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arXiv:2208.02013 · Journal of Applied Physics

Simulation framework for microwave SQUID multiplexer optimization

Constantin Schuster, Mathias Wegner, Sebastian Kempf

Published Jan 28, 2023• 9 citations
arXivHTMLPDF

Abstract

So far, performance prediction and optimization of microwave SQUID multiplexers have largely been based on simple approximate analytical models and experimental results. This is caused by the complexity of the underlying physics and the intricacy of operation and readout parameters. As a simplified description can never account for all potential effects occurring in a real device, we have developed a software framework to simulate the characteristics and performance of a microwave SQUID multiplexer. Our simulation framework is a powerful tool to guide understanding and optimization of microwave SQUID multiplexers and other related devices. It includes common readout schemes such as open-loop or flux ramp-modulated readout as well as the nonlinear behavior of Josephson tunnel junctions. Moreover, it accounts for the non-zero response time of superconducting microwave resonators with high loaded quality factors as well as the most significant noise contributions such as amplifier noise, resonator noise, as well as SQUID noise. This ultimately leads to a prediction of device performance that is significantly better compared to simple analytical methods. Using the simulation framework, we discuss first steps toward full microwave SQUID multiplexer optimization and highlight some other applications for which our simulation framework can be used.

DOI
10.1063/5.0135124

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So far, performance prediction and optimization of microwave SQUID multiplexers have largely been based on simple approximate analytical models and experimental results. This is caused by the complexity of the underlying physics and the intricacy of operation and readout parameters. As a simplified description can never account for all potential effects occurring in a real device, we have developed a software framework to simulate the characteristics and performance of a microwave SQUID multiplexer. Our simulation framework is a powerful tool to guide understanding and optimization of microwave SQUID multiplexers and other related devices. It includes common readout schemes such as open-loop or flux ramp-modulated readout as well as the nonlinear behavior of Josephson tunnel junctions. Moreover, it accounts for the non-zero response time of superconducting microwave resonators with high loaded quality factors as well as the most significant noise contributions such as amplifier noise, resonator noise, as well as SQUID noise. This ultimately leads to a prediction of device performance that is significantly better compared to simple analytical methods. Using the simulation framework, we discuss first steps toward full microwave SQUID multiplexer optimization and highlight some other applications for which our simulation framework can be used.
The Microwave SQUID Multiplexer (μMUX) is the device of choice for the readout of a large number of low-temperature detectors in a wide variety of experiments within the fields of astronomy and particle physics. While it offers large multiplexing factors, the system noise performance is highly dependent on the cold- and warm-readout electronic systems used to read it out, as well as the demodulation domain and parameters chosen. In order to understand the impact of the readout systems in the overall detection system noise performance, first, we extended the available μMUX simulation frameworks, including additive and multiplicative noise sources in the probing tones (i.e., phase and amplitude noise), along with the capability of demodulating the scientific data, either in the resonator’s phase or the scattering amplitude. Then, considering the additive noise as a dominant noise source, the optimum readout parameters to achieve minimum system noise were found for both open-loop and flux-ramp demodulation schemes in the aforementioned domains. Later, we evaluated the system noise sensitivity to multiplicative noise sources under the optimum readout parameters. Finally, as a case study, we evaluated the optimal demodulation domain and the expected system noise level for a typical software-defined radio readout system. This work leads to an improved system performance prediction and noise engineering based on the available readout electronics and the selected demodulation domain.
Abstract We present an advanced model for describing the readout power dependence of the resonance characteristics of a microwave SQUID multiplexer. Our model proves valid for SQUID screening parameters up to β L < 1 , hence covering the full range of practically relevant design parameters. We demonstrate that our model significantly improves agreement with experimental data compared to the existing models, thereby enabling optimization beyond the previously accessible parameter space. Moreover, our model supports non-sinusoidal current-phase relations of the rf-SQUID’s Josephson junction, allowing, for the first time, for the modeling of devices based on Josephson tunnel junctions with inhomogeneous tunnel barriers. We show that the effects of such inhomogeneities are qualitatively similar to, yet distinct from, those of the screening parameter, making their inclusion essential for accurate characterization. Incorporating these effects yields great improved agreement with measurements, even at readout power conditions well beyond typical operating parameters.
