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Metallic magnetic calorimeters (MMCs) are calorimetric low-temperature particle detectors that are currently strongly advancing the state of the art in energy-dispersive single particle detection. They are typically operated at temperatures below 100 mK and make use of a metallic, paramagnetic temperature sensor to transduce the temperature rise of the detector upon the absorption of an energetic particle into a change of magnetic flux which is sensed by a superconducting quantum interference device. This outstanding interplay between a high-sensitivity thermometer and a near quantum-limited amplifier results in a very fast signal rise time, an excellent energy resolution, a large dynamic range, a quantum efficiency close to 100% as well as an almost ideal linear detector response. For this reason, a growing number of groups located all over the world is developing MMC arrays of various sizes which are routinely used in a variety of applications. Within this paper, we briefly review the state of the art of metallic magnetic calorimeters. This includes a discussion of the detection principle, sensor materials and detector geometries, readout concepts, the structure of modern detectors as well as the state-of-the-art detector performance.

The quasiparticle propagation away from the track of a highly ionizing particle in superfluid helium at low temperatures has previously been shown to exhibit anisotropy. We discuss the mechanism responsible for this behavior and show that it occurs for nuclear scattering by dark matter for recoil energies down to a few keV, and perhaps lower. This directionality makes it possible to search for and distinguish galactic dark matter with interaction cross sections that reach into the neutrino fog where coherent neutrino-nucleus scattering presents an irreducible background.

Due to the periodic characteristics of SQUIDs, a suitable linearization technique is required for SQUID-based readout. Flux-ramp modulation is a common linearization technique and is typically applied for the readout of a microwave SQUID multiplexer as well as since recently also for dc-SQUIDs. Flux-ramp modulation requires another stage in the signal processing chain to demodulate the SQUID output signal before further processing. For cryogenic microcalorimeters, the signal contains events that are given by a fast exponentially rising and slowly exponentially decaying pulses shape. The events shall be detected by a trigger engine and recorded by a storage logic. Since the data rate can be decreased significantly by demodulation and event detection, it is desirable to do both steps on the deployed fast FPGA logic during measurement before passing the data to a general-purpose processor. In this contribution, we show the implementation of efficient multi-channel flux-ramp demodulation computed at run-time on a SoC-FPGA. Furthermore, a concept and implementation for an online trigger and buffer mechanism with its theoretical trigger loss rates depending on buffer size is presented. Both FPGA modules can be operated with up to 500 MHz clock frequency and can efficiently process 32 channels. Correct functionality and data reduction capability of the modules are demonstrated in measurements utilizing magnetic microcalorimeter irradiated with an Iron-55 source for event generation and read out by a microwave SQUID multiplexer.

The rapid development of low temperature thermal detectors since the early 1980s has resulted in remarkable improvements in the sensitivity and precision of many types of measurements. We will discuss the operating principles of these detectors in the most general possible terms. We will try to show how the physics of some popular thermometer systems introduces performance limits, and how the different figures of merit and optimizations that result affect various applications.

To our present best knowledge, microwave SQUID multiplexing ( μ MUXing) is the most suitable technique for reading out large-scale low-temperature microcalorimeter arrays that consist of hundreds or thousands of individual pixels which require a large readout bandwidth per pixel. For this reason, the present readout strategy for metallic magnetic calorimeter (MMC) arrays combining an intrinsic fast signal rise time, an excellent energy resolution, a large energy dynamic range, a quantum efficiency close to 100 % as well as a highly linear detector response is based on μ MUXing. Within this paper, we summarize the state of the art in MMC μ MUXing and discuss the most recent results. This particularly includes the discussion of the performance of a 64-pixel detector array with integrated, on-chip microwave SQUID multiplexer, the progress in flux ramp modulation of MMCs as well as the status of the development of a software-defined radio-based room-temperature electronics which is specifically optimized for MMC readout.

The determination of the absolute scale of the neutrino masses is one of the most challenging present questions in particle physics. The most stringent limit, \\(m(\\bar{\\nu }_{\\mathrm {e}})< 2\\) eV, was achieved for the electron anti-neutrino mass. Different approaches are followed to reach a sensitivity on neutrino masses in the sub-eV range. Among them, experiments exploring the beta decay or electron capture of suitable nuclides can provide information on the electron neutrino mass value. We present the electron capture \\(163}\\) Ho experiment ECHo, which aims to investigate the electron neutrino mass in the sub-eV range by means of the analysis of the calorimetrically measured energy spectrum following electron capture in \\(163}\\) Ho. A high precision and high statistics spectrum will be measured with arrays of metallic magnetic calorimeters. We discuss some of the essential aspects of ECHo to reach the proposed sensitivity: detector optimization and performance, multiplexed readout, \\(163}\\) Ho source production and purification, as well as a precise theoretical and experimental parameterization of the calorimetric EC spectrum including in particular the value of \\(Q_{\\mathrm {EC}}\\) . We present preliminary results obtained with a first prototype of single channel detectors as well as a first 64-pixel chip with integrated micro-wave SQUID multiplexer, which will already allow to investigate \\(m(\\nu _{\\mathrm {e}})\\) in the eV range.

