We compare methods for signal classification applied to voltage traces from transition edge sensors (TES) which are photon-number resolving detectors fundamental for accessing quantum advantages in information processing, communication, and metrology. We quantify the effect of numerical analysis on the distinction of such signals. Furthermore, we explore dimensionality reduction techniques to create interpretable and precise photon-number embeddings. We demonstrate that the preservation of local data structures of some nonlinear methods is an accurate way to achieve unsupervised classification of TES traces. We do so by considering a confidence metric that quantifies the overlap of the photon-number clusters inside a latent space. Furthermore, we demonstrate that for our dataset previous methods such as the signal's area and principal component analysis can resolve up to 16 photons with confidence above 90% whereas nonlinear techniques can resolve up to 21 photons with the same confidence threshold. In addition, we showcase implementations of neural networks to leverage information within local structures, aiming to increase confidence in assigning photon numbers. Finally, we demonstrate the advantage of some nonlinear methods to detect and remove outlier signals.
We compare methods for signal classification applied to voltage traces from transition edge sensors (TES) which are photon-number resolving detectors fundamental for accessing quantum advantages in information processing, communication, and metrology. We quantify the effect of numerical analysis on the distinction of such signals. Furthermore, we explore dimensionality reduction techniques to create interpretable and precise photon-number embeddings. We demonstrate that the preservation of local data structures of some nonlinear methods is an accurate way to achieve unsupervised classification of TES traces. We do so by considering a confidence metric that quantifies the overlap of the photon-number clusters inside a latent space. Furthermore, we demonstrate that for our dataset previous methods such as the signal's area and principal component analysis can resolve up to 16 photons with confidence above 90% whereas nonlinear techniques can resolve up to 21 photons with the same confidence threshold. In addition, we showcase implementations of neural networks to leverage information within local structures, aiming to increase confidence in assigning photon numbers. Finally, we demonstrate the advantage of some nonlinear methods to detect and remove outlier signals.
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 (TES’s) are are extremely sensitive calorimeters able to measure energies of the order of a few electronvolts. They are now well-known in the quantum technology community because of their superb combination of high-efficiency— higher than 95% for photons in the near infrared range [1]—essentially zero dark counts, and photon-number resolution. One of the main challenges when working with TES’s is to extract the photon-number information from the continuous output signal of the detectors. The usual procedure is to accumulate signals over some time—typically ~2 GB per minuite—and then use post-processing techniques to obtain photon-number resolution from the recorded signals [2] Here we introduce an FPGA circuit that analyses TES signals in real-time—recording only specific characteristics such as signal area, height, and length—allowing near realtime photon-number resolution and reducing the memory requirements by orders-of-magnitude. Using this new capability, we are able to optimise the number-resolution of the detector to the range we are interested in for each new experiment. In a preliminary study, we calibrated the TES with a weakly-pulsed 820 nm diode laser, and using just the area data from the FPGA were able to discriminate up to 15 photons. We are able to accurately discriminate an n=2 photon Fock state with parts-per-billion precision, dropping to parts-per-hundred precision at n=15 [3]. It is well known that there are physical limits to the precision with which an image can be formed. There are ways in which this limit can be circumvented, for example using super-resolution techniques that exploit the physical structure of the object, or object illumination with entangled states of light. However, in many applications—for example when the object is very far away—we cannot directly interact with the object, or illuminate it with entangled light: the quantum state of the light field is all that is accessible to the observer. Given a finite size imaging system in the far field—i.e., systems with a finite effective numerical aperture—we show the best way to extract the spatial characteristics of the light source. We implement a general imaging method by measuring the complex degree of coherence using linear optics and our photon-number-resolving detectors. In the absence of collective or entanglement-assisted measurements, our method is optimal over a large range of practically relevant values of the complex degree of coherence [4]. We measure the size and position of a small distant source of pseudo-thermal light, and show that our method outperforms the traditional imaging method by an order of magnitude in precision. Additionally, we show that a lack of photon-number resolution in the detectors has only a modest detrimental effect on measurement precision, further highlighting the practicality of this method as a way to gain significant imaging improvements in a wide range of imaging applications. References [1] A. E. Lita, A. J. Miller, and S. W. Nam, Optics Express 16, 3032 (2008). [2] G. Brida, et al., New Journal of Physics 14, 085001, (2012). [3] L. Assis, et al., preprint (2020) [4] L. A. Howard, et al., Physical Review Letters 123, 143604 (2019).
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.
We report a comprehensive approach to analysing continuous-output photon detectors. We employ principal component analysis to maximize the information extracted from output signals, followed by a novel noise-tolerant parameterized approach to the tomography of photon-number resolving detectors. We further propose a measure for rigorously quantifying a detector's photon-number-resolving capability. Our approach applies to all detectors with continuous-output signals. We illustrate our methods by applying them to experimental data obtained from a transition-edge sensor detector.
Superconducting transition-edge sensors (TES) are extremely sensitive microcalorimeters used as photon detectors with unparalleled energy resolution. They have found application from measuring astronomical spectra through to determining the quantum property of photon-number, n ^ = a ^ † a ^ , for energies from 0.6-2.33eV. However, achieving optimal energy resolution requires considerable data acquisition – on the order of 1GB/min – followed by post-processing, which does not allow access to energy information in real time. Here we use a custom hardware processor to process TES pulses while new detections are still being registered, allowing photon-number to be measured in real time as well as reducing data requirements by orders-of-magnitude. We resolve photon number up to n = 16 – achieving up to parts-per-billion discrimination for low photon numbers on the fly – providing transformational capacity for applications of TES detectors from astronomy through to quantum technology.
Improving photon-number resolution of single-photon sensitive detectors is important for many applications, as is extending the range of such detectors. Here we seek improved resolution for a particular superconducting transition-edge sensor (TES) through better processing of the TES output waveforms. With that aim, two algorithms to extract number resolution from TES output waveforms are compared. The comparison is done by processing waveform data sets from a TES illuminated at nine illumination levels by a pulsed laser at 1550 nm. The algorithms are used to sort the individual output waveforms and then create clusters associated with individual photon numbers. The first uses a dot product with the waveform mean (for each illumination level), while the second uses K-means clustering modified to include knowledge of the Poisson distribution. The first algorithm is shown to distinguish adjacent peaks associated with photon numbers up to 19, whereas the second algorithm distinguishes photon numbers up to 23, using the same data.