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Journal of Nanophotonics

Origin and mechanism of the wavelength-dependent timing jitter in superconducting nanowire

Jiang-Hua Guo, Youcheng Tian, Lingxin Long, Hengbin Zhang, Junku Liu, Lin Xiao, Jun Xie

Published Nov 27, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1117/1.jnp.14.046012

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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.
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.
We show that the distributed electronic and geometric inhomogeneity of a superconducting nanowire induces timing jitter of the resulting single-photon detector and this timing jitter could be further exacerbated by localized constrictions. Due to the distributed inhomogeneity, photons absorbed at different locations of the nanowire generate hotspots that “sense” different local properties of the nanowire during the electro-thermal evolutions and thereby produce varying time delays. The localized constrictions limit the bias current, slow down the Joule-heating process, and consequently increase the average time delays and the inhomogeneity-induced timing jitter. We combine the Monte-Carlo method and the electro-thermal simulation to illustrate the inhomogeneity-induced timing jitter.
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 analyze the origin of the intrinsic timing jitter in superconducting nanowire single-photon detectors in terms of fluctuations in the latency of the detector response, which is determined by the microscopic physics of the photon-detection process. We demonstrate that fluctuations in the physical parameters, which determine the latency, give rise to the intrinsic timing jitter. We develop a general description of latency by introducing the explicit time dependence of the internal detection efficiency. By considering the dynamic Fano fluctuations together with static spatial inhomogeneities, we study the details of the connection between latency and timing jitter. We develop both a simple phenomenological model and a more general microscopic model of detector latency and timing jitter based on the solution of the generalized time-dependent Ginzburg-Landau equations for the 1D hotbelt geometry. While the analytical model is sufficient for qualitative interpretation of recent data, the general approach establishes the framework for a more quantitative analysis of detector latency and the fundamental limits of intrinsic timing jitter. These theoretical advances can be used to interpret the results of recent experiments measuring the dependence of detection latency and timing jitter on photon energy to the few-picosecond level.
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.
The results of this theoretical study are important for applications dealing with superconducting nanowire single-photon detectors (SNSPDs), which include quantum information processing. The author shows that the variation in delay time ${\ensuremath{\tau}}_{d}$ (timing jitter) of the voltage response after absorption of a single photon, connected to either position-dependent response or variation in the energy deposited to electrons, could be as small as 1 ps when the current in the superconducting strip approaches the depairing current. Reducing this jitter is a main topic of SNSPD research, and understanding the origins of these variations is necessary to that end.