1. INTRODUCTION

Superconducting nanowire single-photon detectors (SNSPDs) can detect single photons from mid-infrared [1,2] to ultraviolet [3] wavelengths, with efficiencies up to ${\gt}98\%$ [4,5], dark count rates (DCRs) of $6 \times {10^{- 6}}/{\rm s}$ [6], timing jitter of 3 ps FWHM [7], and count rates of up to 800 mega-counts/s (3 dB compression) [8]. They have enabled tests of local realism [9], key demonstrations in quantum information processing [10] and quantum communication [11], and optical communication between the Earth and the Moon [12]. New applications continue to emerge as their performance improves [13]. As quantum communication protocols in particular are leveraging the low jitter of SNSPDs to increase clock rates to 10 GHz and beyond [14,15], it is increasingly important to measure at high count rates while maintaining low jitter and high efficiency.

When an SNSPD absorbs a photon, a hotspot is created, which disrupts the superconductivity and shunts current from the nanowire to the readout electronics [16]. The maximum rate at which an SNSPD can count photons is limited by the time scale at which the hotspot dissipates. One strategy to increase count rate is to decrease the thermal reset time by choice of superconducting material [17] or by using very short nanowires [18]. However, these strategies have led to detectors with lower internal detection efficiency (IDE) as indicated by a lack of saturation in photon count rate (PCR) with bias current, indicating a trade-off between fast thermal reset dynamics and detection efficiency. Another strategy to overcome the count rate limit is to use several parallel nanowires to measure the signal of interest. In these devices, after one nanowire detects a photon, the other wires are still superconducting and optimally biased for detection. For fiber-coupled modes, efforts have focused on connecting the nanowires in parallel with a single readout line [19,20]. The count rate achievable with this method was limited by electrical cross talk between wires. High count rates have also been achieved in free-space-coupled detector arrays [8,21], but these arrays used long nanowires that had significant longitudinal geometric timing jitter [22], leading to a jitter of greater than 50 ps FWHM.

In this work, we present the Performance-Enhanced Array for Counting Optical Quanta (PEACOQ) detector, in which 32 short nanowires in a linear array are read out individually. At the cost of increased readout complexity, this nanowire array can detect photons in a single 1550 nm optical mode at a world-leading count rate of 1.5 giga-counts/s (Gcps) at 3 dB compression, along with a system detection efficiency (SDE) of up to 78% and low timing jitter. We demonstrate a strategy for maintaining a timing jitter below 46 ps FWHM at count rates up to 1 Gcps by building on a recently developed temporal walk correction technique [23]. A detector with high efficiency and low timing jitter at high count rates, as well as low dark counts, is required to detect faint optical signals at high clock rates, such as in quantum communication or deep-space optical communication where amplification of optical pulses is not feasible. For example, the PEACOQ can count single photons at 250 Mcps with an SDE of 70% and, with realistic improvements to our measurement setup, a jitter of 86 ps full-width-at-1%-maximum (FW1%M). This would enable a quantum communication protocol based on a 10 GHz pulsed source with mean photon number per pulse at the detector of $\langle n\rangle = 0.025$.

 

Fig. 1. (a) Photograph of the PEACOQ detector. Inset is a scanning electron micrograph showing the nanowires, microstrips (dark meandered lines), and coplanar waveguides (lighter lines connected to top and bottom of microstrips, also visible on photograph). To aid the eye, the signal traces of the coplanar waveguides connected to nanowire 2 are shown in blue (false color). The active region, indicated by the arrow, is a linear array of nanowires covering an area of $13\;\unicode{x00B5}{\rm m} \times 30\;\unicode{x00B5}{\rm m}$. A schematic of the active region is shown in Fig. 2. (b) Normalized efficiency (black circles, left axis) and dark count rate (red squares connected by solid line, right axis) as a function of bias current in one nanowire. Solid black curve is a fit to the internal detection efficiency equation (see main text). (c) ${I_{{\rm detect}}}$ (blue) and ${I_{{\rm switch}}}$ (red) for all nanowires in the array. Note that the switching currents measured in this readout configuration are slightly lower than in (b) due to different measurement setups (see Section 3).

