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arXiv:2503.11430 · Applied Physics Letters

Markov chain Monte Carlo detector tomography applied to a NbTiN nanobridge

F. B. Baalbergen, Iman Esmaeil Zadeh, Martin P. van Exter, M. J. A. de Dood

Published Jun 16, 2025• 0 citations
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Abstract

We demonstrate the use of a flexible and highly accurate Markov chain Monte Carlo quantum detector tomography method as a minimization algorithm to best describe the response of an efficient 120 nm wide NbTiN superconducting nanobridge single photon detector. Separation of the internal quantum efficiency and external quantum efficiency is possible due to the difference in saturation behavior of an ideal one-photon threshold detector as compared to a detector with non-unity one-photon internal quantum efficiency. From a statistical analysis of our measurements (at T=(4.23 ± 0.01) K, I=(29.4 ± 0.1) μA, I/Iswitch=(0.90 ± 0.01)), we find an external quantum efficiency of η=(1.60 ± 0.05)×10−6, a one-photon internal quantum efficiency of p1=0.568 ± 0.008, and a unity multi-photon (two or more) internal quantum efficiency.

DOI
10.1063/5.0271909

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Superconducting Nanowire Single Photon Detectors (SNSPDs) are a leading technology for quantum optics and information, offering fast recovery, low timing jitter, high detection efficiency, and intrinsic photon number resolution, making them ideal for future quantum applications [1]. We introduce a Monte-Carlo-Markov-Chain (MCMC) approach to Detector Tomography for nanobridge NbTiN devices, separating internal and external quantum efficiencies. This is key to understanding SNSPD detection mechanisms and performance trade-offs.
The optical response of NbTiN superconducting single photon detectors is studied using quantum detector tomography which separates the detector response in single and multiple photon contributions. Three different NbTiN nanodetectors of 70, 100 and 150 nm width are compared based on their detector tomography curves. The energy dependent photon response for the 100 nm nanodetector at two different wavelengths is explored. The detectors present a non-linear behaviour, which complicates the comparison. For the first time, we find that tomography curves saturate above a certain bias current and we compare the current density required to achieve the single photon regime.
Superconducting single photon detectors consist of a narrow and thin wire of superconductor and can detect single photons with high efficiency and high speed. Simultaneous optimization of the detection efficiency and detector response time is difficult because the response time is set by the dimensions of the wire (cross section and length) while the detection efficiency is determined by both the internal detection mechanism and the dimensions of the wire. Wider and shorter wires are easier to fabricate, are more robust and lead to shorter detector reset time, but are generally less efficient. Experiments employing detector tomography provide important insights into the photon detection mechanism and indicate a detection mechanism where the edges of the wire are more efficient. This leads to a position dependent local detection efficiency that can be explained in the context of a photon-assisted-vortex-entry model and predicts an optimum wire width ~70 nm. A 50 nm wide silicon nanowire deposited on top of a 150 nm wide NbN nanowire directs light at 1550 nm wavelength to the edges and improves both the total absorption efficiency and the internal detection efficiency of the wire. The total absorption efficiency can be enhanced by 30% while the internal detection efficiency is increased by 70%. Assuming that the wire covers a similar area the detector response time is reduced 4-fold compared to the standard design using a 70 nm wide wire.
We determine the full photon number response of a NbN superconducting nanowire single photon detector via quantum detector tomography, and the results show the separation of linear, effective absorption efficiency from the internal detection efficiencies. In addition, we demonstrate an error budget for the complete quantum characterization of the detector. We find that for short times, the dominant noise source is shot noise, while laser power fluctuations limit the accuracy for longer timescales. The combined standard uncertainty of the internal detection efficiency derived from our measurements is about 2%.
We present a simple quantum detector tomography protocol, which allows, without ambiguities, to measure the two-spot detection efficiency and extract the hot-spot interaction length of superconducting nanowire single photon detectors (SNSPDs) with unity intrinsic detection efficiency. We identify a significant parasitic contribution to the measured two-spot efficiency, related to an effect of the bias circuit, and find a way to rule out this contribution during data post-processing and directly in the experiment. From the data analysis for waveguide-integrated SNSPD, we find signatures of the saturation of the two-spot efficiency and hot-spot interaction length of order of 100 nm.
N superconducting films and show that a Nb fraction of x = 0.62 allows for the fabrication of detectors from films as thick as 9 nm and covering an active area of 20 µm, with a wide detection saturation plateau at telecom wavelengths and in particular at 1550 nm. This is a signature of an internal detection efficiency saturation, achieved while maintaining the high time resolution associated with NbTiN and operation at 2.5K. With our optimized recipe, we reliably fabricated detectors with high critical current densities reaching a saturation plateau at 1550 nm with 80% system detection efficiency and with a FWHM timing jitter as low as 19.5 ps.