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Numerical analysis of detection-mechanism models of superconducting nanowire single-photon detector

Andreas Engel, A. Schilling

Published Jan 1, 2013• 48 citations
Publisher

Abstract

The microscopic mechanism of photon detection in superconducting nanowire single-photon detectors is still under debate. We present a simple, but powerful theoretical model that allows us to identify essential differences between competing detection mechanisms. The model is based on quasi-particle multiplication and diffusion after the absorption of a photon. We then use the calculated spatial and temporal evolution of this quasi-particle cloud to determine detection criteria of three distinct detection mechanisms, based on the formation of a normal conducting spot, the reduction of the effective depairing critical current below the bias current and a vortex-crossing scenario, respectively. All our calculations as well as a comparison to experimental data strongly support the vortex-crossing detection mechanism by which vortices and antivortices enter the superconducting strip from the edges and subsequently traverse it thereby triggering the detectable normal conducting domain. These results may therefore help to reveal the microscopic mechanism responsible for the detection of photons in superconducting nanowires.

DOI
10.5167/uzh-86020

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The microscopic mechanism of photon detection in superconducting nanowire single-photon detectors is still under debate. We present a simple, but powerful theoretical model that allows us to identify essential differences between competing detection mechanisms. The model is based on quasi-particle multiplication and diffusion after the absorption of a photon. We then use the calculated spatial and temporal evolution of this quasi-particle cloud to determine detection criteria of three distinct detection mechanisms, based on the formation of a normal conducting spot, the reduction of the effective depairing critical current below the bias current and a vortex-crossing scenario, respectively. All our calculations as well as a comparison to experimental data strongly support the vortex-crossing detection mechanism by which vortices and antivortices enter the superconducting strip from the edges and subsequently traverse it thereby triggering the detectable normal conducting domain. These results may therefore help to reveal the microscopic mechanism responsible for the detection of photons in superconducting nanowires.
The microscopic mechanism of photon detection in superconducting nanowire single-photon detectors is still under debate. We present a simple but powerful theoretical model that allows us to identify essential differences between competing detection mechanisms. The model is based on quasi-particle multiplication and diffusion after the absorption of a photon. We then use the calculated spatial and temporal evolution of this quasi-particle cloud to determine detection criteria of three distinct detection mechanisms, based on the formation of a normal conducting spot, the reduction of the effective depairing critical current below the bias current, and a vortex-crossing scenario, respectively. All our calculations as well as a comparison to experimental data strongly support the vortex-crossing detection mechanism by which vortices and antivortices enter the superconducting strip from the edges and subsequently traverse it thereby triggering the detectable normal conducting domain. These results may therefore help to reveal the microscopic mechanism responsible for the detection of photons in superconducting nanowires.
Abstract In this paper we intend to give a comprehensive description of the current understanding of the detection mechanism in superconducting nanowire single-photon detectors. We will review key experimental results related to the detection mechanism, e.g. the variations of the detection probability as a function of bias current, temperature or magnetic field. Commonly used detection models will be introduced and we will analyze their predictions in view of the experimental observations. Although none of the proposed detection models is able to describe all experimental data, it is becoming increasingly clear that vortices are essential for the formation of the initial normal-conducting domain that triggers a detection event.
In a recent publication we have proposed a numerical model that describes the detection process of optical photons in superconducting nanowire single-photon detectors (SNSPD). Here, we review this model and present a significant improvement that allows us to calculate more accurate current distributions for the inhomogeneous quasi-particle densities occurring after photon absorption. With this new algorithm we explore the detector response in standard NbN SNSPD for photons absorbed off-center and for 2-photon processes. We also discuss the outstanding performance of SNSPD based on WSi. Our numerical results indicate a different detection mechanism in WSi than in NbN or similar materials.
We report an experimental test of the photodetection mechanism in a nanowire superconducting single photon detector. Detector tomography allows us to explore the 0.8-8 eV energy range via multiphoton excitations. High accuracy results enable a detailed comparison of the experimental data with theories for the mechanism of photon detection. We show that the temperature dependence of the efficiency of the superconducting single photon detector is determined not by the critical current but by the current associated with vortex unbinding. We find that both quasiparticle diffusion and vortices play a role in the detection event.
To elucidate the photon detection mechanism of superconducting single-photon detectors, we theoretically examine the dynamics of type-II superconductors with a bias current using the two-dimensional time-dependent Ginzburg–Landau and the Maxwell equations. The photon injection that weakens the superconducting order parameter is treated phenomenologically as a local temperature increase, and the injected energy is controlled by the initial hotspot radius. The photon is detected by the voltage change between two electrodes attached to the left and right edges of the superconductor. We find that the detection dynamics in certain parameter ranges can be explained by the conventional hotspot model, whereas those in other parameter ranges are governed by the formation and subsequent dynamics of superconducting vortex and antivortex pairs. The photon detection is possible for an initial hotspot radius that exceeds a threshold value. We find that the generation of a vortex–antivortex pair occurs near the threshold. The flow of the pair perpendicular to the current direction finally creates a normal region for the photon detection. The voltage change for the Ginzburg–Landau parameter close to the transition point from type-II to type-I superconductor shows anomalous behavior that is not associated with the dynamics of the vortex–antivortex pair. We also examine the effects of spatially non-uniform current density on the voltage change and the superconducting order parameter to provide a hint to understand the behavior of wide-strip single-photon detectors. The estimated values of incident photon energy and response time for photon detection are reasonable in comparison with experiments. The present analysis provides useful guidelines for flexible design of device structures.
Superconducting nanowire single-photon detectors have emerged as a promising technology for quantum metrology from the mid-infrared to ultraviolet frequencies. Despite recent experimental successes, a predictive model to describe the detection event in these detectors is needed to optimize the detection metrics. Here, we propose a probabilistic criterion for single-photon detection based on single-vortex (flux quanta) crossing the width of the nanowire. Our model makes a connection between the dark counts and photon counts near the detection threshold. The finite-difference calculations demonstrate that a change in the bias current distribution as a result of the photon absorption significantly increases the probability of single-vortex crossing even if the vortex potential barrier has not vanished completely. We estimate the instrument response function and show that the timing uncertainty of this vortex tunneling process corresponds to a fundamental limit in timing jitter of the click event. We demonstrate a trade-space between this intrinsic (quantum) timing jitter, quantum efficiency, and dark count rate in TaN, WSi, and NbN superconducting nanowires at different experimental conditions. Our detection model can also explain the experimental observation of exponential decrease in the quantum efficiency of SNSPDs at lower energies. This leads to a pulse-width dependency in the quantum efficiency, and it can be further used as an experimental test to compare across different detection models.