The options for primary thermometry at ultra-low temperatures are rather limited. In practice, most laboratories are using 195Pt NMR thermometers in the microkelvin range. In recent years, current sensing direct current superconducting quantum interference devices (DC-SQUIDs) have enabled the use of noise thermometry in this temperature range. Such devices have also demonstrated the potential for primary thermometry. One major advantage of noise thermometry is the fact that no driving current is needed to operate the device and thus the heat dissipation within the thermometer can be reduced to a minimum. Ultimately, the intrinsic power dissipation is given by the negligible back action of the readout SQUID. For thermometry in low-temperature experiments, current noise thermometers and magnetic flux fluctuation thermometers have proved to be most suitable. To make use of such thermometers at ultra-low temperatures, we have developed a cross-correlation technique that reduces the amplifier noise contribution to a negligible value. For this, the magnetic flux fluctuations caused by the Brownian motion of the electrons in our noise source are measured inductively by two DC-SQUID magnetometers simultaneously and the signals from these two channels are cross-correlated. Experimentally, we have characterized a thermometer made of a cold-worked high-purity copper cylinder with a diameter of 5 mm and a length of 20 mm for temperatures between 42 μK and 0.8 K. For a given temperature, a measuring time below 1 min is sufficient to reach a precision of better than 1%. The extremely low power dissipation in the thermometer allows continuous operation without heating effects.

The determination of the effective electron neutrino mass via kinematic analysis of beta and electron capture spectra is considered to be model-independent since it relies on energy and momentum conservation. At the same time the precise description of the expected spectrum goes beyond the simple phase space term. In particular for electron capture processes, many-body electron-electron interactions lead to additional structures besides the main resonances in calorimetrically measured spectra. A precise description of the 163Ho spectrum is fundamental for understanding the impact of low intensity structures at the endpoint region where a finite neutrino mass affects the shape most strongly. We present a low-background and high-energy resolution measurement of the 163Ho spectrum obtained in the framework of the ECHo experiment. We study the line shape of the main resonances and multiplets with intensities spanning three orders of magnitude. We discuss the need to introduce an asymmetric line shape contribution due to Auger–Meitner decay of states above the auto-ionisation threshold. With this we determine an enhancement of count rate at the endpoint region of about a factor of 2, which in turn leads to an equal reduction in the required exposure of the experiment to achieve a given sensitivity on the effective electron neutrino mass.

Due to their excellent energy resolution, the intrinsically fast signal rise time, the huge energy dynamic range, and the almost ideally linear detector response, metallic magnetic calorimeters (MMC)s are very well suited for a variety of applications in physics. In particular, the ECHo experiment aims to utilize large-scale MMC-based detector arrays to investigate the mass of the electron neutrino. Reading out such arrays is a challenging task which can be tackled using microwave SQUID multiplexing. Here, the detector signals are transduced into frequency shifts of superconducting microwave resonators, which can be deduced using a high-end software-defined radio (SDR) system. The ECHo SDR system is a custom-made modular electronics, which provides 400 channels equally distributed in a 4 to 8 GHz frequency band. The system consists of a superheterodyne RF frequency converter with two successive mixers, a modular conversion, and an FPGA board. For channelization, a novel heterogeneous approach, utilizing the integrated digital down conversion (DDC) of the ADC, a polyphase channelizer, and another DDC for demodulation, is proposed. This approach has excellent channelization properties while being resource-efficient at the same time. After signal demodulation, on-FPGA flux-ramp demodulation processes the signals before streaming it to the data processing and storage backend.

The ECHo experiment aims at determining the effective electron neutrino mass by analyzing the endpoint of the 163 Ho electron capture spectrum. High energy resolution detectors with a well-tailored detector response are the essential ingredient for the success of the ECHo experiment. Metallic magnetic calorimeter arrays enclosing 163 Ho have been chosen for the ECHo experiment. The first MMC array, ECHo-1k, showed excellent performances with an average energy resolution of 5.5 eV FWHM @ 5.9 keV. Based on the results obtained with the ECHo-1k array, optimization studies have paved the way towards a new detector design for the next experimental phase, ECHo-100k. The ECHo-100k chip features an optimized single pixel design to improve the detector performance as well as an upgraded on-chip thermalization layout. The newly fabricated ECHo-100k detectors have been fully characterized at room temperature, at 4 K and at millikelvin temperature. The obtained results show that the ECHo-100k array achieved the expected performance with an average energy resolution of 3.5 eV FWHM @ 5.9 keV, fulfilling the requirements for the ECHo-100k experimental phase.