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arXiv:2411.15360 · Optica Quantum

Boosting photon-number-resolved detection rates of transition-edge sensors by machine learning

Zhenghao Li, Matthew J. H. Kendall, Gerard J. Machado, Ruidi Zhu, Ewan Mer, Hao Zhan, Aonan Zhang, Shang Yu, Ian A. Walmsley, Raj B. Patel

Published May 13, 2025• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1364/opticaq.555325

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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.
Transition-edge sensors (TESs) are very versatile superconducting devices used to detect radiation from gamma-rays to visible and submillimeter. The intrinsic capability to measure the energy of the absorbed photons with very high energy resolution and the related possibility to resolve the number of incident photons distinguish photon-number resolving (PNR) devices from any other photon detectors. PNR detectors are fundamental for the measurement of the photon-number distribution of singlephoton emitters and for the progress of quantum information technology and quantum metrology. By reducing the active area of TESs for visible-NIR light from typical values of 10-10m2toward 10-12m2and by increasing the TES operating temperature, we should be able to combine the high energy resolution permitted by very low heat capacity with fast response time. To support the future design and development of this new type of detector, in this work we compare experimental data with circuit simulation results based on the two-fluid theory.
Light sources for applications in quantum information, quantum-enhanced sensing and quantum metrology are attracting increasing scientific interest. To gain inside into the underlying physical processes of quantum light generation, efficient photon detectors and experimental techniques are required to access the photon statistics. In this work, we employ photon-number-resolving (PNR) detectors based on superconducting transition-edge sensors (TESs) for the metrology of photonic microstructures with semiconductor quantum dots (QDs) as emitters. For the PNR analysis, we developed a state of the art PNR detection system based on fiber-coupled superconducting TESs. Our stand-alone system comprises six tungsten TESs, read out by six 2-stage-SQUID current sensors, and operated in a compact detector unit integrated into an adiabatic demagnetization refrigerator. This PNR detection system enables us to directly access the photon statistics of the light field emitted by our photonic microstructures. In this contribution, we focus on the PNR study of deterministically fabricated quantum light sources emitting single indistinguishable photons as well as twin-photon states. Additionally, we present a PNR-analysis of electrically pumped QD micropillar lasers exhibiting a peculiar bimodal behavior. Employing TESs our work provides direct insight into the complex emission characteristics of QD- based light sources. We anticipate, that TES-based PNR detectors, will be a viable tool for implementations of photonic quantum information processing relying on multi-photon states.
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.
Transition-edge sensors (TESs) are photon-number resolving calorimetric spectrometers with near unit efficiency. Their recovery time, which is on the order of microseconds, limits the number resolving ability and timing accuracy in high photon-flux conditions. This is usually addressed by pulsing the light source or discarding overlapping signals, thereby limiting its applicability. We present an approach to assign detection times to overlapping detection events in the regime of low signal-to-noise ratio, as in the case of TES detection of near-infrared radiation. We use a two-level discriminator, inherently robust against noise, to coarsely locate pulses in time and timestamp individual photoevents by fitting to a heuristic model. As an example, we measure the second-order time correlation of a coherent source in a single spatial mode using a single TES detector.
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.