# Probabilistic vortex crossing criterion for superconducting nanowire single-photon detectors

## TL;DR

This paper introduces a probabilistic vortex crossing model for superconducting nanowire single-photon detectors, linking vortex dynamics to detection efficiency, timing jitter, and dark counts, and explaining energy-dependent quantum efficiency behavior.

## Contribution

It presents a novel vortex crossing-based detection criterion that connects dark counts and photon detection, providing insights into timing jitter and quantum efficiency limits.

## Key findings

- Vortex crossing probability increases with photon absorption even without barrier vanishing.
- Timing jitter is fundamentally limited by vortex tunneling dynamics.
- Quantum efficiency decreases exponentially at lower photon energies, affecting pulse-width dependency.

## Abstract

Superconducting nanowire single-photon detectors have emerged as a promising technology for quantum metrology from the mid-infrared to ultra-violet frequencies. Despite the 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.