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arXiv:1901.09291 · Journal of Applied Physics

Probabilistic vortex crossing criterion for superconducting nanowire single-photon detectors

Saman Jahani, Li-Ping Yang, Adrián Buganza Tepole, Joseph C. Bardin, Hong X. Tang, Zubin Jacob

Published Apr 9, 2020• 19 citations

Abstract

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.

DOI: 10.1063/1.5132961

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Predicting the behavior of superconducting nanowire single-photon detectors (SNSPDs) is important as their use becomes more widespread in fields ranging from quantum computing to quantum remote sensing. Here, we present a vortex-crossing theory of photon detection that provides a unified definition of system detection efficiency and dark-count rates. Our approach quantitatively captures the plateau region of system detection efficiency for NbN- and WSi-based SNSPDs. We concurrently predict the temperature dependence of dark-count rates and the intrinsic timing jitter of SNSPDs. We extensively benchmark our model against various experiments to aid in the design of the next generation of SNSPDs.

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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 thorough spectral study of the intrinsic single-photon detection efficiency in superconducting TaN and NbN nanowires with different widths has been performed. The experiment shows that the cut-off of the intrinsic detection efficiency at near-infrared wavelengths is most likely controlled by the local suppression of the barrier for vortex nucleation around the absorption site. Beyond the cut-off quasi-particle diffusion in combination with spontaneous, thermally activated vortex crossing explains the detection process. For both materials, the reciprocal cut-off wavelength scales linearly with the wire width where the scaling factor agrees with the hot-spot detection model.

We argue that photon counts in a superconducting nanowire single-photon detector (SNSPD) are caused by the transition from a current-biased metastable superconducting state to the normal state. Such a transition is triggered by vortices crossing the thin and narrow superconducting strip from one edge to another due to the Lorentz force. Detector counts in SNSPDs may be caused by three processes: (a) a single incident photon with sufficient energy to break enough Cooper pairs to create a normal-state belt across the entire width of the strip (direct photon count), (b) thermally induced single-vortex crossing in the absence of photons (dark count), which at high-bias currents releases the energy sufficient to trigger the transition to the normal state in a belt across the whole width of the strip, and (c) a single incident photon of insufficient energy to create a normal-state belt but initiating a subsequent single-vortex crossing, which provides the rest of the energy needed to create the normal-state belt (vortex-assisted single-photon count). We derive the current dependence of the rate of vortex-assisted photon counts. The resulting photon count rate has a plateau at high currents close to the critical current and drops as a power law with high exponent at lower currents. While the magnetic field perpendicular to the film plane does not affect the formation of hot spots by photons, it causes the rate of vortex crossings (with or without photons) to increase. We show that by applying a magnetic field one may characterize the energy barrier for vortex crossings and identify the origin of dark counts and vortex-assisted photon counts.

Superconducting Nanowire Single Photon Detectors (SNSPDs) have demonstrated timing and efficiency properties that have placed them at the frontier in single photon sensing applications (e.g. photon counting, deep space optical communications, quantum communication, and quantum encryption). Properties such as timing jitter as low as 3 ps, dark counts under 90 counts per day, high detection efficiency (>90%), short dead time and sensitivity over a wide range of photon energies (UV to IR). SNSPDs have a cutoff energy where the photon does not have enough energy to trigger the detection mechanism. In this paper, we lay out the framework and experimental setup to explore a modified approach in detecting photons below the cut off energy typical in an SNSPD. Leveraging the nanowire's change in kinetic inductance from photon absorption, the resulting voltage pulse is measured through a coupled quantum-noise-limited parametric amplifier. We consider nanowires with widths less than the vortex entry limit of w <; 4.4ξ, where ξ is the coherence length, limiting the sources of noise.