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A Recursive Algorithm to Improve the Sampling Rate of Microwave SQUID Multiplexed Readout for Fast Microcalorimeter Signals

Guofu Liao, Congzhan Liu, Zhengwei Li, Yongjie Zhang, Laiyu Zhang, Yu Xu, S. Shu, Daikang Yan, He Gao, Yifei Zhang, X. F. Lu, Xufang Li, Xiangxiang Ren, Xu He, Di Wu

Published Feb 1, 2024• 0 citations
Publisher

Abstract

Abstract The Microwave SQUID Multiplexer ($\mu$MUX) is a critical readout technology for large-scale Superconducting Transition-Edge Sensor (TES) array. It is considered as a promising readout system for both bolometer and calorimeter applications of large-scale TES array. It has been employed in several Cosmic Microwave Background (CMB) experiments, in which the TESes are used as bolometers. However, in the field of calorimeter applications of TESes, such as X-ray detection, the $\mu$MUX system has not been widely used. The main reason is the slew rate of calorimeter pulse signal is much faster than that of bolometer, which will increase the difficulties of data processing in $\mu$MUX electronics. In a typical microwave SQUID Multiplexed readout scheme, the sampling rate is determined by the frequency of the flux-ramp modulation. For CMB experiment, the frequency of the flux-ramp is usually set to about $\mathcal{O}$(10~kHz). However, for X-ray detection, it is necessary to improve the frequency of flux-ramp to about 1~MHz. It is a challenge to implement the high speed data processing with current $\mu$MUX electronics.%The $\mu$Mux readout algorithm is a crucial component.Currently, the implementation of the $\mu$Mux readout algorithm is complex, and the sampling rate for each TES is low, only reaching kHz.We propose a recursive algorithm to reconstruct the fast TES signals with high sampling rate in case of no hardware changes. This algorithm is simple enough to implement in real time data collection. %In this paper, we describe and demonstrate this technique with a reasonable simulation model of $\mu$MUX. The simulation results shows that the recovered sampling rate can break through the frequency limitation of the flux ramp, reaching up to analog-to-digital converter (ADC) sampling rate. The non-linearity is lower to 0.25\% in full dynamic range.

