High-bandwidth frequency domain multiplexed readout of transition-edge sensors for neutrinoless double beta decay searches

TL;DR

This paper presents a high-bandwidth, frequency-domain multiplexing (fMUX) readout for transition-edge sensors (TES) aimed at next-generation cryogenic calorimeters in neutrinoless double beta decay searches (e.g., CUPID). The system uses 10 TES channels in MHz-range LC resonators biased by a carrier-tone comb, with the summed current read by a SQUID and digitally demodulated with Digital Active Nulling (DAN) on an FPGA-based ICEboard, achieving $156 kHz$ sampling. Key results include the observation of all 10 resonances with an average frequency shift of about $4.5%$ due to parasitics, cross-talk within design limits ($XT_{lc}≤0.4-0.6%$), readout noise of $20-50 pA/√Hz$, and a DAN bandwidth of about $3 kHz$ with a $120 μs$ risetime, demonstrated using a dummy payload and a small TES array. The significance lies in validating a scalable, low-thermal-load readout pathway capable of supporting thousands of TES channels for tonne-scale experiments, while outlining remaining challenges in parasitics, data offload, and further optimization to reach full scalability.

Abstract

The next-generation of cryogenic neutrinoless double-beta decay experiments require increasingly fast readout in order to improve background discrimination. These experiments, operated as cryogenic calorimeters at $\sim$10 mK, are usually read out by high-impedance neutron transmutation doped (NTD) thermistors, which provide good energy resolution, but are limited by $\sim$1 ms response times. Superconducting detectors, such as transition-edge sensors (TESs) with a time resolution of $\sim$100 $μ$s, offer superior timing performance over NTD semiconductor bolometers. To make this technology viable for an application to a thousand or more channels, multiplexed readout is necessary in order to minimize the thermal load and radioactive contamination induced by the readout. Frequency-domain multiplexing readout (fMux) for TESs, previously developed at Berkeley Lab and McGill University, is currently in use for mm-wave telescopes with detector sampling rates in the order of 100 Hz. We demonstrate a new readout system, based on the McGill/Berkeley digital fMux readout, to satisfy the higher bandwidth and noise requirements of the next generation of TES-instrumented cryogenic calorimeters. The new readout samples detectors at 156 kHz, three orders of magnitude faster than its cosmology-oriented predecessor. Each multiplexing readout module comprises ten superconducting resonators in the MHz range and a superconducting quantum interference device (SQUID), interfaced to high-bandwidth field programmable gate array (FPGA)-based electronics for digital signal processing and low-latency feedback.

Figures (8)

• Figure 1: Simplified circuit schematic of a single module of the fMUX TES readout. The colours indicate the components installed at different temperatures inside and outside the cryostat. The FPGA-based ICEboard sits at room temperature with the carrier and nuller DACs, the demod ADC, and the SQUID controller circuitry. The still stage at $\sim$700 mK hosts the LC resonator board and the SQUID, while the TESs are located at the mixing chamber stage at around 12 mK. The TESs are voltage biased with carrier tones and their respective currents summed up at the SQUID summing junction. When the digital active nulling (DAN) is active, these currents flow predominantly through the nuller line instead of the SQUID input coil, keeping the SQUID in the linear operating regime. Figure from Adamic:noise.
• Figure 2: Cryogenic resonator board with the LC resonator chip in the center and the NIST SA13 SQUID at the bottom, together with the snubber (R1) and bias (R3) chip resistors. The board is placed in an aluminum box at the still stage at $\sim$700 mK inside the cryostat.
• Figure 3: McGill's ICEboard warm readout electronics. The blue motherboard hosts the FPGA for digital processing, while the red mezzanine cards contain the ADCs and DACs. The DB-37 cable at the bottom connects to the SQUID Controller Board (not shown here), while the Ethernet cable at the top interfaces with the host PC. The board supports the readout of up to 8 fMUX modules, although we only use one in this work.
• Figure 4: Core architecture of the high-bandwidth, 10-channel fMUX firmware module for CUPID, clocked at 200 MHz. The main difference compared to McGill's SPT firmware Bender:2014nnc is the absence of polyphase filter banks (PFBs) and a new decimation path. The DAN loop remains the same, albeit it runs at a higher sampling rate. The operation of the firmware is controlled via 125 MHz control interfaces, marked in red, which ultimately connect to the ARM processor through an on-board SPI link. There is also a Global Positioning System (GPS)-derived input in IRIG-B format, which attaches timestamps to the data packets (in blue).
• Figure 5: Top panel: DAN network analysis of the system with 0.5 $\Omega$ SMD resistors. All 10 resonances are visible, with peaks corresponding to chosen detector bias points. Middle panel: shift in frequency between the measured resonance values (in the top panel) and the design ones, with the point x-axis corresponding to design resonance frequencies. Mean and standard deviation are shown by the solid line and the shaded red region, respectively. Bottom panel: the distance between neighboring resonances for measured (blue) and design (red) values -- note that the red and blue dots overlap in three cases. The contribution of the leakage cross-talk is overlaid in shades of purple.