We then characterize the potential for high-speed operation of our system.

Figure 1 shows a schematic view of our 16-element SNSPD array system. The 16-element SNSPD array consists of two eight-interleaved NbTiN nanostrips (strip width 100 nm, gap 100 nm) adjacent to each other on a Si substrate with a 240 nm thick ${\rm{Si}}{{\rm{O}}_2}$ layer, covering an area of ${15.0} \times {16.2}\;{\unicode{x00B5}}{{\rm{m}}^2}$. On top of the nanostrip area, a cavity structure consisting of a SiO cavity and Ti–Au mirror was formed to enhance the absorption efficiency of incident photons [18]. The SFQ multiplexer has 16 input ports with magnetically coupled DC/SFQ (MC-DC/SFQ) converters. These converters generate SFQ pulses at the rising edge of each input pulse, where the SFQ pulse is a tiny voltage pulse whose duration and amplitude are, respectively, about 4 ps and 0.5 mV for an SFQ circuit consisting of Josephson junctions of critical current density of ${2.5}\;{\rm{kA}}/{{\rm{cm}}^2}$. The generated SFQ pulses were transmitted to the multiplexing unit consisting of confluence buffers to multiplex the signals to a single output line. Multiplexed SFQ pulses are then sent to a voltage driver consisting of eight superconducting quantum interference device (SQUID) stacks and converted to electrical pulses with an amplitude of 1.8 mV and pulse width of ${\sim}{0.6}\;{\rm{ns}}$. The SNSPD array device and SFQ multiplexer are implemented in a package in which they are connected through microstrip lines on a specially designed printed circuit board (PCB). The length of the transmission lines on the SNSPD array chip, PCB, and SFQ chip were carefully designed so that the propagation time between the output from the superconducting nanostrip and input to the MC-DC/SFQ converter in the SFQ circuit is the same for each element. The single-mode (SM) fiber for telecommunication wavelength with the gradient index (GRIN) lens spliced to the end face was set on the back side of the SNSPD array chip and aligned so that the incident light could be efficiently coupled to the photosensitive area [19]. The bias current to the 16-element SNSPD array is supplied by a single cable and is split into each element in parallel via a 2.4 kΩ resistor located on the SFQ chip. Because four cables are required to supply the DC bias current to the SFQ multiplexer and a single cable is required to read the output signals, six cables are required to operate the system, which is less than when each element operates independently without any multiplexing in a cryocooler. This number does not change even if the number of elements increases, which is beneficial for increasing the number of elements in the SNSPD array system. A package surrounded with a magnetic shield was implemented in a 0.1 W Gifford–McMahon (GM) cryocooler system and cooled down to 2.15 K, while the operation of the SFQ multiplexer slightly increased the temperature to 2.25 K. We first confirmed the correct operation of the system through system DE measurement. Figure 2 shows the measured system DE as a function of the bias current for each element, when all the elements are operated simultaneously and the signals are counted through the SFQ multiplexer. For the measurement, a 1550 nm wavelength continuous wave (CW) light source was used as incident light, which was attenuated to ${{10}^5}$ photons/s at the input port of the detector system. For comparison, the sum of the system DE of each element when it operates independently without the SFQ multiplexer is estimated. As shown in the figure, these curves are identical, indicating that all 16 elements are adequately biased and operated. The SFQ multiplexer also bundles the 16 input signals into a single output line correctly. In addition, a system DE of ${\sim}{{80}}\%$ was obtained, which is comparable to those obtained with our single-element SNSPD device [18]. When all the elements were operated with the SFQ multiplexer, we also characterized the timing jitter of the detector system. For the measurement, we used a sub-ps pulsed laser as an incident light; we attenuated it to 0.1 photons/pulse, and measured the timing correlation between the synchronized output from the pulsed laser and the output signals from the SFQ multiplexer. Figure 3 shows the time-correlated histogram and obtained FWHM jitter of 45 ps. This value is superior to those of our single SNSPD device [18], because the signal from the SNSPD is captured by a low-timing jitter SFQ circuit implemented close to the SNSPD array chip in a cryogenic environment.

 

Fig. 1. Schematic diagram of a 16-element SNSPD array with SFQ multiplexer circuit. The red rectangles, blue squares, and green circles show the resistor, MC-DC/SFQ converter, and confluence buffer, respectively. The system requires a bias line to the SNSPD array, four bias lines to the SFQ multiplexer, and an output line from the SFQ multiplexer.

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Fig. 2. System DE at 1550 nm wavelength as a function of bias current to each element, during simultaneous operation with SFQ multiplexer (red circles) and independent operation without SFQ circuit (blue triangles).

