Daniel S. Swetz

We present a new instrument for soft x-ray absorption and emission spectroscopy based on the latest generation of transition edge sensor array optimized for soft x-ray detection, built on microwave superconducting quantum interference device multiplexing readout, and cooled with a dilution refrigerator. Its extreme collecting efficiency enables spectroscopy measurements on dilute systems. It also enables shorter acquisition time and large energy-range spectra. We describe the design and operation of the spectrometer and characterize its performance in terms of energy resolution, photon collecting efficiency, and stability. A resolution of 0.7–1.8 eV in the energy range 260–900 eV with a high detection rate of up to 10 000 photons per second across the array is achieved with minimal performance degradation. In addition, the use of the dilution refrigerator to cool the detector results in a robust and stable energy calibration over time. The spectrometer is attached to a dedicated ultra-high vacuum sample chamber equipped with a fully motorized sample cryostat for experiments at temperatures between 10 and 300 K, multi-sample mounting, and electric field-gated devices. The spectrometer-sample chamber is installed at a beamline providing full polarization control. We demonstrate the capabilities of the setup using two representative examples of XES on extremely low-concentration systems, namely monolayer hexagonal boron nitride and the K3[Fe(CN)6] molecular system at sub-millimolar concentration.

We present measurements of the Kα_{1} and Kα_{2} natural x-ray linewidths of uranium, neptunium, and plutonium (Z=92, 93, 94) obtained using a superconducting transition-edge sensor microcalorimeter array. The relative uncertainties range from 0.5% to 1.5%, improving upon previous values by factors ranging from 3 to 8. These refined linewidths reduce systematic errors in gamma-ray spectroscopy assays of Pu-bearing materials, where Kα x-rays overlap with diagnostic gamma lines. We also present multiconfiguration Dirac-Fock calculations of the Kα linewidths for U, Np, and Pu, providing a benchmark for theory and experiment. These calculations reveal a discrepancy between ab initio theory and experiment possible to observe only with the improved experimental accuracy achieved in this work.

Hybrid photon counting detectors (HPCDs) have unlocked new capabilities for X-ray-based measurements at synchrotrons around the world in the last 30 years. By leveraging independently optimized sensor and readout layers, they offer high quantum efficiency (>80 %), ultra-low dark counts, sub-pixel point-spread function, and high count rates (>106 counts per pixel per second). Furthermore, their small pixel size and large active area endow them with excellent coverage and resolution for both real-space and reciprocal space imaging. Here, we demonstrate that HPCDs are also well-suited for laboratory-based nanoscale X-ray tomography (nano-xCT). We perform nano-xCT on an integrated circuit fabricated at the 130-nm node and produce a 3D reconstruction with over 40 times more photons collected more than 20 times faster than in this group’s previous work, for an overall speedup of over 800×. We review the technical considerations of using an HPCD for tabletop tomography. We quantify our reconstruction image quality using well-established metrics, including the modulation transfer function (MTF), Fourier shell correlation (FSC), and contrast-to-noise (CNR), to validate our choice of experimental parameters that provide sufficient resolution and imaging speed. We determine that under current experimental conditions, 160-nm wiring features are reconstructed at 75–80 nm spatial resolution.

We formulate an energy resolution model for optical transition-edge sensors which combines aspects of existing models with the goal of better defining and constraining energy resolution optimization. The combined model is found to be in better agreement with experimental data, while also allowing for theoretical exploration of phonon trapping for energy resolution enhancement. Additionally, we present preliminary data from our recent low critical temperature ($T_\textrm {c}$ = 50 mK to 100 mK) tungsten Transition Edge Sensors (TESs) for the optical to Near Infra-Red (NIR) regime. Our tungsten TES detectors are shown to exhibit curious ‘inverse’ proximity effects compared to what is generally reported in the literature. A variety of wiring scheme test structures are analyzed under varying magnetic field shielding conditions in an effort to mitigate and characterize these spurious effects on the device $T_\textrm {c}$. We develop an electron beam lithography fabrication method in order to reduce the edge roughness of our tungsten TES devices, and demonstrate a more uniform $T_\textrm {c}$ across various TES sizes when these e-beam lithography devices are measured within superconducting magnetic shielding.