Download Full Size | PDF

2. PEACOQ OVERVIEW

Figure 1(a) shows the PEACOQ detector. The active area of the detector consists of a linear array of 32 parallel niobium nitride (NbN) nanowires on a 400 nm pitch. The wires are 120 nm wide, 30 µm long, straight sections (no meanders). A two-part transmission line connects each side of each nanowire to bonding pads at the edges of the PEACOQ chip. The first part is an adiabatically tapered microstrip transmission line, which provides a way to control the kinetic inductance of the nanowire. The second part is a coplanar waveguide (CPW), which has negligible kinetic inductance and simply transmits the signal to the bonding pads at the edge of the chip. The microstrip comprises an NbN conductor, a dielectric layer (${{\rm SiO}_2}$), and a gold mirror plane below. The CPW comprises NbN and contact metals (Ti/Nb/Ti/Au/Ti) on ${{\rm SiO}_2}$ (no gold plane), with a conductor width of 9 µm, and a conductor-to-ground spacing of 3.625 µm. There is a short tapered region connecting the conductors of the microstrip and CPW. The symmetric coupling on both sides of the wire allows for differential readout. In combination with a differential amplifier, differential readout enables cancellation of geometric jitter [24], common-mode noise rejection, and larger signal to noise, all of which can reduce overall timing jitter.

The total inductance of the nanowire, which is dominated by the kinetic inductance of the superconducting NbN (nanowire and transmission lines), is a key design parameter that affects the maximum count rate (MCR) and timing jitter. The microstrips serve the purpose of increasing the kinetic inductance of the nanowires, to prevent latching. Short nanowires are used in the design to minimize longitudinal geometric jitter [7], but the kinetic inductance of the 30 µm long nanowire of $\approx 50\;{\rm nH}$ is too low, and would lead to latching of the device at low bias currents [25]. Each microstrip has a kinetic inductance of $\approx 315\;{\rm nH}$, controlled by varying the width profile along the taper, with ${L_k} = {L_{{\rm sq}}}\int_0^\ell \frac{1}{{w(s)}}{\rm d}{\rm s}$, where ${L_{{\rm sq}}} = 194\;{\rm pH}$ is the sheet inductance, $w(s)$ is the width along the microstrip (which varies between 120 nm and 1.5 µm), and $\ell$ is the arc length of the microstrip. The microstrips are meandered to allow them to be roughly equal in length, leading to equal inductance across the 32 nanowires in the array. The sheet inductance is estimated from the reset time of the device ${\tau _{{\rm reset}}} = \frac{{{L_k}}}{{{R_L}}}$, which is measured in Section 5. Device fabrication is described in Supplement 1.

Figure 1(a) also shows the overall shape of the detector chip. The circular area at the bottom in the picture is 2.5 mm in diameter, designed to align with a standard FC/PC fiber ferrule. The face of the ferrule sits in contact with the detector chip, and the optical fiber mode is centered on the 32-nanowire array. Self-alignment between the optical mode and the detector active area [26] is enabled by a custom designed ceramic sleeve with a wider opening (1.9 mm) that fits around both ferrule and detector.

Figure 1(b) shows the normalized PCR versus bias current for nanowire 16. This measurement is done at low count rates—here 82 kcps at saturation. The saturation of the count rate for currents above 10.5 µA indicates unity IDE, which means that any photon absorbed in the nanowire will create an output pulse that can be detected [27]. The PCR curve was fit to an idealized model of the IDE as a function of current in the nanowire, $\eta = \frac{1}{2}{\rm erfc}({- \frac{{{I_{{\rm nanowire}}} - {I_{{\rm detect}}}}}{\sigma}})$, where ${I_{{\rm detect}}}$ is the inflection point, and $\sigma$ is a fit parameter describing the slope of the inflection. At low count rates, the current in the nanowire is assumed to be equal to the bias current (${I_{{\rm nanowire}}} = {I_{{\rm bias}}}$), meaning the nanowire is not recovering from a previous detection when it absorbs a photon. Figure 1(b) also shows the DCR of the same nanowire. In this measurement, dark counts are mostly due to ambient photons coupling to the detector, as indicated by the plateau of 0.4 counts/s at bias currents below ${I_{{\rm switch}}}$. No filtering or special enclosure was used to minimize the DCR. Shortly before ${I_{{\rm switch}}}$, the DCR shows the typical exponential increase. After ${I_{{\rm switch}}}$, the nanowire enters a regime of relaxation oscillations, then the count rate starts decreasing, indicating latching. We define ${I_{{\rm latch}}}$ as the nanowire current at which DCR starts to decrease. Figure 1(c) shows ${I_{{\rm detect}}}$ and ${I_{{\rm switch}}}$ for all nanowires (see Fig. S1 in Supplement 1 for PCR curves). ${I_{{\rm detect}}}$ values were similar, indicating that the nanowires are fairly uniform across the array, though the slightly higher variation in switching current indicates varying degrees of constriction in the wires. All wires had large plateaus in IDE versus current, indicating that they all have unity IDE when biased along their plateau. Since the IDE exceeds 90% for ${I_{{\rm bias}}} \gt {I_{{\rm detect}}} + \sigma$, a measure of the plateau is ${I_{{\rm switch}}} - ({I_{{\rm detect}}} + \sigma)$, which ranged from 0.7 µA to 3.9 µA for the wires in the array, with an average of 2.8 µA. To take advantage of this long detection plateau, the nanowires were biased at 95% of their individual switching currents for all measurements.