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Fig. 3. Histogram of timing correlation normalized by the peak counts between laser pulses and output signals during simultaneous all-element operation with an SFQ multiplexer.

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Fig. 4. (a) Output waveforms through the SFQ multiplexer circuit observed when pulsed laser with 1 GHz repetition rate is used as incident light and two adjacent output signals are continuously generated at time intervals of 1, 2, and 3 ns. (b) Histogram of two adjacent output pulses.

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To verify the capability of detecting incoming single photons at short time intervals, we irradiate the incident light using a pulsed laser source at 1 GHz repetition rate, which was attenuated by attenuators so that the energy of the incident pulse becomes 0.1 photon/pulse at the input port of the cryocooler system; this reduces the probability of multi-photon incidence. Figure 4(a) shows the output waveforms through the SFQ multiplexer circuit observed by a digital oscilloscope with an 8 GHz bandwidth (Agilent Technologies, Infinium DSO80804A) when two adjacent output signals are continuously generated at time intervals of 1, 2, and 3 ns. The full width at half maximum (FWHM) pulse width from the SFQ multiplexer was typically 0.6 ns. The output pulses were clearly distinguishable even at a time interval of 1 ns. We should note that these waveforms were deliberately picked up to match the time intervals of 1, 2, and 3 ns. Therefore, to eliminate deliberate manipulation, we observed the histogram of two adjacent output pulses, as shown in Fig. 4(b), by starting with the first output pulse as a trigger and accumulating the signals that exceed the threshold level. The peak at the timing of 0 ns shows an extremely high intensity because it appears as a result of the accumulation of the triggered first pulses. The other clear peaks correspond to the accumulation of the second output pulse. These peaks were clearly separated and appeared at 1 ns time intervals, indicating that our SNSPD array system successfully produced two distinguishable output pulses through a single output line by capturing two adjacent incident photons from the pulsed laser, even at a time interval of 1 ns. It is also apparent that the minimum time interval at which two adjacent pulses can be distinguished is restricted by the output pulse width from the SFQ multiplexer circuit, which is much larger than the timing jitter of the SNSPDs. The voltage driver in the SFQ multiplexer is currently designed to generate output pulses with sufficiently wide durations to be detected easily by room-temperature electronics with 1 GHz bandwidths. If we adopt room-temperature electronics and readout cables with wider bandwidths, a readout with a 10 GHz repetition rate will be possible [20].

Figure 5 shows the histogram of two adjacent output pulses obtained by the same procedure as in Fig. 4, but by irradiation from the CW light source. The incident light source was attenuated to ${{10}^6}$ photons/s at the input port of the cryocooler system; here, three or more photon detection events rarely occur in the observed time domain. Unlike with a pulsed laser source, the incident photons arrive randomly in time; hence, the histogram should be flat if there is no autocorrelation between the output pulses. In fact, the obtained histogram is flat in the time domain longer than the dead time of the SNSPD element. Conversely, when the time domain was shorter than the dead time (${\sim}{{10}}\;{\rm{ns}}$), the counts of the histogram slightly decreased. This is because once the SNSPD element detects incident photons, it does not react during the dead time; hence, the overall DE decreases. However, because other elements can still detect the incident photon, the degree of reduction could be suppressed to approximately 0.93 (=15/16), which is considerably improved compared to the case of a single element device [18]. Optimistically, it is possible to improve the degree of this decrease by further increasing the number of SNSPD elements.

 

Fig. 5. Histogram of two adjacent output pulses normalized by the average value in the temporal domain from 20 to 100 ns, by irradiation with CW laser source. Inset shows temporal range from 0 to 40 ns.

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In conclusion, we developed a 16-element SNSPD array with an SFQ multiplexer. All 16 elements were biased by a single cable, and their signals were merged by an SFQ multiplexer into a single output line. The system showed a system DE of 80% at a wavelength of 1550 nm and an FWHM timing jitter of 45 ps as a result of careful adjustment of transmission delays between each element and SFQ multiplexer. Because the SFQ multiplexer generates an output pulse with a width of 0.6 ns, the detector system can distinguish incident photons at 1 ns time intervals. The decrease in DE during the dead time of the SNSPD can be suppressed to ${\sim}{0.93}$, and this suppression would be reduced by increasing the number of SNSPD elements. Though the Joule heating originating from the DC bias current for the SFQ circuit and the residual resistance from the connectors in the cryocooler is an issue for scaling up the number of SNSPD elements, it can be suppressed by future technical improvements. At least, it is feasible to scale up the array to 64 elements with an SFQ multiplexer because we have already demonstrated the SFQ encoder circuit with 64 input ports [21]. Further characterizations for high-speed operations, such as the maximum counting rate, need to be clarified, which will be the subject of future studies.