The state-of-the-art technology of X-ray microcalorimeters based on superconducting transition-edge sensors (TESs), for applications in astrophysics and particle physics, is reviewed. We will show the advance in understanding the detector physics and describe the recent breakthroughs in the TES design that are opening the way towards the fabrication and the read-out of very large arrays of pixels with unprecedented energy resolution. The most challenging low temperature instruments for space- and ground-base experiments will be described.

We present the performances and the strain sensitivity of the first spherical gravitational wave detector equipped with a capacitive transducer and readout by a low noise two-stage SQUID amplifier and operated at a temperature of 5 K. We characterized the detector performance in terms of thermal and electrical noise in the system output signal. We measured a peak strain sensitivity of $1.5\times {10}^{-20}{\mathrm{Hz}}^{-1/2}$ at 2942.9 Hz. A strain sensitivity of better than $5\times {10}^{-20}{\mathrm{Hz}}^{-1/2}$ has been obtained over a bandwidth of 30 Hz. We expect an improvement of more than 1 order of magnitude when the detector will operate at 50 mK. Our results represent the first step towards the development of an ultracryogenic omnidirectional detector sensitive to gravitational radiation in the 3 kHz range.

We report on the development and demonstration of MHz frequency domain multiplexing (FDM) technology to readout arrays of cryogenic transition edge sensor (TES) x-ray microcalorimeters. In our FDM scheme, TESs are AC biased at different resonant frequencies in the low MHz range through an array of high-Q LC resonators. The current signals of all TESs are summed at superconducting quantum interference devices (SQUIDs). We have demonstrated multiplexing for a readout of 31 pixels using room temperature electronics, high-Q LC filters, and TES arrays developed at SRON, and SQUID arrays from VTT. We repeated this on a second setup with 37 pixels. The summed x-ray spectral resolutions $@$ 5.9 keV are $\Delta E_{31\text{pix}\hspace{0.17em}\text{MUX}}=2.14\hspace{0.17em}\pm \hspace{0.17em}0.03$ eV and $\Delta E_{37\text{pix}\hspace{0.17em}\text{MUX}}=2.23\hspace{0.17em}\pm \hspace{0.17em}0.03$ eV. The demonstrated results are comparable with other multiplexing approaches. There is potential to further improve the spectral resolution, to increase the number of multiplexed TESs, and to open up applications for TES x-ray microcalorimeters.

We report very-low-noise, fast-response, middle-scale multiplexing in a microwave superconducting quantum interference device multiplexer (MW-Mux) as a transition-edge sensor (TES) readout. Our MW-Mux is able to read 40 channels with 500 kHz sampling and has a low readout noise of $0.9\hspace{0.17em}\mu {\Phi }_0/\sqrt{\text{Hz}}$ (where ${\Phi }_0$ is the magnetic flux quantum), equivalent to $9\hspace{0.17em}\text{pA}/\sqrt{\text{Hz}}$ . By contrast, a multiplexer of less than 10 pixels with 500 kHz sampling and $\sim 2\hspace{0.17em}\mu {\Phi }_0/\sqrt{\text{Hz}}$ readout noise has so far been reported in the literature. Owing to the 500 kHz sampling, our MW-Mux exhibits a fast response to detect a TES pulse with a rise time around $12\hspace{0.17em}\mu \mathrm{s}$ . We demonstrated simultaneous readout of 38 pixels from an array of x-ray TES microcalorimeters. The measured full-width values at half-maximum spectral resolution ranged from 2.79 to 4.56 eV, with a median value of 3.30 eV at 5.9 keV, including a $\sim 10\%$ contribution of readout noise, i.e., 0.9–1.7 eV.

We present a detailed analysis of the fundamental noise sources in superconducting transition-edge sensors (TESs), ac voltage biased at MHz frequencies and treated as superconducting weak links. We have studied the noise in the resistive transition as a function of bath temperature of several detectors with different normal resistances and geometries. We show that the “excess” noise, typically observed in the TES electrical bandwidth, can be explained by the equilibrium Johnson noise of the quasiparticles generated within the weak link. The fluctuations at the Josephson frequency and higher harmonics contribute significantly to the measured voltage noise at the detector bandwidth through the nonlinear response of the weak link with a sinusoidal current-phase relation.

We report the results of a detailed numerical analysis of a real resonant spherical gravitational wave antenna operating with six resonant two-mode capacitive transducers read out by superconducting quantum interference devices (SQUID) amplifiers. We derive a set of equations to describe the electromechanical dynamics of the detector. The model takes into account the effect of all the noise sources present in each transducer chain: the thermal noise associated with the mechanical resonators, the thermal noise from the superconducting impedance matching transformer, the backaction noise, and the additive current noise of the SQUID amplifier. Asymmetries in the detector signal-to-noise ratio and bandwidth, coming from considering the transducers not as pointlike objects but as a sensor with physically defined geometry and dimension, are also investigated. We calculate the sensitivity for an ultracryogenic, 30 ton, 2 m in diameter, spherical detector with optimal and nonoptimal impedance matching of the electrical readout scheme to the mechanical modes. The results of the analysis are useful not only to optimize existing smaller mass spherical detector like MiniGrail, in Leiden, but also as a technological guideline for future massive detectors. Furthermore we calculate the antenna patterns when the sphere operates with one, three, and six transducers. The sky coverage for two detectors based in The Netherlands and Brazil and operating in coincidence is also estimated. Finally, we describe and numerically verify a calibration and filtering procedure useful for diagnostic and detection purposes in analogy with existing resonant bar detectors.