3. MEASUREMENT SETUP

The PEACOQ array was measured in two different cryostats at a temperature of 0.9 K. One cryostat (Setup A) was used to read out all 32 channels simultaneously. Setup A was initially developed as a testbed for the Deep Space Optical Communications project [28]. The second cryostat (Setup B) was used to perform low-jitter measurements of a single detector channel. Further details of this setup can be found in Korzh 2020. In each case, the device was wire-bonded to a custom PCB board, designed for differential readout of each of the 32 nanowires, and packaged to accommodate self-aligned fiber coupling [26]. One side of each nanowire was terminated with a 50 Ω resistor at 0.9 K for a single-ended readout of each wire. Future work will focus on a fully differential readout.

In Setup A, microcoaxial cables connected the signal from each nanowire to a cryogenic readout board at 40 K. The cryogenic readout board contained a resistive bias-tee and a two-stage cryogenic amplifier composed of a DC-coupled HEMT (Avago ATF 35143) and a SiGe LNA (RFMD SGL0622Z) for each channel. At room temperature, the pulses were further amplified by a third stage of amplifiers (Minicircuits RAM 8A+) to an amplitude of $\approx 500\;{\rm mV} $, then converted to time stamps using a custom 128-channel time-to-digital converter (TDC) from Dotfast Consulting. The optical source comprised either a continuous or pulsed laser at 1550 nm, a variable attenuator, polarization controller, and a switch that sent light to either the PEACOQ or a power meter. An SMF-28 optical fiber was used to couple light to the detector. The face of the optical fiber ferrule had an anti-reflective coating optimized for 1550 nm. The pulsed laser had a pulse width of 0.5 ps and a repetition rate of 20 MHz. Using a phase-locked loop, the sync signal of the pulsed laser was converted to a 10 MHz signal to synchronize the TDC. The timing jitter of the readout system (TDC and of the phase-locked loop) was measured to be 71 ps FWHM.

Setup B had lower noise and superior timing jitter, but could measure only one nanowire a time. In Setup B, the signal from the SNSPD was amplified with a silicon germanium cryogenic amplifier from Cosmic Microwave Technologies at 4 K (LF1-5 K). The amplifier had a built-in bias-tee with a 5 kΩ resistor. In parallel with the amplifier, an inductive shunt to ground (1.1 µH, 50 Ω) was used to provide a path to ground low frequencies. Jitter measurements were performed with a 1550 nm, 1 GHz mode locked laser and a Swabian time tagger. Note that a larger switching current was measured in this setup compared to Setup A [compare Figs. 1(b) and 1(c)]. This was likely due to differences in the readout electronics such as lower load impedance and lower noise on the biasing current in Setup B.

4. EFFICIENCY AND POLARIZATION SENSITIVITY

High SDE in the PEACOQ detector was enabled by good spatial overlap between the optical mode and array in the device plane, and an optical cavity. Figure 2 shows the fraction of input photons detected by each nanowire, measured at a low total array count rate of 7 Mcps. A Gaussian fit to the mode profile gives an offset of ${-}760\;{\rm nm} $ in the direction perpendicular to the nanowires and suggests that 98.2% of photons fall inside the active area of the array, indicating good spatial overlap. The measured SDE of the array was $78\% \pm 4\%$. The SDE is defined as the fraction of photons incident on the input fiber port of the cryostat that are detected by any wire in the array. The PEACOQ was designed to be polarization insensitive, and we measured no significant difference in SDE while sweeping through input polarization.

 

Fig. 2. PEACOQ array sampling SMF-28 optical fiber mode. The height of the red bars represents fraction of input photons detected by each nanowire, the horizontal position of the bars represents the wire position, and the width of bars corresponds to the wire width. Black curve represents a fit to the Gaussian mode of an SMF-28 optical fiber with a mode field diameter of 10.4 µm at 1550 nm, fit for amplitude and offset. Below the graph is a sketch of the array and optical mode in perspective. The total SDE of the array was 78%, and the total DCR was 158 counts/s across the array.