DOI
10.21203/rs.3.rs-3909169/v1

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Abstract The Microwave SQUID Multiplexer (μ\muμMUX) is a critical readout technology for large-scale Superconducting Transition-Edge Sensor (TES) array. It is considered as a promising readout system for both bolometer and calorimeter applications of large-scale TES array. It has been employed in several Cosmic Microwave Background (CMB) experiments, in which the TESes are used as bolometers. However, in the field of calorimeter applications of TESes, such as X-ray detection, the μ\muμMUX system has not been widely used. The main reason is the slew rate of calorimeter pulse signal is much faster than that of bolometer, which will increase the difficulties of data processing in μ\muμMUX electronics. In a typical microwave SQUID Multiplexed readout scheme, the sampling rate is determined by the frequency of the flux-ramp modulation. For CMB experiment, the frequency of the flux-ramp is usually set to about O\mathcal{O}O(10kHz). However, for X-ray detection, it is necessary to improve the frequency of flux-ramp to about 1MHz. It is a challenge to implement the high speed data processing with current μ\muμMUX electronics.%The μ\muμMux readout algorithm is a crucial component.Currently, the implementation of the μ\muμMux readout algorithm is complex, and the sampling rate for each TES is low, only reaching kHz.We propose a recursive algorithm to reconstruct the fast TES signals with high sampling rate in case of no hardware changes. This algorithm is simple enough to implement in real time data collection. %In this paper, we describe and demonstrate this technique with a reasonable simulation model of μ\muμMUX. The simulation results shows that the recovered sampling rate can break through the frequency limitation of the flux ramp, reaching up to analog-to-digital converter (ADC) sampling rate. The non-linearity is lower to 0.25% in full dynamic range.
Abstract A microwave SQUID multiplexer ( μ MUX) with a high multiplexing factor is a promising readout approach for large-scale superconducting transition-edge sensor (TES) bolometer arrays. This paper reports on the characteristics of 16-channel μ MUX prototype chips and a 60-channel readout module developed to read out TES bolometers for the Ali cosmic microwave background polarization telescope (AliCPT). We designed two different coupling structures between the resonator and the radio-frequency superconducting interference device: design A with a mutual inductance ( M T ) of 2.3 pH and design B with an M T of 6.5 pH. For design A, the mean resonator bandwidth ( Δ f BW ) and peak-to-peak frequency shift ( Δ f pp ) are approximately 610 kHz and 290 kHz, respectively. The measured mean open-loop current noise is less than 40 pA / Hz . Preliminary results indicate that crosstalk between adjacent channels is below 1% in our design A μ MUX chip. A measured channel with design B shows a Δ f BW of 586 kHz and a current noise of 33 pA / Hz , similar to the design A channels. In comparison, the Δ f pp of 803 kHz is much larger than the design A channels due to a larger M T . The readout module, consisting of two design A chips and two design B chips, shows 60 resonances, corresponding to a yield of 94%. In the future, we will place 32 design A channels within the same chip dimension to increase the channel density and build a larger readout module suitable for AliCPT TES arrays.
We report very-low-noise, fast-response, middle-scale multiplexing in a microwave superconducting quantum interference device multiplexer (MW-Mux) as a transition-edge sensor (TES) readout. Our MW-Mux is able to read 40 channels with 500 kHz sampling and has a low readout noise of 0.9 μΦ0/Hz (where Φ0 is the magnetic flux quantum), equivalent to 9 pA/Hz. By contrast, a multiplexer of less than 10 pixels with 500 kHz sampling and ∼2 μΦ0/Hz readout noise has so far been reported in the literature. Owing to the 500 kHz sampling, our MW-Mux exhibits a fast response to detect a TES pulse with a rise time around 12 μs. We demonstrated simultaneous readout of 38 pixels from an array of x-ray TES microcalorimeters. The measured full-width values at half-maximum spectral resolution ranged from 2.79 to 4.56 eV, with a median value of 3.30 eV at 5.9 keV, including a ∼10% contribution of readout noise, i.e., 0.9–1.7 eV.
To enable the next-generation of bolometric cameras, we are developing the microwave SQUID multiplexer (μMUX). Upcoming receivers such as Simons Observatory, CCAT-prime, BICEP array, Ali-CPT, and CMB-S4 plan to instrument focal planes with 50,000-500,000 sensors. Sensor count is achieved by tiling many 150 mm-diameter densely packed detector arrays into these focal planes. The fabrication and quality of large-format bolometer arrays has been demonstrated and is now mature. In contrast, the readout technology required for next-generation receivers needs development. The sensitivity, low cross-talk, high multiplexing density, and small component size make the μMUX well-suited for this goal. In this approach, the TES signal modulates the inductance of an rf-SQUID that loads a high-Q microwave resonator. The coupled signal therefore modulates the microwave resonance frequency, which may be read out using homodyne techniques. By