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The Beryllium Electron capture in Superconducting Tunnel junctions (BeEST) experiment searches for evidence of heavy neutrino mass eigenstates in the nuclear electron capture decay of $^7$Be by precisely measuring the recoil energy of the $^7$Li daughter. In Phase-III, the BeEST experiment has been scaled from a single superconducting tunnel junction (STJ) sensor to a 36-pixel array to increase sensitivity and mitigate gamma-induced backgrounds. Phase-III also uses a new continuous data acquisition system that greatly increases the flexibility for signal processing and data cleaning. We have developed procedures for signal processing and spectral fitting that are sufficiently robust to be automated for large data sets. This article presents the optimized procedures before unblinding the majority of the Phase-III data set to search for physics beyond the standard model.

Despite their high relative abundance in our Universe, neutrinos are the least understood fundamental particles of nature. They also provide a unique system to study quantum coherence and the wavelike nature of particles in fundamental systems due to their extremely weak interaction probabilities. In fact, the quantum properties of neutrinos emitted in experimentally relevant sources are virtually unknown and the spatial extent of the neutrino wavepacket is only loosely constrained by reactor neutrino oscillation data with a spread of 13 orders of magnitude. Here, we present the first direct limits of this quantity through a new experimental concept to extract the energy width, $\sigma_{\textrm{N},E}$, of the recoil daughter nucleus emitted in the nuclear electron capture (EC) decay of $^7$Be. The final state in the EC decay process contains a recoiling $^7$Li nucleus and an electron neutrino ($\nu_e$) which are entangled at their creation. The $^7$Li energy spectrum is measured to high precision by directly embedding $^7$Be radioisotopes into a high resolution superconducting tunnel junction that is operated as a cryogenic sensor. The lower limit on the spatial uncertainty of the recoil daughter was found to be $\sigma_{\textrm{N}, x} \geq 6.2$\,pm, which implies the final-state system is localized at a scale more than a thousand times larger than the nucleus itself. From this measurement, the first direct lower limits on the spatial extent of the neutrino wavepacket were extracted using two different theoretical methods. These results have wide-reaching implications in several areas including the nature of spatial localization at sub-atomic scales, interpretation of neutrino physics data, and the potential reach of future large-scale experiments., Comment: 20 pages, 3 figures, v3 corrects and updates one of the wavepacket width calculations

We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency Superconducting Quantum Interference Devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the $N\times N \times 2$ overlapping metamaterial array, where we develop an understanding of the many ($8N^2-8N+3$) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10-30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.

The atomic exchange effect will lead to a significant increase in the probability density of $\beta$ decays below a few keV. This effect is very important for scientific experiments that performed by low-energy electron spectroscopy measurements. However, the atomic exchange effect involves multi-electron interactions, especially for a system with 82 electrons such as lead. Different parameters will lead to different trends in the energy spectrum predicted by the theory, so it is urgent to carry out experimental measurements to provide parameter limits for the theory. The probability increase brought about by the atomic exchange effect is most obvious near 0keV, and the $\beta$ energy spectrum is accurately measured near this energy point, so as to provide constraints for the physical model of atomic exchange. However, it is extremely difficult to measure the $\beta$ energy spectrum at 0keV due to the limitations of electronic noise and internal conversion effects. The excited decay path of $^{210}$Pb was taken as the observation object,by measuring the total energy spectrum of $\beta$ rays and cascaded gamma rays, the precise measurement of the $\beta$ energy spectrum near 0keV has been completed. The analysis of the $\beta$ energy spectrum of $^{210}$Pb gives the following conclusions. The experimental results first verified the theory that the exchange effect causes the probability increase at the low energy end near 0keV. At the same time, the experimental results are higher than the existing predictions of the atomic exchange effect. At least for Pb element, all the electron shells have played a role in improving the probability density of the low end of the $\beta$ energy spectrum. This discovery will promote the theoretical calculation of the $\beta$ energy spectrum of $^{214}$Pb, at the same time, it also indicates that the reactor neutrinos have a higher probability density at the omnipotent end.

The Transition Edge Sensor is extremely sensitive to the change of temperature, combined with the high-Z metal of a certain thickness, it can realize the high energy resolution measurement of particles such as X-rays. X-rays with energies below 10 keV have very weak penetrating ability, so only a few microns thick of gold or bismuth can obtain quantum efficiency higher than 70\%. Therefore, the entire structure of the TES X-ray detector in this energy range can be realized in the microfabrication process. However, for X-rays or gamma rays from 10 keV to 200 keV, sub-millimeter absorber layers are required, which cannot be realized by microfabrication process. This paper first briefly introduces a set of TES X-ray detectors and their auxiliary systems built by ShanghaiTech University, then focus on the introduction of the TES $\gamma$-ray detector, with absorber based on an sub-millimeter lead-tin alloy sphere. The detector has a quantum efficiency above 70\% near 100 keV, and an energy resolution of about 161.5eV@59.5keV., Comment: 13 pages, 12 figures