Download Full Size | PDF

With a pitch of 400 nm, the 32-nanowire array covers 12.8 µm, which contains 98.6% of the power in the optical mode in the case of perfect alignment. The pitch of 400 nm was found to be the lowest at which there was negligible cross talk. Cross talk describes when a detection in one wire leads to an output pulse in a neighboring wire, typically due to thermal effects, leading to double-counting and lower fidelity of detection [29]. We measured cross talk contributing less than 0.5% of total counts, which decreased significantly when using a lower bias current (see Supplement 1). Alignment between the optical mode and the center of the array is also important for achieving high SDE. The mechanical alignment between the optical fiber and the array was robust: the offset differed each time an optical fiber was coupled to the detector, but was always within ${\pm}1.5\;\unicode{x00B5}{\rm m}$, which should lead to a deviation in SDE from the ideally aligned case of ${\lt}1.7\%$. In the self-aligned coupling scheme, the greatest deviations from concentricity are typically in the direction of the slot in the ceramic sleeve. The array wires were therefore oriented along this axis, and the length of the active area was chosen to be longer than its width.

The optical cavity consisted of a gold mirror and a 240 nm layer of ${{\rm SiO}_2}$ below the nanowire layer, and a four-layer distributed Bragg reflector composed of ${{\rm SiO}_2}/{{\rm TiO}_2}/{{\rm SiO}_2}/{{\rm TiO}_2}$ above. The optical stack design was optimized for high SDE at 1550 nm for both polarizations (electric field parallel and perpendicular to the nanowire) using rigorous coupled-wave analysis. The optical absorption bandwidth was $\approx 200\;{\rm nm}$ (see Supplement 1 for details).

5. MAXIMUM COUNT RATE

Detection at high count rates enables applications such as quantum communication at high data rates, time-of-flight mass spectrometry [30], where faint signals are measured in quick succession, and photon time-tagging LIDAR [31], where high dynamic range is important. Figure 3(a) shows the relative efficiency as a function of the measured count rate for the PEACOQ array and for an individual nanowire. We define the MCR as the count rate at which the relative efficiency of detection decreases by 3 dB.

 

Fig. 3. Maximum count rate of array. (a) Normalized efficiency of the 32-wire array versus measured count rate (black circles). Error bars show $\sqrt {{N_{{\rm photons}}}}$ (shot noise) uncertainty. Solid black line is a third order polynomial fit to the data, used to guide the eye and interpolate. Intersecting dashed lines indicate the 1.5 Gcps MCR of the array (3 dB compression point). Blue circles show the normalized efficiency for nanowire 16. Error bars show shot noise uncertainty. Blue line is a theoretical curve computed using measured parameters and the ${\tau _{{\rm reset}}}$ value from (c). The MCR of this wire was 73 Mcps (3 dB compression). (b) SDE of wires across the array at different total array count rates. Black curve is the Gaussian fit from Fig. 2. In each panel, the highest single-wire count rate is shown in gray. (c) Dead time and reset time. Blue line shows the histogram of counts in nanowire 16 as a function of delay since the last count. For long delays (not shown), the histogram has an exponential decay as predicted by the Poisson statistics of the continuous-wave laser. Red curve is a fit to the theoretical IDE of one nanowire as a function of time since the last detection, computed using measured device parameters, and fit to these data to extract the reset time of this nanowire ${\tau _{{\rm reset}}} = 6.8\;{\rm ns}$. Inset shows a representative pulse from nanowire 16 (blue dots), and an exponential function with a decay time of 6.8 ns, fit for amplitude and offset (solid red line).

Download Full Size | PDF

The MCR for the PEACOQ array was measured to be 1.5 Gcps. Because the optical mode is split among the 32 nanowires, each wire detects only a small fraction of the incoming photons, so the MCR of the array was approximately 25 times higher than the MCR of the individual nanowires, which ranged from 48–73 Mcps. Besides the MCR of the individual wires comprising it, the array MCR also depends on the profile of the optical mode. The central wires couple more strongly to the optical mode and saturate before the others as shown in Fig. 3(b). Figure 3(a) also shows a dynamic range of more than six orders of magnitude. The largest count rate measured with the array was 3.0 GHz. This was deep in the saturated regime, where the SDE was 8%.

