Analytical model of the readout power and SQUID hysteresis parameter dependence of the resonator characteristics of microwave SQUID multiplexers

We report on the development of an analytical model describing the readout power and SQUID hysteresis parameter dependence of the resonator characteristics used for frequency encoding in microwave SQUID multiplexers. Within the context of this model, we derived the different dependencies by analyzing the Fourier components of the non-linear response of the non-hysteretic rf-SQUID. We show that our model contains the existing model as a limiting case, leading to identical analytical expressions for small readout powers. Considering the approximations we made, our model is valid for rf-SQUID hysteresis parameters $\beta_{\mathrm{L}} < 0.6$ which fully covers the parameter range of existing multiplexer devices. We conclude our work with an experimental verification of the model. In particular, we demonstrate a very good agreement between measured multiplexer characteristics and predictions based on our model.Comment: This article has been submitted to Superconductor Science and Technolog

Magnetic microcalorimeter with paramagnetic temperature sensors and integrated dc-SQUID readout for high-resolution X-ray emission spectroscopy

We present two variants of a magnetic microcalorimeter with paramagnetic temperature sensors and integrated dc-SQUID readout for high-resolution X-ray emission spectroscopy. Each variant employs two overhanging gold absorbers with a sensitive area of 150$\mu$m x 150$\mu$m and a thickness of 3$\mu$m, thus providing a quantum efficiency of 98% for photons up to 5keV and 50% for photons up to 10keV. The first variant turned out to be fully operational, but, at the same time, to suffer from Joule power dissipation of the Josephson junction shunt resistors, athermal phonon loss, and slew rate limitations of the overall setup. Overall, it only achieved an energy resolution $\Delta E_\mathrm{FWHM} = 8.9eV$. In the second variant, we introduced an innovative `tetrapod absorber geometry' as well as a membrane-technique for protecting the temperature sensors against the power dissipation of the shunt resistors. By this, the second variant achieves an outstanding energy resolution of $\Delta E_\mathrm{FWHM} =1.25(18)eV$ and hence provides, to our knowledge, the present best energy resolving power $E/\Delta E_\mathrm{FWHM}$ among all existing energy-dispersive detectors for soft and tender X-rays.Comment: submitted to Applied Physics Letter

Development and characterisation of high-resolution microcalorimeter detectors for the ECHo-100k experiment

The goal of the ECHo experiment is a direct determination of the absolute scale of the neutrino mass by the analysis of the end-point region of the Ho-163 electron capture (EC) spectrum. The results of the first phase of the experiment, ECHo-1k, have paved the way for the current phase, ECHo-100k, which aims at a sensitivity below 2 eV on the effective electron neutrino mass. In order to reach this goal, a new generation of high-resolution magnetic microcalorimeters with embedded Ho-163 have been developed and characterised. The design has been optimised to meet all the challenging requirements of the ECHo-100k experimental phase, such as excellent energy resolution, wafer scale implantation and multi-chip operation with multiplexing read-out. We present the optimisation studies, the final design of the detector array and the first characterisation studies. The results demonstrate that the detectors fully match and even surpass the requirements for the current experimental phase, ECHo-100k

Measuring Magnetic 1/f Noise in Superconducting Microstructures and the Fluctuation-Dissipation Theorem

The performance of superconducting devices like qubits, SQUIDs, and particle detectors is often limited by finite coherence times and 1/f noise. Various types of slow fluctuators in the Josephson junctions and the passive parts of these superconducting circuits can be the cause, and devices usually suffer from a combination of different noise sources, which are hard to disentangle and therefore hard to eliminate. One contribution is magnetic 1/f noise caused by fluctuating magnetic moments of magnetic impurities or dangling bonds in superconducting inductances, surface oxides, insulating oxide layers, and adsorbates. In an effort to further analyze such sources of noise, we have developed an experimental set-up to measure both the complex impedance of superconducting microstructures, and the overall noise picked up by these structures. This allows for important sanity checks by connecting both quantities via the fluctuation-dissipation theorem. Since these two measurements are sensitive to different types of noise, we are able to identify and quantify individual noise sources. The superconducting inductances under investigation form a Wheatstone-like bridge, read out by two independent cross-correlated dc-SQUID read-out chains. The resulting noise resolution lies beneath the quantum limit of the front-end SQUIDs and lets us measure noise caused by just a few ppm of impurities in close-by materials. We present measurements of the insulating SiO2 layers of our devices, and magnetically doped noble metal layers in the vicinity of the pickup coils at T = 30 mK - 800 mK and f = 1 Hz - 100 kHz.Comment: 13 pages, 5 figure

Flux ramp modulation based MHz frequency-division dc-SQUID multiplexer

We present a MHz frequency-division dc-SQUID multiplexer that is based on flux ramp modulation and a series array of $N$ identical current-sensing dc-SQUIDs with tightly coupled input coil. By running a periodic, sawtooth-shaped current signal through an additional modulation coil being tightly, but non-uniformly coupled to the individual SQUIDs, the voltage drop across the array changes according to the superposition of the flux-to-voltage characteristics of the individual SQUIDs within each cycle of the modulation signal. In this mode of operation, an input signal injected in the input coil of one of the SQUIDs and being quasi-static within a time frame adds a constant flux offset and leads to a phase shift of the associated SQUID characteristics. The latter is inherently proportional to the input signal and can be inferred by channelizing and down-converting the sampled array output voltage. Using a prototype multiplexer as well as a self-developed high-speed readout electronics for real-time phase determination, we demonstrate the simultaneous readout of four signal sources with MHz bandwidth per channel.Comment: The article has been submitted to Applied Physics Letter

Simultaneous MMC readout using a tailored {\mu}MUX based readout system

Magnetic microcalorimeters (MMCs) are cryogenic, energy-dispersive single-particle detectors providing excellent energy resolution, intrinsically fast signal rise time, quantum efficiency close to 100\%, large dynamic range as well as almost ideal linear response. One of the remaining challenges to be overcome to ultimately allow for the utilization of large-scale MMC based detector arrays with thousands to millions of individual pixels is the realization of a SQUID based multiplexing technique particularly tailored for MMC readout. Within this context, we report on the first truly multiplexed readout of an MMC based detector array using a frequency-division multiplexing approach realized by a custom microwave SQUID multiplexer based readout system.Comment: Conference: ASC2022 (accepted for publication in IEEE Transactions on Applied Superconductivity

DELight: a Direct search Experiment for Light dark matter with superfluid helium

To reach ultra-low detection thresholds necessary to probe unprecedentedly low Dark Matter masses, target material alternatives and novel detector designs are essential. One such target material is superfluid $^4$He which has the potential to probe so far uncharted light Dark Matter parameter space at sub-GeV masses. The new ``Direct search Experiment for Light dark matter'', DELight, will be using superfluid helium as active target, instrumented with magnetic micro-calorimeters. It is being designed to reach sensitivity to masses well below 100\,MeV in Dark Matter-nucleus scattering interactions.Comment: IDM2022 proceedings submitted to SciPos