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Applied Physics Letters

Inhomogeneity-induced timing jitter of superconducting nanowire single-photon detectors

Yuhao Cheng, Chao Gu, Xiaolong Hu

Published Aug 7, 2017• 30 citations
Publisher

Abstract

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.

DOI
10.1063/1.4985226

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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 investigate the timing properties of single-photon-triggered vortex (or anti-vortex) crossing in a current-biased superconducting nanowire and find that the time delays caused in the vortex-crossing process vary with the transverse positions on the nanowire where the photons are absorbed. The position-dependent time delays indicate that the vortex-crossing process induces timing jitter of a superconducting nanowire single-photon detector (SNSPD). The magnitude of this timing jitter further depends on various parameters, including the polarization of the incident photon, the bias current, and the width of the nanowire. This vortex-crossing-induced timing jitter might represent the lower bound of the timing jitter of the SNSPD and fundamentally limit its time-resolving capability.
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.
Nanowire superconducting single-photon detectors (SSPDs) are promising devices for single-photon detection applications at telecom wavelengths, in terms of high efficiency, low dark count rate and short dead time. They consist of a long, 100 nm wide, superconducting niobium nitride nanowire folded into a meander pattern and biased close to the critical current. Photons incident on the SSPD locally break the superconductivity which results in a resistive barrier across the nanowire. The voltage drop across this barrier is measured. The devices presented in this thesis are fabricated on a gallium arsenide substrate: a material system that allows integration of single-photon sources and detectors on a single chip. Such quantum photonic integrated circuits (QPICs) are of major importance for scalable quantum computing.Measurements on nominally identical SSPDs show large variations in critical current and efficiency of the devices . This is a huge problem for applications where arrays of SSPDs are needed such as linear optical quantum computing. The authors of [1] attribute the observations to geometrical constrictions: regions in the nanowire where the cross section is reduced. This reduces the critical current of the wire and the SSPD cannot be biased efficiently anymore. In this thesis, it is shown that the continuously distributed inhomogeneity of the nanowire dimension or the crystal structure, instead of localized constrictions, is the origin of the limited detection efficiency and poor uniformity of our SSPDs.To investigate the effect of inhomogeneities, SSPDs with lengths in the range from 100 nm to 15 µm are fabricated and characterized electrically and optically. The two main observations from the electrical characterization are a decrease of the critical current with increasing length and a decrease of the spread in critical current values with increasing length. These measurements also indicate that the length scale of the inhomogeneities is 100 nm or smaller. The main result of the optical characterization is a decrease of the detection efficiency with increasing wire length.Simple assumptions on how the inhomogeneities influence the critical current of the wires allowed us to create a numerical model that quantitatively reproduces the measured variations of the critical current. This result is used to model also the detection efficiency of the SSPDs. This model qualitatively reproduces the general trends in the efficiency measurements, although some deviations are observed for the longer wires. Nanowire superconducting single-photon detectors (SSPDs) are promising devices for single-photon detection applications at telecom wavelengths, in terms of high efficiency, low dark count rate and short dead time. They consist of a long, 100 nm wide, superconducting niobium nitride nanowire folded into a meander pattern and biased close to the critical current. Photons incident on the SSPD locally break the superconductivity which results in a resistive barrier across the nanowire. The voltage drop across this barrier is measured. The devices presented in this thesis are fabricated on a gallium arsenide substrate: a material system that allows integration of single-photon sources and detectors on a single chip. Such quantum photonic integrated circuits (QPICs) are of major importance for scalable quantum computing.Measurements on nominally identical SSPDs show large variations in critical current and efficiency of the devices . This is a huge problem for applications where arrays of SSPDs are needed such as linear optical quantum computing. The authors of [1] attribute the observations to geometrical constrictions: regions in the nanowire where the cross section is reduced. This reduces the critical current of the wire and the SSPD cannot be biased efficiently anymore. In this thesis, it is shown that the continuously distributed inhomogeneity of the nanowire dimension or the crystal structure, instead of localized constrictions, is the origin of the limited detection efficiency and poor uniformity of our SSPDs.To investigate the effect of inhomogeneities, SSPDs with lengths in the range from 100 nm to 15 µm are fabricated and characterized electrically and optically. The two main observations from the electrical characterization are a decrease of the critical current with increasing length and a decrease of the spread in critical current values with increasing length. These measurements also indicate that the length scale of the inhomogeneities is 100 nm or smaller. The main result of the optical characterization is a decrease of the detection efficiency with increasing wire length.Simple assumptions on how the inhomogeneities influence the critical current of the wires allowed us to create a numerical model that quantitatively reproduces the measured variations of the critical current. This result is used to model also the detection efficiency of the SSPDs. This model qualitatively reproduces the general trends in the efficiency measurements, although some deviations are observed for the longer wires.
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.
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.