The MCR of each nanowire is intrinsically tied to the time scale at which its IDE recovers following a detection. Figure 3(c) shows a histogram of measured counts in one nanowire as a function of time since the previous count. There were no counts detected during the first $\approx 5\;{\rm ns}$ after a detection event, which we refer to as the detector dead time. Supplement 1 Fig. S4 shows the corresponding histogram for the full PEACOQ array. The time scale of efficiency recovery depends on two factors: the reset time of the nanowire, ${\tau _{{\rm reset}}}$ and the length of its IDE plateau [Fig. 1(b)]. We modeled the bias current in the nanowire as a function of time since the previous detection as ${I_{{\rm nanowire}}}(t) = {I_{{\rm bias}}}(1 - {e^{- t/{\tau _{{\rm reset}}}}})$. Using ${I_{{\rm nanowire}}}(t)$ as the nanowire current in $\eta$, the expression for the nanowire IDE defined in Section 2 gives a theoretical expression for efficiency versus delay $\eta (t)$, which we fit to the histogram in Fig. 3(c) at low time delays. We extracted ${\tau _{{\rm reset}}} = 6.8\;{\rm ns}$ from this fit. The inset shows that ${\tau _{{\rm reset}}} = 6.8\;{\rm ns}$ also visually fits the decay of the pulses as measured on an oscilloscope in Setup B. Fitting the pulse decay to an exponential directly to extract ${\tau _{{\rm reset}}}$ is less reliable due to filtering and reflections in the readout that distort the pulse shape.

Using ${R_L} = 100 \; \Omega$ as the impedance of the readout path, we find ${L_k} = 680\;{\rm nH}$ from ${\tau _{{\rm reset}}}$. Note that ${R_L} = 100 \;\Omega$ is a sum of the 50 Ω impedance of the amplifier and the 50 Ω resistor on the other end of the nanowire. This setup allowed a lower ${\tau _{{\rm reset}}} \propto \frac{1}{{{R_L}}}$ and higher MCR while avoiding reflections that would result from a mismatch between the amplifier impedance and 50 Ω readout coaxial lines.

Using the method described by Rosenberg et al. [32], the relative efficiency versus count rate for one wire in Fig. 3(a) (blue curve) was computed from the IDE curve in Fig. 3(c). The agreement among reset time, dead time, and the MCR emphasizes that the limit to the MCR in one wire is well understood (additional discussion in Supplement 1).

The readout chain was optimized for high MCR by using a DC-coupled amplifier as the first amplification stage (or an inductive shunt in Setup B). This configuration provides a well-defined impedance for all frequencies contained within a detection pulse, which improves the MCR by increasing the latching current and therefore the length of the IDE plateau [33]. The threshold level of the TDC also influenced the MCR. Any detection event that happens as the current in the nanowire is recovering from a previous detection event will lead to a smaller pulse. To maximize MCR, all pulses must be counted, meaning that the ideal threshold of detection is just above the noise floor of the amplifier chain. We placed the threshold level at 25% of the pulse amplitude for each wire (33% of pulse amplitude for nanowire 14). See Supplement 1 for more details.

6. JITTER

The timing jitter of a detector characterizes the uncertainty in the measured arrival time of a photon. We measured the jitter by sending in short attenuated laser pulses and collecting a histogram of arrival times, from which we extracted two metrics: FWHM and FW1%M. The FW1%M metric is important since a significant number of events fall outside of the FWHM for most distributions (24% for a normal distribution). More importantly, although the intrinsic jitter in SNSPDs can be very small, the instrument response function (IRF) is non-Gaussian [7,34], and thus one needs to characterize the effect of events in the tail of the distribution when considering the impact on applications. In communication protocols based on time-bin encoding, it is convenient to set the time-bin to be larger than the FW1%M value of the IRF to reduce errors from counts falling into the wrong time slot below the 1% level.

The jitter for the nanowire in the array (nanowire 1) was characterized using Setup B. The green curve in Fig. 4(a) shows the histogram of arrival times at low count rates, with a timing jitter of 20.9 ps FWHM/67.1 ps FW1%M. This was limited by the jitter of the readout electronics, and a tighter bound on the intrinsic jitter of the nanowire is 16.8 ps FWHM/44.7 ps FW1%M, which was measured for the same nanowire with a different timing card (see Supplement 1 for details). The low timing jitter for individual wires was a result of the low latency of NbN, the large plateau in IDE versus bias current, and the high bias current used ($0.95 \times {I_{{\rm sw}}}$), all of which contributed to achieve low intrinsic jitter [7]. The small length of the wires (30 µm) led to low longitudinal geometric jitter [7]. The noise jitter was minimized by having pulses with amplitudes well above the amplifier noise level and choosing the smallest possible kinetic inductance for the nanowire, leading to a high slew rate [35].

