The Differential SNSPD

The differential single pixel SNSPD

SNSPDs offer high efficiency, low dark count rates, high count rates, and low timing jitter. However, traditional SNSPD designs face challenges in achieving both high detection efficiency and low jitter, especially for large-area detectors. Marco Colangelo et al. ¹ proposed a new device design for SNSPDs that combines differential readout and impedance matching tapers to overcome these challenges. This design enables high detection efficiency and low jitter simultaneously along with pixel-level imaging capabilities and photon-number resolution.

Detectors of the type demonstrated by Colangelo et al. ¹ have been fabricated at JPL (Fig. 1 a) for the duration of this PhD research, and are used primarily for three projects detailed in this thesis: the low dark count rate project, the Pulse Position Modulation (PPM) and Photon Number Resolution (PNR) project, and the high rate entanglement project. Given the significance of the differential tapered SNSPD to much of this body of work, we review its key design and performance features here.

fig:diff — Figure 1: **Differential single pixel** a) Two packaged differential single pixel detectors. Coupled fibers highlighted in green, differential SMA readout highlighted in red b) Magnified images of the detector’s lollipop-shaped wafer, highlighting where the tapers and efficiency-enhancing optical stack are located c) Integrated 2D histogram showing different heights and shapes of RF pulse rising edge in response to incident multi-photon optical pulses.

Jitter cancellation through differential readout

Two main types of jitter arise in high efficiency SNSPD designs: amplifier jitter and geometric jitter. Amplifier jitter is the effect of readout electrical noise on timing jitter. In contrast, geometric jitter originates from propagation delays due to detection events happening at varying locations along the nanowires’ twist. Nanowires made of thin-film materials exhibit high kinetic inductance and behave like transmission lines with high characteristic impedance and slow phase velocity. These transmission line properties result in pulse propagation delays that contribute to the timing jitter of the detector. The arrival time of voltage pulses from the detector to time tagging equipment depends on the location of photon absorption in the nanowire, as detections closer to the ground termination and farther from the single readout must travel farther at low phase velocity through the nanowire before exiting. For large detectors, geometric jitter can contribute tens of picoseconds to the total system jitter. Increasing detector size for resolving a given optical mode usually improves detection efficiency. Thus, using single-ended readout leads to a tradeoff between system detection efficiency and jitter induced by longitudinal geometric effects.

Adopting a differential readout approach can resolve the aforementioned issues. Instead of just isolating the positive voltage pulse, the negative pulse from the other end of the nanowire is also collected. Simple processing of both pulses reveals information about photon arrival time as well as photon arrival location.

If the measurements of arrival time \(t_F\) and absorption location along the nanowire are both significant to the application, then the timing of the \(t_{neg}\) negative and positive \(t_{pos}\) voltage pulses may be read out with two time taggers or high-speed oscilloscope channels. The difference of arrival time \(t_{pos} - t_{neg}\) of these signals constitutes the photon absorption location information, while the average \((t_{pos} + t_{neg})/2\) of the arrival times constitutes the photon arrival time information. For practical single photon counting applications, however, the photon arrival time information is typically sufficient and real-time processing of two time tags per detection event is not practical. Therefore, a 2:1 balun transformer can be used to perform an equivalent hardware difference of the positive and negative pulses (analogous to the averaging of timetags \(t_{pos}, t_{neg}\)). After amplification, the two sides of the detector are connected to the differential inputs of the balun, with the output being sent to a TCSPC or equivalent time tagging module. The threshold voltage of the time tagger can be set to minimize the spread of time tag distribution, corresponding to the condition where the timing measurement \(t_{tagger} \approx t_F\) so that the photon arrival location information is negated.

Impedance matching tapers

In a typical SNSPD, the nanowire exhibits impedance on the order of \(\mathrm{k} \Upomega\), while the readout circuit has an impedance of 50 \(\Upomega\). This mismatch can lead to RF pulses that exhibit reflections and distortions. These effects reduce slew rate and lower Signal to Noise Ratio, bringing about higher amplifier jitter ²³.

The higher jitter that results from the impedance mismatch can be mitigated by designing the SNSPD to preserve the integrity of the output pulse. An impedance-matching taper interfacing the nanowire to the readout line can be integrated. Thanks to the gradual impedance transformation of a Klopfenstein-style taper, the output pulse has a higher amplitude and a faster slew rate. In a simplified theoretical SNSPD model by Colangelo et al. ¹, the incorporation of a taper increases pulse amplitude by a factor of 3.3.

For the research in this thesis, these detectors are usually used with a differencing balun for geometric jitter cancellation. The type fabricated at JPL typically has active areas of \(22 \times 15 \ \mathrm{\upmu m}\), formed by a meander of 100 nm-wide and 5-nm-thick niobium nitride (NbN) nanowires on a 500 nm pitch (Fig. 1 b). They are embedded in an efficiency-enhancing optical stack made of alternating layers of TiO\(_2\) and SiO\(_2\) and a gold mirror layer and typically have FWHM timing jitter of about 14 ps. The FW1%M jitter, which is a measure of the width of the jitter response function or histogram at 1% height, is an important metric for quantum or classical communication protocols that expect to reliably place photon timing measurements into time bins measured with respect to a clock. This is the case for pulsed Quantum Key Distribution and classical Pulse Position Modulation communication protocols. The differential single pixel SNSPDs exhibit FW1%M jitter of 49 ps.

Impedance matching tapers can also help distinguish between instances when one or multiple photons are absorbed in the nanowire on a short timescale (\(< 100~\mathrm{ps}\)). The absorption of different numbers of photons results in variations in RF pulse height and slew rate (Fig. 1 c). This phenomenon gives the detector photon number resolution (PNR) whereby the specific number of photons in a optical pulse can be measured. This is in contrast to the more common binary detection capability offered by conventional SNSPDs that only indicates if one or more photons are absorbed. Chapter 4 explores how the manifestation of photon number resolution in this detector type presents an issue for accurate time-correlated measurements of multi-photon light pulses. Once properly managed, both arrival time and photon number resolution may be resolved accurately, which is potentially useful for various quantum communication and computing applications.

Colangelo, M., Korzh, B., Allmaras, J. P., Beyer, A. D., Mueller, A. S., Briggs, R. M., Bumble, B., et al. (2023). Impedance-matched differential superconducting nanowire detectors. Physical Review Applied, 19(4), 044093. doi:10.1103/PhysRevApplied.19.044093 ↩↩↩
Korzh, B., Zhao, Q. Y., Allmaras, J. P., Frasca, S., Autry, T. M., Bersin, E. A., Beyer, A. D., et al. (2020). Demonstration of sub-3 ps temporal resolution with a superconducting nanowire single-photon detector. Nature Photonics, 14(4), 250–255. doi:10.1038/s41566-020-0589-x ↩
Santavicca, D. F., Noble, B., Kilgore, C., Wurtz, G. A., Colangelo, M., Zhu, D., & Berggren, K. K. (2019). Jitter characterization of a dual-readout snspd. IEEE Transactions on Applied Superconductivity, 29(5), 1–4. doi:10.1109/TASC.2019.2895609 ↩