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We report on the x-ray background rate measured with transition-edge sensors (TES) micro-calorimeters under frequency-domain multiplexing (FDM) readout as a possible technology for future experiments aiming at a direct detection of axion-like particles. Future axion helioscopes will make use of large magnets to convert axions into photons in the keV range and x-ray detectors to observe them. To achieve this, a detector array with high spectral performance and extremely low background is necessary. TES are single-photon, non-dispersive, high-resolution micro-calorimeters and represent a possible candidate for this application. We have been developing x-ray TES micro-calorimeters and an FDM readout technology in the framework of the space-borne x-ray astronomical observatories. We show that the current generation of our detectors is already a promising technology for a possible axion search experiment, having measured an x-ray background rate of 2.2(2) × 10-4 cm-2 s-1 keV-1 with a cryogenic demonstrator not optimized for this specific application. We then make a prospect to further improve the background rate down to the required value (<10-7 cm-2 s-1 keV-1) for an axion-search experiment, identifying no fundamental limits to reach such a level., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

We demonstrate multiplexed readout of 43 transition edge sensor (TES) bolometers operating at 90 mK using a frequency division multiplexing (FDM) readout chain with bias frequencies ranging from 1 to 3.5 MHz and a typical frequency spacing of 32 kHz. We improve the previously reported performance of our FDM system by two important steps. First, we replace the coplanar wires with microstrip wires, which minimize the cross talk from mutual inductance. From the measured electrical cross talk (ECT) map, the ECT of all pixels is carrier leakage dominated. Only five pixels show an ECT level higher than 1%. Second, we reduce the thermal response speed of the TES detectors by a factor of 20 by increasing the heat capacity of the TES, which allows us to bias all TES detectors below 50% in transition without oscillations. We compare the current-voltage curves and noise spectra of the TESs measured in single-pixel mode and multiplexing mode. We also compare the noise equivalent power (NEP) and the saturation power of the bolometers in both modes, where 38 pixels show less than 10% difference in NEP and 5% difference in saturation power when measured in the two different modes. The measured noise spectrum is in good agreement with the simulated noise based on measured parameters from an impedance measurement, confirming that our TES is dominated by phonon noise.

The Transition-Edge Sensor (TES) is an extremely sensitive device, which is used to measure the energy of individual x-ray photons. For astronomical spectrometry applications, SRON develops a frequency domain multiplexing readout system for kilopixel arrays of such TESs. Each TES is voltage biased at a specific frequency in the range of 1-5 MHz. Isolation between the individual pixels is obtained through very narrow-band (high-Q) lithographic LC resonators. To prevent energy resolution degradation due to intermodulation line noise, the bias frequencies are distributed on a regular grid. The requirements on the accuracy of the LC resonance frequency are very high. The deviation of the resonance frequencies due to production tolerances is significant with respect to the bandwidth, and a controller is necessary to compensate for the LC series impedance. We present two such controllers: a simple orthogonal proportional-integral controller and a more complex impedance estimator. Both controllers operate in baseband and try to make the TES current in-phase with the bias voltage, effectively operating as phase-locked loops. They allow off-LC-resonance operation of the TES pixels while preserving the TES thermal response and energy resolution. Extensive experimental results-published in a companion paper recently-with the proposed methods show that these controllers allow the preservation of single pixel energy resolution in multiplexed operation.

In the frequency-domain multiplexing (FDM) scheme, transition-edge sensors (TESs) are individually coupled to superconducting LC filters and AC biased at MHz frequencies through a common readout line. To make efficient use of the available readout bandwidth and to minimize the effect of non-linearities, the LC resonators are usually designed to be on a regular grid. The lithographic processes, however, pose a limit on the accuracy of the effective filter resonance frequencies. Off-resonance bias carriers could be used to suppress the impact of intermodulation distortions, which, nonetheless, would significantly affect the effective bias circuit and the detector spectral performance. In this paper, we present a frequency shift algorithm (FSA) to allow off-resonance readout of TESs, while preserving the on-resonance bias circuit and spectral performance, demonstrating its application to the FDM readout of an x-ray TES microcalorimeter array. We discuss the benefits in terms of mitigation of the impact of intermodulation distortions at the cost of increased bias voltage and the scalability of the algorithm to multi-pixel FDM readout. We show that with FSA, in the multi-pixel and frequencies shifted on-grid, the line noises due to intermodulation distortion are placed away from the sensitive region in the TES response and the x-ray performance is consistent with the single-pixel, on-resonance level.

We have characterized and mapped the electrical cross talk (ECT) of a frequency division multiplexing (FDM) system with a transition edge sensor (TES) bolometer array, which is intended for space applications. By adding a small modulation at 120 Hz to the AC bias voltage of one bolometer and measuring the cross talk response in the current noise spectra of the others simultaneously, we have for the first time mapped the ECT level of 61 pixels with a nominal frequency spacing of 32 kHz in a 61 × 61 matrix and a carrier frequency ranging from 1 MHz to 4 MHz. We find that about 94% of the pixels show an ECT level of less than 0.4%. Only the adjacent pixels reach this level, and the ECT for the rest of the pixels is less than 0.1%. We also observe higher ECT levels, up to 10%, between some of the pixels, which have bundled long, parallel coplanar wires connecting TES bolometers to inductor-capacitor filters. In this case, the high mutual inductances dominate. To mitigate this source of ECT, the coplanar wires should be replaced by microstrip wires in the array. Our study suggests that an FDM system can have a relatively low ECT level, e.g., around 0.4% if the frequency spacing is 30 kHz. Our results successfully demonstrate a low electrical cross talk for a space FDM technology.

Dilution and adiabatic demagnetization refrigerators based on pulse tube cryocoolers are nowadays used in many low temperature physics experiments, such as atomic force and scanning tunneling microscopy, quantum computing, radiation detectors, and many others. A pulse tube refrigerator greatly simplifies the laboratory activities being a cryogen-free system. The major disadvantage of a pulse tube cooler is the high level of mechanical vibrations at the warm and cold interfaces that could substantially affect the performance of very sensitive cryogenic instruments. In this paper, we describe the performance of a very simple mechanical attenuation system used to eliminate the pulse-tube-induced low frequency noise of the superconducting transition-edge sensors under development for the instruments of the next generation of infra-red and X-ray space observatories.

At SRON we are studying the performance of a Goddard Space Flight Center single pixel TES microcalorimeter operated in an AC bias configuration. For x-ray photons at 6 keV the pixel shows an x-ray energy resolution Δ E FWHM =3.7 eV, which is about a factor 2 worse than the energy resolution observed in an identical DC-biased pixel. In order to better understand the reasons for this discrepancy we characterised the detector as a function of temperature, bias working point and applied perpendicular magnetic field. A strong periodic dependency of the detector noise on the TES AC bias voltage is measured. We discuss the results in the framework of the recently observed weak-link behaviour of a TES microcalorimeter.