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arXiv:1806.07183 · Physical review. B./Physical review. B

Timing jitter in photon detection by straight superconducting nanowires: Effect of magnetic field and photon flux

Mariia Sidorova, Alexej D. Semenov, Heinz‐Wilhelm Hübers, Artem A. Kuzmin, Steffen Doerner, K. Ilin, M. Siegel, Ilya Charaev, Denis Yu. Vodolazov

Published Oct 11, 2018• 25 citations
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Abstract

We studied the effects of the external magnetic field and photon flux on timing jitter in photon detection by straight superconducting NbN nanowires. At two wavelengths 800 and 1560 nm, statistical distribution in the appearance times of photon counts exhibits Gaussian shape at small times and an exponential tail at large times. The characteristic exponential time is larger for photons with smaller energy and increases with external magnetic field while variations in the Gaussian part of the distribution are less pronounced. Increasing photon flux drives the nanowire from the discrete quantum detection regime to the uniform bolometric regime that averages out fluctuations of the total number of nonequilibrium electrons created by the photon and drastically reduces jitter. The difference between standard deviations of Gaussian parts of distributions for these two regimes provides the measure for the strength of electron-number fluctuations; it increases with the photon energy. We show that the two-dimensional hot-spot detection model explains qualitatively the effect of magnetic field.

