Impedance-Matched Differential Superconducting Nanowire Detectors

Superconducting nanowire single-photon detectors (SNSPDs) are the highest-performing photon-counting technology in the near-infrared region. Because of delay-line effects, large-area SNSPDs typically trade off timing resolution and detection efficiency. This unavoidable fundamental constraint might limit their future deployment in demanding scientific applications. Here we introduce a detector design based on transmission-line engineering and differential readout for device-level signal conditioning, enabling a high system detection efficiency and a low detector jitter simultaneously. To make our differential detectors compatible with single-ended time taggers, we also engineer analog differential-to-single-ended readout electronics, with minimal impact on the system timing resolution. Our best niobium nitride differential SNSPD achieves a system detection efficiency of $(83.3\pm 4.3)\mathrm{\%}$ at $1550\mathrm{nm}$ and $(78\pm 5)\mathrm{\%}$ at $775\mathrm{nm}$. The lowest system jitter is $13.0\pm 0.4\mathrm{ps}$ at $1550\mathrm{nm}$ and $9.7\pm 0.4\mathrm{ps}$ at $775\mathrm{nm}$, limited by intrinsic contributions. These detectors also achieve sub-100-ps timing response at 1/100 of the maximum level, $30.7\pm 0.4\mathrm{ps}$ at 775 nm and $47.6\pm 0.4\mathrm{ps}$ at $1550\mathrm{nm}$, enabling time-correlated single-photon counting with high-dynamic-range response functions. Furthermore, because of the differential impedance-matched design, our detectors exhibit delay-line imaging capabilities and photon-number resolution. The properties and high-performance metrics achieved by our system make it a versatile photon-detection solution for quantum computing, quantum communication, and many other scientific applications.

Figure 1

Differential single-pixel superconducting nanowire single-photon detector. (a) Optical micrograph of a representative device. The detector die (lollipop) is connected to the parent wafer before packaging. Inset (i) shows an optical micrograph of the detector. The nanowire is embedded in an optical cavity to increase the detection efficiency. Inset (ii) shows an optical micrograph of the detector active area. (b) Artistic sketch of the SNSPD architecture realized in this work. Each meander end is interfaced with the readout through an impedance-matching taper. Note that the proportions of the elements in the figure are not to scale.

Figure 2

Simulated SNSPD dynamics in several readout configurations. For (a)–(d), the shading of the curves (dark to light) indicates the pulses generated by photon absorption in different locations of the meander (near the center to near the edge). The schematics shown in the insets in (a)–(c) show the simulated readout setups. For simplicity, the nanowire meander is pictured as a straight wire. The blue (red) lines indicate the positive (negative) pulses generated by the photon absorption in the wire. The dashed lines indicate the reflection of the original pulses generated by impedance mismatch. (a) The SNSPD is configured for single-ended readout. (b) The SNSPD is configured for an impedance-matched single-ended readout. (c) The SNSPD is configured for an impedance-matched differential readout. (d) A partial cancellation of the geometric contribution can be achieved by processing the difference of the complementary pulses, $V_{\mathrm{diff}}$.

Figure 3

Various differential single-pixel readout setups and pulse processing. The pulses are shown for two arbitrary hotspot locations along the meander. (a) A high-resolution real-time oscilloscope is used to collect the complementary pulses. (b) The complementary pulses are fed, after amplification, to the differential input of a balun that performs an operation equivalent to an analog difference of the pulses. (c) The complementary pulses are fed, after amplification, to the input of a differential comparator.

Figure 4

(a) Complementary pulses from device A upon illumination. The main signal discontinuities are attributed to reflections from the low-noise amplifier. The high-frequency ripple is attributed to internal reflection in the impedance-matching taper due to the limited design bandwidth. The inset shows positive pulse slew rate (SR). The impedance-matching taper boosts the slew rate. (b) Time-tagging procedure for $V_{\mathrm{pos}}$, $V_{\mathrm{neg}}$, and $V_{\mathrm{diff}}$. (c) Time-tag distributions for $123348$ detection events.