 

Fig. 4. Timing jitter and time-walk correction. (a) Jitter histogram for a single wire at a low count rate (filled in green curve) and at 40 Mcps (blue lines). The lightest blue line shows the jitter at 40 Mcps as measured, and the darker (darkest) shade shows a time-walk correction to first order (second order). The colors of the horizontal lines showing the widths of the histograms have the same meaning as in (c). The smaller peak at $\approx - 50\;{\rm ps}$ is likely due to two-photon detection events in the nanowire, which have a higher slew rate. (b) Estimated jitter for the 32-nanowire array at 250 Mcps. Darker shades indicate time-walk correction, and red and black lines have the same meaning as in (c). (c) Timing jitter for nanowire 1 as a function of count rate. Lightest red line shows the FWHM of the uncorrected jitter histograms for different count rates. Light gray line shows the corresponding FW1%M. The darker (darkest) lines show the FWHM and FW1%M with a first (second) order time-walk correction. Blue line highlights the jitter at 40 Mcps count rate, represented in detail in (a). Inset shows a schematic of time-walk-induced jitter.

Download Full Size | PDF

At higher count rates, the timing jitter of SNSPD detectors suffers from time-walk: pulses occurring during detector recovery are smaller, which results in a time delay when using a constant threshold level to convert pulses to time tags [see inset to Fig. 4(c)] [23]. The pulse shape can also be distorted due to reflections of previous pulses in the readout chain. Both effects lead to increased timing jitter at higher count rates. The lightest lines in Fig. 4(c) show the jitter FWHM and FW1%M for nanowire 1 as a function of measured count rate. Note that time-walk effects appear at count rates significantly below the MCR, which for this nanowire was 58 Mcps. We used a technique for correcting time-walk-induced jitter, which relies on the fact that the pulse height variation as a function of the time since the previous detection is deterministic, and can be calibrated out [23]. The calibration is performed once on a sample data set, after which it can be used to correct time-walk-induced jitter for additional data either in real time or in post-processing. We refer to the correction process described in [23] as first order correction, since it takes into account the effect of one previous detection on the amplitude of the pulse. We also used second order time-walk correction, which takes into account the effect of the previous two pulses (see Supplement 1 for details). Second order correction is a novel technique not described in [23]. Figure 4(a) shows the uncorrected jitter histogram for nanowire 1 at 40 Mcps, and the effects of both first and second order time-walk correction. Figure 4(c) shows the effect of time-walk correction on jitter for count rates from 110 kcps to 60 Mcps. Second order correction was found to improve the jitter significantly more than the first order correction for rates above 10 Mcps.

Using Setup A, the total timing jitter of the PEACOQ array was measured to be 84.3 ps FWHM/202.3 ps FW1%M (see Fig. S6b in Supplement 1), limited by the jitter of that readout system (71 ps FWHM). To estimate the timing jitter expected for the PEACOQ with an improved measurement setup (i.e., a multi-channel TDC with lower jitter and a new readout chain with amplification at the 4 K stage), we estimated the array jitter based on the measurements for one nanowire in Setup B. We used the known distribution of count rates across the nanowires for a given array count rate [as in Fig. 3(b)] and the jitter histogram for a single nanowire at each count rate [as in Fig. 4(a)] to construct a simulated histogram of arrival times in the array. Figure 4(b) shows the estimated jitter histograms for the array at 250 Mcps. Without any correction, there was a large tail in the distribution. The tail was effectively reduced with second order time-walk correction, leading to a jitter of 22 ps FWHM/86 ps FW1%M, a significant improvement for FW1%M in particular.

With a FW1%M below 100 ps at 250 Mcps, the PEACOQ detector could be used in quantum communication protocols operating at 10 GHz with a relatively high mean photon number per pulse of $\langle n\rangle = 0.025$, arriving at the detector. To put this performance into perspective for quantum communication, one can estimate the expected secret key rate of a quantum key distribution (QKD) protocol [36], where the typical mean photon number per qubit is of the order of 0.2 at the transmitter. This would permit a fiber link of $\approx 100\;{\rm km} $ (20 dB of link loss assuming 0.2 dB/km loss in standard telecom fiber) while maintaining 250 Mcps at the receiver. With typical secret key fractions, this would correspond to ${\gt}70 \;{\rm Mbps}$ of secret key generation rate, which is almost a factor of three faster than the current state of the art [37]. Through the use of two or more PEACOQ detectors, QKD secret key rates above 100 Mbps would be achievable. Entanglement swapping protocols, both space-to-ground and fiber based, would also benefit from the PEACOQ’s ability to maintain very low jitter at high count rates, especially for approaches based on continuous-wave sources, which relieve stringent requirements on source synchronization [38]. During the review process, we learned of an independent work on high-rate QKD using multi-element SNSPD arrays to generate secret keys at a rate of 64 Mbps [39], demonstrating the relevance of this approach.

