CryoDE: a Digital Cryogenic Detector Emulator for Microwave SQUID Multiplexed Systems

TL;DR

This work tackles the challenge of evaluating room-temperature readout electronics for large-scale cryogenic detector arrays employing microwave SQUID multiplexing by introducing CryoDE, a modular FPGA-based detector emulator. CryoDE generates encoded detector pulses, SQUID-phase modulation, and internally produced carrier signals to replicate the full cryogenic umux response within a Hardware-in-the-Loop framework, enabling firmware development and testing without cryogenic hardware. The authors validate CryoDE by integrating four instances into a Zynq RFSoC-based readout for the ECHo-100k experiment, achieving accurate pulse reconstruction after demodulation with RMSE $0.0032$, MAE $0.0026$, and $R^2=0.9995$, while maintaining a compact resource footprint. The work demonstrates a practical, tunable, and resource-efficient testing platform that supports TDD and iterative firmware development for flux-ramp demodulation and real-time triggering, accelerating progress toward large-scale cryogenic detector deployments.

Abstract

Simultaneous readout of large-scale cryogenic detector arrays relies on multiplexing schemes such as the FDM (Frequency-Division Multiplexing) with microwave SQUID multiplexers and highly customized readout electronics. In traditional detector systems, where mixed-signal ASICs are used in detector front-ends and typically provide a digital interface, HIL (Hardware-in-the-Loop) testing can be readily implemented by reusing the existing digital logic of the front-end for emulation purposes. Such straightforward emulation is not possible for FDM low-temperature detectors, where the sensor signal is encoded in a high-frequency microwave carrier via a two-stage modulation scheme depending on the cryogenic resonators and the SQUID response. To address this challenge, we present CryoDE, a digital cryogenic-detector emulator for microwave SQUID multiplexed detector systems. CryoDE generates the encoded detector signals, including realistic pulse responses, enabling full HIL testing of the room-temperature DAQ system without requiring the cryogenic hardware. This resource-efficient FPGA-based detector twin integrates seamlessly into existing DAQ systems and allows experiment-specific adjustment of detector-signal parameters. We describe the internal architecture and capabilities of CryoDE within our custom HIL framework and demonstrate its use in evaluating the performance of real-time signal processing firmware optimized for different microwave SQUID multiplexed cryogenic-detector experiments.

Figures (6)

• Figure 1: Top-level architecture of CryoDE for a single umux channel. The three blocks in the top row emulate the detector signal, which is used as the phase-modulating input for the SQUID response. The colored borders around certain blocks are explained in more detail in Subsections \ref{['subsec_trigger']} and \ref{['subsec_squid_response']}
• Figure 2: Model of the SQUID response. Due to flux-ramp modulation, the SQUIDs periodically shift the resonance frequency. Using a static carrier tone at frequency $f_{exc}$, this frequency shift results in a change of amplitude. For simplicity, this amplitude modulation is approximated by a sine wave.
• Figure 3: Model of the SQUID response. Due to flux-ramp modulation, the SQUIDs periodically shift their resonance frequency. Using a static carrier tone at frequency $f_{exc}$, this frequency shift appears as a change in amplitude. For simplicity, this amplitude modulation is modeled as a sine wave.
• Figure 4: Phase encoding of the detector signal in the SQUID response. For successful demodulation of the signal, the frequency of the SQUID response must be significantly higher than the bandwidth of the detector signal, ensuring that the phase-encoded signal remains effectively constant within at least one period of the SQUID response.
• Figure 5: Characterization of the emulator performance with a count rate set to 10 Bq. On the left, the distribution of the actual event count is compared to the pmf of the theoretical Poisson distribution. The right plot illustrates the long-term behavior of the event rate compared to the expected cumulative events.