Figure 5

System-detection-efficiency (${\eta }_S$) curves for detectors A, B, C and D at $0.84\mathrm{K}$. Solid lines indicate the system detection efficiency, and the markers indicate the dark count rate. All the detectors achieve saturation of the internal detection efficiency.

Figure 6

Single-mode differential delay-line imaging. When differential readout is used and the speed of signal propagation is on the order of a few micrometers per picosecond, differential detectors can be used for localization of the light beam. (a) A single LP01 mode illuminates the center of an $L\times W$-area meander with a $w$-wide nanowire. (b) The LP01 mode is aligned with the detector center. (c) Simulation of the differential time $t_{\mathrm{\Delta }}$ histogram. (d) The LP01 mode and the meander centers are misaligned by $\mathrm{\Delta }x=3\text{μ}\mathrm{m}$ and $\mathrm{\Delta }y=5\text{μ}\mathrm{m}$. (e) Simulation of the differential time $t_{\mathrm{\Delta }}$ histogram. (f) Differential time distribution $t_{\mathrm{\Delta }}$ for detector A. (g) Differential time distribution $t_{\mathrm{\Delta }}$ for detector B.

Figure 7

(a) Dependence of the detector jitter, $j_{\mathrm{\Sigma }}$, across several detectors designs, wavelengths, and bias currents. The trends indicate that the dominant contribution is intrinsic. (b)–(e) Histograms corresponding to the points indicated in (a). Comparison of detector jitter and system jitter obtained with the methods described in the paper. The system jitter obtained with the differential-to-single-ended readout is at most 6 greater than the detector jitter, showing that the additional readout electronics have a minimal impact on the overall timing resolution.

Figure 8

Timing response for detector A at $\lambda =1550\mathrm{nm}$ in combination with the differential comparator and the TCSPC module, and for detector B at $\lambda =775\mathrm{nm}$ in combination with the balun and the TCSPC module.

Figure 9

Detector output and counting statistics under coherent-state illumination. (a) Sample of detector output $V_{\mathrm{diff}}$ for a pulsed laser with $\tilde{\mu }\approx 0.73$. The pulses are grouped and colored by pulse height. (b) Gaussian fitting of the pulse-amplitude histograms for $\tilde{\mu }\approx 0.73$, sampling the first peak [dashed line in (a)].

Figure 10

Simulation of the nanowire-stripline parameters: characteristic impedance and phase-velocity factor versus conductor width for a sheet kinetic inductance $L_{\mathrm{k}}=80\mathrm{pH}$ per square.

Figure 11

Schematics of the spice simulation for an impedance-matched differential detector. The taper is modeled as cascaded transmission lines (300 sections) with varying impedance and phase velocities unique to each section. The nanowire is simulated as a lossy transmission line (LTRA) with $L=800.6\text{μ}\mathrm{H}/\mathrm{m}$ and $C=75.27\mathrm{pF}/\mathrm{m}$. In this specific scheme, the length of the symmetric transmission lines is set to $500\text{μ}\mathrm{m}$. Note that L1, C1, L2, and C2 constitute bias-tee elements. Their values are selected arbitrarily.

Figure 12

The material stack.

Figure 13

Measurement setups. (a) Measurement setup for the characterization of the detector pulses, detector jitter $t_{\mathrm{\Sigma }}$, differential time $t_{\mathrm{\Delta }}$ histogram, and photon-number resolution. (b) Measurement setup for the characterization of the system detection efficiency and for the measurement of the system jitter $j_{\mathrm{diff}}$ using the balun in combination with the TCSPC module. (c) Measurement setup for the characterization of the system jitter $j_{\mathrm{diff}}$ using the cryogenic comparator in combination with the TCSPC module. LNA, low-noise amplifier.

Figure 14

Sketches for derivation of delay-line-imaging formulas. (a) Fiber spot misalignment reference on the meander for (b),(c). (b) The spot is vertically misaligned. (c) The spot is horizontally misaligned.

Figure 15

Photon-number resolution. (a) Gaussian fitting of the pulse-amplitude histograms for several effective photon numbers. (b) Photon-counting statistics reconstructed from the pulse-height distributions under different illumination conditions.