Table 1 summarizes the timing jitter estimated at three count rates using second order time-walk correction. At 1 Gcps, second order time-walk correction was not as effective in reducing jitter (see Fig. S6c in Supplement 1). At this count rate, more than half of the nanowires are measuring at 30 Mcps or more, where even second order correction does not fully compensate for count-rate-dependent jitter, as seen in Fig. 4(c). It is likely that a correction to third order or higher would improve jitter further. However, at sufficiently high count rates, the current in the nanowire seldom fully recovers between pulses, leading to a lower effective bias current in the nanowire, which increases the intrinsic jitter of the device [7]. The limit where time-walk correction is no longer effective in improving jitter merits further study.

Table 1. SDE and Estimated Timing Jitter at Different Array Count Rates^a

View Table

7. DISCUSSION

Improving the performance of the PEACOQ detector will have to balance the trade-offs among MCR, efficiency, and jitter. There are five design parameters to consider: array pitch, nanowire dimensions, kinetic inductance, superconducting and dielectric materials, and the optical stack.

The pitch of the PEACOQ was chosen as the smallest pitch leading to minimal cross talk. If the pitch were decreased, the distance between nanowires would be smaller, increasing both thermal and electrical coupling and thereby increasing the likelihood of cross talk between wires. The array MCR would increase with decreasing pitch, since the center of the optical mode will be shared among a larger number of wires, thereby decreasing saturation in those central wires. The SDE of the array at low count rates would decrease, since the total width of the array is smaller relative to the optical mode (see Supplement 1 for a quantitative analysis). This can be compensated for by increasing the number of nanowires in the array, at the cost of increased readout complexity. The loss in efficiency would be mitigated by the increased absorption in the nanowire layer that is expected with a lower fill factor.

The width of the PEACOQ nanowires was chosen as a compromise between pulse height, which increases with width, and length of the PCR plateau, which decreases with width. If the width of the wires were decreased, the absorption in the nanowire layer would be lower, which could lead to a decrease in array efficiency, though this can be compensated for with a higher-finesse optical cavity. The consequence of decreasing wire width on MCR is more complicated, since there are several competing effects: (1) ${I_{{\rm switch}}} \le {J_{{\rm critical}}} \times {A_{{\rm cross} - {\rm section}}}$, where ${J_{{\rm critical}}}$ is the critical current density of the superconductor, would decrease as the cross section of the wire decreases, and since the pulse amplitude is proportional to ${I_{{\rm bias}}} \lt {I_{{\rm switch}}}$, the smaller pulses created by detection events during the recovery of current in the nanowire can become lost in the amplifier noise, which would decrease MCR; (2) as ${I_{{\rm switch}}}$ decreases, ${\tau _{{\rm reset}}}$ can be decreased without inducing latching (as explained further on), leading to higher MCR; (3) the plateau in IDE versus bias current is expected to increase as ${I_{{\rm detect}}}/{I_{{\rm depairing}}}$ decreases [40] (where ${I_{{\rm depairing}}}$ is the depairing current in the superconducting film, and an upper bound for ${I_{{\rm switch}}}$), which would decrease dead time and therefore increase MCR. We found that a decrease in width from 120 nm to 100 nm slightly increased MCR, with an MCR as high as 88 Mcps measured for an individual wire. Decreasing wire width is likely to have a detrimental effect on jitter since noise jitter from the amplifier would have a larger effect as the pulse size becomes smaller. Narrower wires would lead to less thermal cross talk, as the hotspot energy, which scales with the bias current, would be smaller. However, narrower wires are also likely to have a higher rate of constrictions, which is always detrimental to nanowire performance [41].

Decreasing the thickness of the superconducting film is another way to decrease ${A_{{\rm cross} - {\rm section}}}$, and would therefore have effects similar to those described above. However, the relationship between MCR and nanowire thickness is non-linear, because a thinner superconductor also has a lower critical temperature and therefore a lower critical current [42]. We found that decreasing the film thickness by a factor of $\approx 1.5$, as estimated from an increase of $1.5 \times$ in film resistance at room temperature, reduced the MCR of individual wires by a factor of $\approx 2$.