DOI
10.1103/physrevb.98.134504

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We studied the effects of the external magnetic field and photon flux on timing jitter in photon detection by straight superconducting NbN nanowires. At two wavelengths 800 and 1560 nm, statistical distribution in the appearance times of photon counts exhibits Gaussian shape at small times and an exponential tail at large times. The characteristic exponential time is larger for photons with smaller energy and increases with external magnetic field while variations in the Gaussian part of the distribution are less pronounced. Increasing photon flux drives the nanowire from the discrete quantum detection regime to the uniform bolometric regime that averages out fluctuations of the total number of nonequilibrium electrons created by the photon and drastically reduces jitter. The difference between standard deviations of Gaussian parts of distributions for these two regimes provides the measure for the strength of electron-number fluctuations; it increases with the photon energy. We show that the two-dimensional hot-spot detection model explains qualitatively the effect of magnetic field.
We studied timing jitter in the appearance of photon counts in meandering nanowires with different fractional amount of bends. Intrinsic timing jitter, which is the probability density function of the random time delay between photon absorption in current-carrying superconducting nanowire and appearance of the normal domain, reveals two different underlying physical mechanisms. In the deterministic regime, which is realized at large photon energies and large currents, jitter is controlled by position-dependent detection threshold in straight parts of meanders. It decreases with the increase in the current. At small photon energies, jitter increases and its current dependence disappears. In this probabilistic regime jitter is controlled by Poisson process in that magnetic vortices jump randomly across the wire in areas adjacent to the bends.
Timing jitter inherent in photon detection by superconducting nanowire single-photon detectors has different values and behaves differently for detection events originating in bends and in straights of nanowires. Generally, jitter is larger for events in bends. Although, for typical meandering nanowire, contribution of bends to the integral jitter is almost negligible due to small geometric weight of bends in the meander, it reduces the accuracy of extracting the value of local jitter in straights. Here we report on the intrinsic jitter, which was measured in a straight nanowire without bends. Standard deviation in the intrinsic jitter for detection events in the straight nanowire is smaller than 6.5 ps for photons with the wavelength 794 nm and 7.7 ps for 1560 nm. This value is less than jitter magnitudes in straights, which were extracted from the jitter measured previously for the meandering nanowire. Coupling of photons to the nanowire through sufficiently long optical fiber increases integral jitter and causes asymmetry in the jitter histogram. However, this optical asymmetry differs qualitatively from the asymmetry caused by the detection process itself at small photon energies.
We present a direct observation of the geometrical jitter in single photon detection by a straight superconducting nanowire. Differential measurement technique was applied to the 180-μm long nanowire similar to those commonly used in the technology of superconducting nanowire single photon detectors (SNSPD). A non-Gaussian geometrical jitter appears as a wide almost uniform probability distribution (histogram) of the delay time (latency) of the nanowire response to detected photon. White electrical noise of the readout electronics causes broadened, Gaussian-shaped edges of the histogram. Subtracting noise contribution, we found for the geometrical jitter a standard deviation of ≈8.5 ps and the full width at half maximum (FWHM) of the distribution of ≈29 ps. FWHM corresponds to the propagation speed of the electrical signal along the nanowire of ≈6.2 × 106m/s or 0.02 of the speed of light. Alternatively the propagation speed was estimated from the central frequency of the measured first-order self-resonance of the nanowire. Both values agree well with each other and with previously reported values. As the intensity of the incident photon flux increases, the wide probability distribution collapses into a much narrower Gaussian distribution with a standard deviation dominated by the noise of electronics. We associate the collapse of the histogram with the transition from the discrete, single photon detection to the uniform bolometric regime.
A 2D hot spot diffusion model for describing the superconducting nanowire response to single photon is presented. We develop the 1D hot belt model to 2D hot spot model and can capture the initial stage of the hot spot evolution after photon absorption, this is helpful to comprehensive understand the origins and underlying physics of time jitter in superconducting nanowire-based single-photon detectors. Furthermore, the developed model can qualitatively explain the asymmetry and photon wavelength dependent probability density function (PDF) of the delay time. We find that the left and right half of the PDF distributions respective exhibit the Gauss and non-Gauss shape as increasing the excitation wavelength or decreasing the bias current, and the origins are discussed and analyzed in the framework of newly developed 2D model. The proposed 2D hot spot diffusion model will not only sheds light on the origin and influence of the timing jitter but will also reveal the work principle of the superconducting nanowire devices.
A 2D hot spot diffusion model for describing the superconducting nanowire response to a single photon is presented. Compared to the 1D hot belt model, the 2D hot spot model can capture the initial stage of the hot spot evolution after photon absorption, which is beneficial for achieving a more comprehensive understanding of the origins and underlying physics of the timing jitter in superconducting nanowire-based single-photon detectors. Based on the established 2D diffusion model, the cross-section effect induced by the random radial position of the photon absorption is investigated, which can qualitatively explain the asymmetry and non-Gaussian shape of the probability density function (PDF) distributions of the time delay. Furthermore, the shift of the right half of the PDF distributions with increasing photon wavelength can also be clarified in the framework of the innovative 2D diffusion model. Considering the spatial inhomogeneity along the nanowire, the calculated results of the timing jitter based on the Monte Carlo methods are in good agreement with the experimental observations. The proposed 2D hot spot diffusion model will not only shed light on the origin and influence of the timing jitter but also reveal the working principle of superconducting nanowire devices.
Detection jitter quantifies variance introduced by the detector in the determination of photon arrival time. It is a crucial performance parameter for systems using superconducting nanowire single photon detectors (SNSPDs). In this work, we have demonstrated that the detection timing jitter is limited in part by the spatial variation of the photon detection events along the length of the wire. We define this jitter source as a geometric jitter since it is related to the length and area of the SNSPD. To characterize the geometric jitter, we have constructed a differential cryogenic readout with less than 7 ps of an electronic jitter that can amplify the pulses generated from the two ends of an SNSPD. By differencing the measured arrival times of the two electrical pulses, we were able to partially cancel out the difference of the propagation times and thus reduce the uncertainty of the photon arrival time. We proved that the variation of the differential propagation time was a few ps for a 3 μm × 3 μm device, while it increased up to 50 ps for a 20 μm × 20 μm device. In a 20 μm × 20 μm large SNSPD, we achieved a 20% reduction in the overall detection timing jitter for detecting the telecom-wavelength photons by using the differential cryogenic readout.