Muon catalyzed fusion (μCF) is a plasma-free process in which the formation of muonic hydrogen molecules precedes and enables fusion between their constituent nuclei. Despite decades of study, the reaction dynamics of μCF remain elusive. Recent theories predict that resonance states of the muonic molecules play a key role and that these states can be probed using x-ray techniques. Using an array of transition-edge sensor microcalorimeters with 10-fold improved energy resolution compared to conventional silicon detectors, we observed x-rays from resonance states of muonic deuterium molecules despite an intense background. The spectrum is well explained by high-precision calculations incorporating the vibrational states. This work identifies the long-overlooked resonance state pathway as crucial in μCF and provides the direct evidence of the efficient muonic molecular formation.

A bstract: We present a comprehensive phenomenological analysis of the calorimetric electron capture (EC) decay spectrum of ¹⁶³ Ho as measured by the HOLMES experiment. Using high-statistics data, we unfold the instrumental energy resolution from the measured spectrum and model it as a sum of Breit-Wigner resonances and shake-off continua, providing a complete set of parameters for each component. Our approach enables the identification and tentative interpretation of all observed spectral features, including weak and overlapping structures, in terms of atomic de-excitation processes. We compare our phenomenological model with recent ab initio theoretical calculations, finding good agreement for both the main peaks and the spectral tails, despite the limitations of current theoretical and experimental precision. The model delivers an accurate description of the endpoint region, which is crucial for neutrino mass determination, and allows for a realistic treatment of backgrounds such as pile-up and tails of low-energy components. Furthermore, our decomposition facilitates the generation of Monte Carlo toy spectra for sensitivity studies and provides a framework for investigating systematic uncertainties related to solid-state and detector effects. This work establishes a robust foundation for future calorimetric neutrino mass experiments employing ¹⁶³ Ho, supporting both data analysis and experimental design.

It is often desirable to steer light within a cryostat and have a well focussed laser spot incident upon a detector. We demonstrate the operation of superconducting transitionedge sensor microcalorimeters with a fibre-coupled laser scanning device co-located on the 20mK mixing plate of a dilution refrigerator. The scanner directs a 515nm laser beam with spot size $< 40\mu$m over a range of $\pm$ 14mm in two orthogonal axes (covering 784mm${}^{2}$). We present the optical elements of the system, show that the detector noise spectrum is unchanged when the scanner is operating or off, and observe less than 340 nW power dissipation in our use-case. This device will allow detector calibration up to 10 keV on a pixel-by-pixel basis with simultaneous X-ray measurements. Further, this device will enable more effective characterisation of certain detector artifacts including cross-talk, position dependences, and drift corrections.

Hybrid photon counting detectors (HPCDs) have unlocked new capabilities for x-ray-based measurements at synchrotrons around the world in the last 30 years. By leveraging independently optimized sensor and readout layers, they offer high quantum efficiency ($> 80 \%$), ultra-low dark counts, sub-pixel point-spread function, and high count rates ($> 10^{6}$ counts per pixel per second). Furthermore, their small pixel size and large active area endow them with excellent coverage and resolution for both real-space and reciprocal space imaging. Here, we demonstrate that HPCDs are also well-suited for laboratory-based nanoscale x-ray tomography (nano-xCT). We perform nano-xCT on an integrated circuit fabricated at the 130-nm node and produce a 3D reconstruction with 40 times more photons collected 20 times faster than in this group's previous work, for an overall speedup of 800$\times$. We review the technical considerations of using an HPCD for tabletop tomography. We quantify our reconstruction image quality using well-established metrics, including the modulation transfer function (MTF), Fourier shell correlation (FSC), and contrast-to-noise (CNR), to validate our choice of experimental parameters that provide sufficient resolution and imaging speed. Using these metrics, we determine that even under current experimental conditions, 160 nm wiring features are reconstructed at 75-80 nm spatial resolution.