The total kinetic inductance of the PEACOQ nanowires was controlled by changing the profile of the microstrip transmission line. Both MCR and jitter benefit from a lower kinetic inductance—the former because ${\tau _{{\rm reset}}} \propto {L_k}$ is reduced, and the latter because the rise time of the pulses ${\tau _{{\rm rise}}} \propto {L_k}$ is reduced, which leads to lower noise jitter [35]. However, there is a lower bound to how small ${\tau _{{\rm reset}}}$ can be: if it is so low that the current returns to the wire before the hotspot dissipates, the nanowire enters a permanently resistive state known as latching [25]. The time scale of hotspot dissipation depends on the device temperature, nanowire and substrate materials, and hotspot energy $E \approx \frac{1}{2}{I_{{\rm bias}}}L_k^2$ [25,43]. Latching occurs at bias currents above a threshold ${I_{{\rm latch}}}$, which decreases with ${\tau _{{\rm reset}}}$ [33,43]. Given a nanowire with switching current ${I_{{\rm switch}}}$, a good strategy is to decrease ${\tau _{{\rm reset}}}$ via ${L_k}$ until ${I_{{\rm latch}}}$ is just above ${I_{{\rm switch}}}$. This way, the nanowires can be biased close to ${I_{{\rm switch}}}$, the optimal bias point for minimizing jitter and maximizing count rate [33,35]. As shown in Fig. 1(b), the nanowires in this work are close to satisfying this condition. For the 100 nm wide wires measured, the kinetic inductance could be decreased to $\approx 430 \;{\rm nH}$, which led to a faster reset time and higher MCR.

An important design consideration is the choice of superconducting and dielectric materials. Of superconductors known to make efficient SNSPDs at 1550 nm (NbN, tungsten silicide, molybdenum silicide, niobium-titanium nitride [5]), NbN was chosen as a low-latency material [7], which is important for achieving low timing jitter. Also important for jitter is the interface between superconductor and dielectric, which in this case is ${{\rm SiO}_2}$. In future studies, lattice mismatch between the two materials could be used to decrease phonon escape and decrease intrinsic jitter [34,44]. Additionally, choosing a superconductor–dielectric combination that maximizes the thermal boundary conductance at the nanowire–substrate interface could be used to optimize the MCR [45].

The PEACOQ nanowires showed a plateau in PCR, indicating that any photon absorbed by a nanowire was converted to an electric pulse. However, the SDE of the PEACOQ was less than unity, limited by the probability of a input photon being absorbed by a nanowire. Known sources of loss include: 2.5% loss in the optical fiber in the cryostat, absorption in the gold mirror, estimated to be 5.5%, and 9% of light being reflected from the stack due to imperfect impedance matching. Using a distributed Bragg reflector instead of a gold mirror could improve efficiency by eliminating the absorption in the gold [4]. Additionally, without absorption in the gold, a higher-finesse optical cavity could be designed to increase absorption in the nanowire layer.

The performance of the PEACOQ detector depends on the design parameters in complicated ways: there are trade-offs among different metrics, and in some cases changing one parameter can have two opposing effects on the same metric, so a quantitative study is necessary. Additionally, PEACOQ-style detectors can be optimized to work with different optical fibers. For example, a multi-mode fiber used in tandem with a mode scrambler has a flatter mode profile and could therefore be used with a PEACOQ-style detector to achieve an even higher array MCR. There is still room to explore the optimization of PEACOQ-style detectors for specific applications, whether a higher count rate, higher efficiency, or lower jitter is desired.

8. CONCLUSION

We have demonstrated a detector that measures single telecommunication-wavelength photons at high count rates with high SDE and low timing jitter. The 32-nanowire array measured photons from a directly coupled SMF-28 optical fiber at up to 250 Mcps with an SDE $\geq 70\%$. We measured jitter as low as 44.7 FW1%M for an individual channel. While the array jitter measured with our current 128-channel readout system was higher (202 ps FW1%M at low count rates), our estimates show that with an improved readout system, the timing jitter of the array could be below 100 ps FW1%M at count rates up to 250 Mcps.

The MCR of the PEACOQ was 1.5 Gcps at 3 dB compression, and the highest measured count rate was 3 Gcps at an SDE of 8%. This is a factor of two improvement over the highest count rate we are aware of in an SNSPD array [8]. Low timing jitter at high count rates was made possible by an improved time-walk correction scheme. Future work should focus on implementing a differential readout architecture, which, together with a lower-jitter multi-channel TDC, would take full advantage of the PEACOQ’s low-jitter design.