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Journal of Low Temperature Physics

Calculation and Proposal for Improving the Timing Jitter of Transition-Edge Sensors

A. Kato, K. Hattori, Sachiko Takasu, Joern Beyer, Daiji Fukuda

Published Jan 7, 2026• 1 citation
Publisher

Abstract

Abstract In photonic quantum computing and quantum information processing, photon number resolution is crucial for generating highly non-classical quantum states. Superconducting transition-edge sensors (TESs) are considered one of the most effective photon number-resolving detectors for this purpose. However, the current timing properties of TESs, such as timing jitter (a few ns) and recovery time (several hundred ns), are insufficient, limiting the operational speed of quantum applications. To address the potential for improving TES timing performance, we have proposed an improved calculation to derive TES timing jitter. Our calculations including the effect of the SQUID noise indicate that expanding the electrical bandwidth of the external voltage amplifier and optimizing the inductance to match that bandwidth, can significantly improve timing jitter. According to our model, timing jitter 1 ns FWHM is achievable with an input inductance of 0.35 nH and an electrical bandwidth of 1 GHz. Additionally, we have shown that with our TES and SQUID parameters, the lowest achievable timing jitter is approximately 0.71 ns FWHM. Achieving an even lower jitter would require a redesign aimed at further reducing the SQUID noise.

DOI
10.1007/s10909-025-03359-3

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Abstract In photonic quantum computing and quantum information processing, photon number resolution is crucial for generating highly non-classical quantum states. Superconducting transition-edge sensors (TESs) are considered one of the most effective photon number-resolving detectors for this purpose. However, the current timing properties of TESs, such as timing jitter (a few ns) and recovery time (several hundred ns), are insufficient, limiting the operational speed of quantum applications. To address the potential for improving TES timing performance, we have proposed an improved calculation to derive TES timing jitter. Our calculations including the effect of the SQUID noise indicate that expanding the electrical bandwidth of the external voltage amplifier and optimizing the inductance to match that bandwidth, can significantly improve timing jitter. According to our model, timing jitter 1 ns FWHM is achievable with an input inductance of 0.35 nH and an electrical bandwidth of 1 GHz. Additionally, we have shown that with our TES and SQUID parameters, the lowest achievable timing jitter is approximately 0.71 ns FWHM. Achieving an even lower jitter would require a redesign aimed at further reducing the SQUID noise.
Recently, photon number resolving detectors, which are based on micro-calorimeters with superconducting transition edge sensors (TESs) [1], have shown excellent performances such as high quantum efficiency of 89 %, and high energy resolution of 0.2 eV [2]. To extend their applications to quantum telecommunication fields, however, the detectors should have high timing properties of the low timing jitters and the fast recovering time. To achieve these properties, we have developed new TES detectors with a titanium-based superconductor. Titanium has the transition temperature (Tc) at 0.39 K in bulk. This will improve the timing properties of TES devices because the operating temperature at Tc is strongly related to the intrinsic time constant of the device and the thermal diffusions of the incident photon energy.
Abstract The transition edge sensor (TES) is known for its superior energy resolution and utilized in diverse physics experiments. TESs with micrometer dimensions have photon-number-resolving capabilities in infrared wavelengths, serving as a key device particularly for non-Gaussian quantum state generation in optical quantum information processing. Although theoretical timing limits for these devices are expected to be sub-nanosecond, such fast responses have remained unobserved with conventional superconducting quantum interference device (SQUID) readouts alone. In this study, we probe the sub-nanosecond timing properties of a micron-scale TES under near-infrared laser irradiation via a proposed parallel SQUID-semiconductor readout scheme. In this scheme, the SQUID performs energy measurement, while the semiconductor readout, which is inductively decoupled from the SQUID, performs timing measurement. We employed a high electron mobility transistor (HEMT) for the timing measurement. Under high-photon-number irradiation that drove the TES into its normal state, we achieved a timing jitter below 200 ps, compared with several nanoseconds for conventional readouts. Note that this value does not represent the single-photon timing jitter since it was obtained under high-photon-number irradiation; single-photon timing measurement remains a key objective for future study. The findings of this study will broaden the future applications of TESs in various fields requiring high timing resolution with energy-resolving capabilities.
Photon-number resolving transition-edge sensors (TESs) with near unity system detection efficiency enable novel approaches to quantum computing, for example, heralding robust Gottesman–Kitaev–Preskill qubit states. Increasing the speed of the detectors increases the rate at which these states can be heralded. In addition, depending on the details of the scheme, faster detectors can reduce the complexities of the hardware implementation. In previous work, we demonstrated that adding a small amount of gold between the tungsten film and silicon substrate can increase thermal conductance and reduce detector recovery time. In that study, the readout electronics imposed limitations on stable biasing conditions of the TES detector, and the TES could only be biased at higher than ideal values. In this report, we demonstrate the operation of the TES illuminated by a heavily attenuated pulsed laser running at 1 MHz repetition rate and examine the limits to adding gold to speed up device recovery times using a higher bandwidth readout system. The best performance was achieved by combining a 15×15μm2 tungsten TES with 5μm3 of gold, which resulted in a recovery time faster than 250 ns, with an energy resolution of 0.25 eV full-width at half maximum at 0.8 eV photon energy.
A transition edge sensor (TES) is one of superconducting photon detectors, which has a photon number resolving ability in light pulses. The TES device is a kind of calorimeters operated at an extremely low temperature, and the energy of the photons is measured as a resistance change in a superconducting transition region of the TES. The advantages of the TESs are an excellent energy resolution and a high quantum efficiency. However a response speed is limited due to slow thermal recovery time. To overcome this, we fabricated new TES devices which are based on a titanium superconductor. The critical temperature of our titanium films is around 410 mK, which greatly improves the thermal recovery time. The observed decay time constant of response signals to the light pulses is around several hundreds of ns, that make it possible to operate the devices at a counting rate over 1 MHz. The photon number resolving power is 0.35 eV(FWHM) for a 5 μm size device even at the high operating temperature. The system quantum efficiency is 65 % by embedding the TES films in an optical structure with a high reflection dielectric mirror and an anti-reflection coatings fabricated by an ion beam assisted sputtering method. These features are very promising for high speed photon number resolving applications in the quantum information field.
Transition edge sensors (TES) have the highest reported efficiencies (>98%) for detection of single photons in the visible and near infrared. Experiments in quantum information and foundations of physics that rely critically on this efficiency have started incorporating these detectors into con- ventional quantum optics setups. However, their range of applicability has been hindered by slow operation both in recovery time and timing jitter. We show here how a conventional tungsten-TES can be operated with jitter times of < 4 ns, well within the timing resolution necessary for MHz clocking of experiments, and providing an important practical simplification for experiments that rely on the simultaneous closing of both efficiency and locality loopholes.
Transition-edge sensors (TESs) are very effective photon-number-resolving (PNR) detectors that have enabled many photonic quantum technologies. However, their relatively slow thermal recovery time severely limits their operation rate in experimental scenarios compared with leading non-PNR detectors. In this work, we develop an algorithmic approach that enables TESs to detect and accurately classify photon pulses without waiting for a full recovery time between detection events. We propose two machine-learning-based signal processing methods: one supervised learning method and one unsupervised clustering method. By benchmarking against data obtained using coherent states and squeezed states, we show that the methods extend the TES operation rate to 800 kHz, achieving at least a four-fold improvement, whilst maintaining accurate photon-number assignment up to at least five photons. Our algorithms will find utility in applications where high rates of PNR detection are required and in technologies that demand fast active feed-forward of PNR detection outcomes.