© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1108.4004 · Physical Review B

Vortex-assisted photon counts and their magnetic field dependence in single-photon superconducting detectors

Lev N. Bulaevskii, Matthias J. Graf, V. G. Kogan

Published Jan 17, 2012• 130 citations

Abstract

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.

DOI: 10.1103/physrevb.85.014505

Related papers

Vortex-assisted mechanism of photon counting in a superconducting nanowire single-photon detector revealed by external magnetic field

Denis Yu. Vodolazov, Yu. P. Korneeva, Alexander V. Semenov +2 more

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 $\mathrm{\ensuremath{\Delta}}$.

arXiv:1505.04689•Physical Review B•Sep 4, 2015•68 citations

Effect of magnetic field on the photon detection in thin superconducting meander structures

R. Lusche, Alexej D. Semenov, Yu. P. Korneeva +4 more

We have studied the influence of an externally applied magnetic field on the photon and dark count rates of meander-type niobium nitride superconducting nanowire single-photon detectors. Measurements have been performed at a temperature of 4.2 K, and magnetic fields up to 250 mT have been applied perpendicularly to the meander plane. While photon count rates are field independent at weak applied fields, they show a strong dependence at fields starting from approximately \ifmmode\pm\else\textpm\fi{}25 mT. This behavior, as well as the magnetic field dependence of the dark count rates, is in good agreement with the recent theoretical model of vortex-assisted photon detection and spontaneous vortex crossing in narrow superconducting lines. However, the local reduction of the superconducting free energy due to photon absorption, which is the fitting parameter in the model, increases much slower with the photon energy than the model predicts. Furthermore, changes in the free-energy during photon counts and dark counts depend differently on the current that flows through the meander. This indicates that photon counts and dark counts occur in different parts of the meander.

Physical Review B•Mar 19, 2014•21 citations

Dependence of count rate on magnetic field in superconducting thin-film TaN single-photon detectors

Andreas Engel, A. Schilling, K. Ilin +1 more

We have studied the magnetic-field dependence of both dark-count rates and photon-count rates in a superconducting nanowire single-photon detector made of TaN in external magnetic fields $|{\ensuremath{\mu}}_{0}H|<10$ mT perpendicular to the plane of the underlying meander structure and at $T=4$ K. The dark-count rates show a characteristic field dependence, which is asymmetric with respect to magnetic-field direction. The field and the current dependence of the dark counts can be quantitatively well explained if one assumes that the critical current is reduced to $\ensuremath{\approx}$$50%$ at the ${180}^{\ensuremath{\circ}}$ meander turns when compared to a straight strip, and the observed asymmetry can be modeled assuming that the turnarounds are not all strictly equal. Surprisingly, the photon-count rates do not show any significant field dependence, which seems to be at odds with existing detection models invoking vortex crossings.

arXiv:1206.4579•Physical Review B•Oct 22, 2012•35 citations

Probabilistic vortex crossing criterion for superconducting nanowire single-photon detectors

Saman Jahani, Li-Ping Yang, Adrián Buganza Tepole +3 more

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.

arXiv:1901.09291•Journal of Applied Physics•Apr 9, 2020•19 citations

Vortex-crossing-induced timing jitter of superconducting nanowire single-photon detectors

Hao Wu, Chao Gu, Yuhao Cheng +1 more

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.

Applied Physics Letters•Aug 7, 2017•31 citations

Characterization of MoSi superconducting single-photon detectors in magnetic field

Alexander A. Korneev, Yu. P. Korneeva, M. Yu. Mikhaı̆lov +9 more

We investigate the response mechanism of nanowire superconducting single-photon detectors (SSPDs) made of amorphous MoxSi1-x. We study the dependence of photon count and dark count rates on bias current in magnetic fields up to 113 mT at 1.7 K temperature. The observed behavior of photon counts is similar to the one recently observed in NbN SSPDs. Our results show that the detecting mechanism of relatively high-energy photons does not involve the vortex penetration from the edges of the film, and on the contrary, the detecting mechanism of low-energy photons probably involves the vortex penetration from the film edges.

IEEE Transactions on Applied Superconductivity•Jan 1, 2014•11 citations

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.

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 have studied the influence of an externally applied magnetic field on the photon and dark count rates of meander-type niobium nitride superconducting nanowire single-photon detectors. Measurements have been performed at a temperature of 4.2 K, and magnetic fields up to 250 mT have been applied perpendicularly to the meander plane. While photon count rates are field independent at weak applied fields, they show a strong dependence at fields starting from approximately \ifmmode\pm\else\textpm\fi{}25 mT. This behavior, as well as the magnetic field dependence of the dark count rates, is in good agreement with the recent theoretical model of vortex-assisted photon detection and spontaneous vortex crossing in narrow superconducting lines. However, the local reduction of the superconducting free energy due to photon absorption, which is the fitting parameter in the model, increases much slower with the photon energy than the model predicts. Furthermore, changes in the free-energy during photon counts and dark counts depend differently on the current that flows through the meander. This indicates that photon counts and dark counts occur in different parts of the meander.

We have studied the magnetic-field dependence of both dark-count rates and photon-count rates in a superconducting nanowire single-photon detector made of TaN in external magnetic fields $|{\ensuremath{\mu}}_{0}H|<10$ mT perpendicular to the plane of the underlying meander structure and at

T=4

K. The dark-count rates show a characteristic field dependence, which is asymmetric with respect to magnetic-field direction. The field and the current dependence of the dark counts can be quantitatively well explained if one assumes that the critical current is reduced to $\ensuremath{\approx}$

50%

at the ${180}^{\ensuremath{\circ}}$ meander turns when compared to a straight strip, and the observed asymmetry can be modeled assuming that the turnarounds are not all strictly equal. Surprisingly, the photon-count rates do not show any significant field dependence, which seems to be at odds with existing detection models invoking vortex crossings.

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.

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.

We investigate the response mechanism of nanowire superconducting single-photon detectors (SSPDs) made of amorphous MoxSi1-x. We study the dependence of photon count and dark count rates on bias current in magnetic fields up to 113 mT at 1.7 K temperature. The observed behavior of photon counts is similar to the one recently observed in NbN SSPDs. Our results show that the detecting mechanism of relatively high-energy photons does not involve the vortex penetration from the edges of the film, and on the contrary, the detecting mechanism of low-energy photons probably involves the vortex penetration from the film edges.