We present the design and implementation of a mechanical low-pass filter vibration isolation used to reduce the vibrational noise in a cryogen-free dilution refrigerator operated at 10 mK, intended for scanning probe techniques. We discuss the design guidelines necessary to meet the competing requirements of having a low mechanical stiffness in combination with a high thermal conductance. We demonstrate the effectiveness of our approach by measuring the vibrational noise levels of an ultrasoft mechanical resonator positioned above a superconducting quantum interference device. Starting from a cryostat base temperature of 8 mK, the vibration isolation can be cooled to 10.5 mK, with a cooling power of 113 µW at 100 mK. We use the low vibrations and low temperature to demonstrate an effective cantilever temperature of less than 20 mK. This results in a force sensitivity of less than 500 zN/$\sqrt{\mathrm{\text{Hz}}}$ and an integrated frequency noise as low as 0.4 mHz in a 1 Hz measurement bandwidth.

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 are developing large Transition Edge Sensor (TES) arrays in combination with a frequency domain multiplexing readout for the next generation of X-ray space observatories. For operation under an AC-bias, the TESs have to be carefully designed and optimized. In particular, the use of high aspect ratio devices will help us to mitigate non-ideal behavior due to the weak-link effect. In this paper, we present a full characterization of a TES array containing five different device geometries, with aspect ratios (width:length) ranging from 1:2 up to 1:6. The complex impedance of all geometries is measured in different bias configurations to study the evolution of the small-signal limit superconducting transition parameters $\alpha$ and $\beta$ , as well as the excess noise. We show that high aspect ratio devices with properly tuned critical temperatures (around 90 mK) can achieve excellent energy resolution, with an array average of $2.03\pm 0.17$ eV at 5.9 keV and a best achieved resolution of $1.63\pm 0.17$ eV. This demonstrates that AC-biased TESs can achieve a very competitive performance compared to DC-biased TESs. The results have motivated a push to even more extreme device geometries currently in development.

Uniform large transition-edge sensor (TES) arrays are fundamental for the next generation of x-ray space observatories. These arrays are required to achieve an energy resolution ΔE < 3 eV full width at half maximum (FWHM) in the soft x-ray energy range. We are currently developing x-ray microcalorimeter arrays for use in the future laboratory and space-based x-ray astrophysics experiments and ground-based spectrometers. In this contribution, we report on the development and the characterization of a uniform 32 × 32 pixel array with 140 × 30 μm² Ti/Au TESs with the Au x-ray absorber. We report on extensive measurements on 60 pixels in order to show the uniformity of our large TES array. The averaged critical temperature is T_c = 89.5 ± 0.5 mK, and the variation across the array (∼1 cm) is less than 1.5 mK. We found a large region of detector’s bias points between 20% and 40% of the normal-state resistance where the energy resolution is constantly lower than 3 eV. In particular, results show a summed x-ray spectral resolution ΔE_FWHM = 2.50 ± 0.04 eV at a photon energy of 5.9 keV, measured in a single-pixel mode using a frequency domain multiplexing readout system developed at SRON/VTT at bias frequencies ranging from 1 MHz to 5 MHz. Moreover, we compare the logarithmic resistance sensitivity with respect to temperature and current (α and β, respectively) and their correlation with the detector’s noise parameter M, showing a homogeneous behavior for all the measured pixels in the array.

Transition-edge-sensor (TES) microcalorimeters and bolometers are used for a variety of applications. The sensors are based on the steep temperature-dependent resistance of the normal-to-superconducting transition, and are thus intrinsically sensitive to magnetic fields. Conventionally the detectors are shielded from stray magnetic fields using external magnetic shields. However, in particular for applications with strict limits on the available space and mass of an instrument, external magnetic shields might not be enough to obtain the required shielding factors or field homogeneity. Additionally, these shields are only effective for magnetic fields generated external to the TES array, and are ineffective to mitigate the impact of internally generated magnetic fields. Here we present an alternative shielding method based on a superconducting groundplane deposited directly on the backside of the silicon nitride membrane on which the TESs are located. We demonstrate that this local shielding for external magnetic fields has a shielding factor of at the least approximately $80$, and is also effective at reducing internal self-induced magnetic fields, as demonstrated by measurements and simulation of the eddy current losses in our ac-biased detectors. Measurements of 5.9-keV x-ray photons show that our shielded detectors have a high resilience to external magnetic fields, showing no degradation of the energy resolution or shifts of the energy-scale calibration for fields of several microtesla, values higher than expected in typical real-world applications.

Transition-edge sensors (TESs) are the selected technology for future spaceborne x-ray observatories, such as Athena, Lynx, and HUBS. These missions demand thousands of pixels to be operated simultaneously with high energy-resolving power. To reach these demanding requirements, every aspect of the TES design has to be optimized. Here we present the experimental results of tests on different devices where the coupling between the x-ray absorber and the TES is varied. In particular, we look at the effects of the diameter of the coupling stems and the distance between the stems and the TES bilayer. Based on measurements of the ac complex impedance and noise, we observe a reduction in the excess noise as the spacing between the absorber stem and the bilayer is decreased. We identify the origin of this excess noise to be internal thermal fluctuation noise between the absorber stem and the bilayer. In addition, we see an impact of the coupling on the superconducting transition in the appearance of kinks. Our observations show that these unwanted structures in the transition shape can be avoided with careful design of the coupling geometry. The stem diameter appears to have a significant effect on the smoothness of the TES transition. This observation is still poorly understood, but is of great importance for both ac and dc biased TESs.