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arXiv:1407.3710 · Superconductor Science and Technology

Intrinsic detection efficiency of superconducting nanowire single photon detector in the modified hot spot model

A N Zotova, D Yu Vodolazov

Published Oct 31, 2014• 54 citations
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Abstract

We theoretically study the dependence of the intrinsic detection efficiency (IDE) of a superconducting nanowire single photon detector on the applied current, I , and magnetic field, H . We find that the current, at which the resistive state appears in the superconducting film, depends on the position of the hot spot (a region with suppressed superconductivity around the place where the photon has been absorbed) with respect to the edges of the film. This circumstance leads to inevitable smooth dependence IDE(I) when IDE , even for a homogenous straight superconducting film and in the absence of fluctuations. For IDE , a much sharper current dependence comes from the fluctuation-assisted vortex entry to the hot spot, which is located near the edge of the film. We find that a weak magnetic field strongly affects IDE when the photon detection is connected with fluctuation-assisted vortex entry to the hot spot (IDE ), and it weakly affects IDE when the photon detection is connected with the current-induced vortex nucleation in the film with the hot spot (IDE ).

DOI
10.1088/0953-2048/27/12/125001

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We theoretically study the dependence of the intrinsic detection efficiency (IDE) of a superconducting nanowire single photon detector on the applied current, I , and magnetic field, H . We find that the current, at which the resistive state appears in the superconducting film, depends on the position of the hot spot (a region with suppressed superconductivity around the place where the photon has been absorbed) with respect to the edges of the film. This circumstance leads to inevitable smooth dependence IDE(I) when IDE , even for a homogenous straight superconducting film and in the absence of fluctuations. For IDE , a much sharper current dependence comes from the fluctuation-assisted vortex entry to the hot spot, which is located near the edge of the film. We find that a weak magnetic field strongly affects IDE when the photon detection is connected with fluctuation-assisted vortex entry to the hot spot (IDE ), and it weakly affects IDE when the photon detection is connected with the current-induced vortex nucleation in the film with the hot spot (IDE ).
We evaluate experimentally the intrinsic detection efficiency (IDE) of superconducting NbN nanowire single-photon detectors in the range of wire thicknesses from 4 to 12 nm. The study is performed in the broad spectral interval between near-ultraviolet (wavelength 400 nm) and near-infrared (wavelength 2000 nm) light with plane waves at normal incidence. For visible light the IDE of the thinnest detectors reaches 70%. We use numerically computed absorptance of the nanowire-structures for the analysis of the experimental data. Variations in the detection efficiency with both the wire thickness and the wavelength evidence the red boundary of the hot-spot photon-detection mechanism. We explain the detection at larger wavelengths invoking thermal excitation of magnetic Pearl vortices over the potential barrier at the edges of the wire.
We use an external magnetic field to probe the detection mechanism of a superconducting nanowire single-photon detector. We argue that the hot belt model (which assumes partial suppression of the superconducting order parameter $\mathrm{\ensuremath{\Delta}}$ across the whole width of the superconducting nanowire after absorption of the photon) does not explain observed weak-field dependence of the photon count rate (PCR) for photons with $\ensuremath{\lambda}=450\phantom{\rule{4.pt}{0ex}}\mathrm{nm}$ and noticeable decrease of PCR (with increasing the magnetic field) in a range of the currents for photons with wavelengths $\ensuremath{\lambda}=450--1200\phantom{\rule{4.pt}{0ex}}\mathrm{nm}$. Found experimental results for all studied wavelengths can be explained by the vortex hot spot model (which assumes partial suppression of $\mathrm{\ensuremath{\Delta}}$ in the area with size smaller than the width of the nanowire) if one takes into account nucleation and entrance of the vortices to the photon induced hot spot and their pinning by the hot spot with relatively large size and strongly suppressed $\mathrm{\ensuremath{\Delta}}$.
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.
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.
While magnetic fields and superconductors are both central to classical and quantum technologies, their combined use is often challenging, as magnetic fields significantly affect superconducting device performance. In superconducting nanowire single-photon detectors (SNSPDs), magnetic fields drastically reduce detection efficiencies, hampering their application in magnetically-active classical and quantum photonics. Here, we systematically characterize the performance of NbTiN SNSPDs under magnetic fields and show the enhancement of their intrinsic detection efficiency (IDE) at lower bias currents and its suppression at higher currents. This leads to SNSPD performance degradation through reduced or disappearing saturation plateaus. We show that the magnitude of this degradation is highly dependent on nanowire width and demonstrate width-optimized SNSPDs with saturating IDE for a wide range of photon energies under application-relevant magnetic fields. Minimizing degradation in superconducting devices under magnetic fields enables applications like detector-integrated spin-optic and atomic quantum processors, high-sensitivity magnetometry, and quantum transduction.
Superconducting nanowire single-photon detectors (SNSPDs) have attracted considerable attention owing to their excellent detection performance; however, the underlying physics of the detection process is still unclear. In this study, we investigate the wavelength dependence of the intrinsic detection efficiency (IDE) for NbN SNSPDs. We fabricate various NbN SNSPDs with linewidths ranging from 30 nm to 140 nm. Then, for each detector, the IDE curves as a function of bias current for different incident photon wavelengths of 510–1700 nm are obtained. From the IDE curves, the relations between photon energy and bias current at a certain IDE are extracted. The results exhibit clear nonlinear energy–current relations for the NbN detectors, indicating that a detection model only considering quasiparticle diffusion is unsuitable for the meander-type NbN-based SNSPDs. Our work provides additional experimental data on SNSPD detection mechanism and may serve as an interesting reference for further investigation.