coupling each resonator to the same microwave feedline, many detectors can be read out on a single coaxial cable pair. The multiplexing density is in practice limited by signal bandwidth, allowable cross-talk, and the digitization bandwidth of room-temperature readout electronics. We present the design and performance of a scalable 64-channel multiplexer chip optimized for bolometric applications. We utilize a new quarter wave resonator design that increases the physical linear density by a factor of two, therefore achieving a smaller footprint for simplified detector packaging. Measurements of this design show 100 kHz resonator bandwidth, uniform 1.8 MHz frequency spacing, and an input referred current noise of 35 pA/√Hz that is well below the level of an optimized, background-limited TES bolometer. Using 8 daisy-chained and frequency scaled chips, we create a 512-channel multiplexer and use it to readout a 512 TES-bolometer array. We present the results of this large-scale μMUX demonstration including system yield, signal cross-talk, and an analysis of noise in various TES bias configurations. The result demonstrates the multiplexing density required to read out 2,000 sensors between 4-8 GHz.
Key performance characteristics are demonstrated for the microwave SQUID multiplexer (μ\muμMUX) coupled to transition edge sensor (TES) bolometers that have been optimized for cosmic microwave background (CMB) observations. In a 64-channel demonstration, we show that the μ\muμMUX produces a white, input referred current noise level of 29~pA/Hz/\sqrt{\mathrm{Hz}}/Hz​ at -77~dB microwave probe tone power, which is well below expected fundamental detector and photon noise sources for a ground-based CMB-optimized bolometer. Operated with negligible photon loading, we measure 98~pA/Hz/\sqrt{\mathrm{Hz}}/Hz​ in the TES-coupled channels biased at 65% of the sensor normal resistance. This noise level is consistent with that predicted from bolometer thermal fluctuation (i.e., phonon) noise. Furthermore, the power spectral density exhibits a white spectrum at low frequencies (∼\sim∼~100~mHz), which enables CMB mapping on large angular scales that constrain the physics of inflation. Additionally, we report cross-talk measurements that indicate a level below 0.3%, which is less than the level of cross-talk from multiplexed readout systems in deployed CMB imagers. These measurements demonstrate the μ\muμMUX as a viable readout technique for future CMB imaging instruments.
Key performance characteristics are demonstrated for the microwave SQUID multiplexer (µmux) coupled to transition edge sensor (TES) bolometers that have been optimized for cosmic microwave background (CMB) observations. In a 64-channel demonstration, we show that the µmux produces a white, input referred current noise level of [Formula: see text] at -77 dB microwave probe tone power, which is well below expected fundamental detector and photon noise sources for a ground-based CMB-optimized bolometer. Operated with negligible photon loading, we measure [Formula: see text] in the TES-coupled channels biased at 65% of the sensor normal resistance. This noise level is consistent with that predicted from bolometer thermal fluctuation (i.e. phonon) noise. Furthermore, the power spectral density is white over a range of frequencies down to ~ 100 mHz, which enables CMB mapping on large angular scales that constrain the physics of inflation. Additionally, we report cross-talk measurements that indicate a level below 0.3%, which is less than the level of cross-talk from multiplexed readout systems in deployed CMB imagers. These measurements demonstrate the µmux as a viable readout technique for future CMB imaging instruments.
Transition Edge Sensors (TESs) are highly sensitive cryogenic detectors widely used in astronomy, high-energy physics and nuclear radiation detection. As TES is increasingly deployed in large-scale arrays to improve sensitivity and effective collecting area, multiplexed readout becomes essential for reducing system complexity. Microwave SQUID multiplexing (μMUX) technology combining superconducting resonators with radio-frequency superconducting quantum interference devices (RF-SQUIDs), represents a state-of-the-art solution. In this work, a room-temperature readout prototype for TES μMUX readout was designed. The system features a scalable two-stage architecture, including a highly integrated, chassis-independent front-end signal processing module and back-end event-reconstruction module. A high-frequency-resolution frequency-comb signal generation method with real-time, per-tone frequency and phase tunability was developed. In addition, optimization of the firmware implementation effectively overcomes the computational-resource bottleneck of the Field Programmable Gate Array (FPGA). The prototype supports autonomous frequency sweeping, parameter diagnostics, and online event reconstruction. Self-test shows S 21 phase noise better than −110 dBc/Hz at −30 dBm, remaining stable with increasing channel count. Joint tests with a μMUX cryogenic system successfully captured the RF-SQUID response and achieved an equivalent noise current of 44 pA/√Hz referred to the TES, validating the prototype as a practical solution of the room-temperature system for TES μMUX readout.