Abstract We report on the development of an analytical model describing the readout power and superconducting quantum interference device (SQUID) hysteresis parameter dependence of the resonator characteristics used for frequency encoding in microwave SQUID multiplexers. Within the context of this model, we derived the different dependencies by analyzing the Fourier components of the non-linear response of the non-hysteretic rf-SQUID. We show that our model contains the existing model as a limiting case, leading to identical analytical expressions for small readout powers. Considering the approximations we made, our model is valid for rf-SQUID hysteresis parameters β L < 0.6 which fully covers the parameter range of existing multiplexer devices. We conclude our work with an experimental verification of the model. In particular, we demonstrate a very good agreement between measured multiplexer characteristics and predictions based on our model.
This thesis describes a multiplexer of Superconducting Quantum Interference Devices (SQUIDs) with low-noise, ultra-low power dissipation, and great scalability. The multiplexer circuit measures the magnetic flux in a large number of unshunted rf SQUIDs by coupling each SQUID to a superconducting microwave resonator tuned to a unique resonance frequency and driving the resonators from a common feedline. A superposition of microwave tones measures each SQUID simultaneously using only two coaxial cables between the cryogenic device and room temperature. This multiplexer will enable the instrumentation of arrays with hundreds of thousands of low-temperature detectors for new applications in cosmology, materials analysis, and nuclear non-proliferation.\nThe driving application of the Microwave SQUID Multiplexer is the readout of large arrays of superconducting transition-edge sensors, by some figures of merit the most sensitive detectors of electromagnetic signals over a span of more than nine orders of magnitude in energy, from 40 GHz microwaves to 200 keV gamma rays. Modern transition-edge sensors have noise-equivalent power as low as 10-20 W / [square root] Hz and energy resolution as good as 2 eV at 6 keV. These per-pixel sensitivities approach theoretical limits set by the underlying signals, motivating a rapid increase in pixel count to access new science. Compelling applications, like the non-destructive assay of nuclear material for treaty verification or the search for primordial gravity waves from inflation use arrays of these detectors to increase collection area or tile a focal plane.\nWe developed three generations of SQUID multiplexers, optimizing the first for flux noise (0.17 mu Phi0 / [square root] Hz) the second for input current noise (19 pA / [square root] Hz) and the last for practical multiplexing of large arrays of cosmic microwave background polarimeters based on transition-edge sensors. Using the last design we demonstrated multiplexed readout of prototype polarimeters with the performance required for the future development of a large-scale astronomical instrument.
We are developing a microwave readout multiplexer for arrays of superconducting quantum interference devices (SQUIDs). A series of microwave resonators with frequencies ∼10 GHz are each loaded by a dc SQUID to a degree that depends on the flux state of the SQUID. By using resonators with high quality factors and slightly different resonance frequencies, many of these resonator‐coupled SQUIDs may be read out with a single excitation line and cryogenic amplifier. Our multiplexer is similar to the one demonstrated by Irwin and Lehnert except for the use of higher‐frequency, fully‐lithographed transmission line resonators. We discuss a technique for modulating the SQUID array in series that alleviates the need to individually flux‐bias the SQUIDs. The multiplexer has applications to the readout of detector arrays for astronomy as well as medical magnetic imaging.
The quality factors and noise performances of superconducting resonators play an important role in microwave SQUID multiplexer (MW-MUX). Since we develop microwave SQUID multiplexer for transition edge sensor arrays, the operation temperature is around 100 mK where the effects of two level system (TLS) can be significant. In this paper, we have investigated the electrode-material or wafer dependence of noise performance of MW-MUX by characterizing four types of resonators. Although the temperature dependence of resonance frequency and the power dependence of Qu show clear difference among the materials, frequency noises which contribute the readout noise of MW-MUX are similar. Theoretical model predicts that not TLS but other loss dominates Qu in the power region suitable for the low-noise operation of our MW-MUX. Further, the estimated flux noise calculated from the measured frequency noise and the conversion √ coefficient from frequency to flux were 1-5 (μΦ0/√Hz) @ 1 Hz, 0.2-0.8 (μΦ0/√Hz) @ 3 kHz. These results indicate the noise of our MW-MUX has small material dependence and the compatible low noise operation to typical dc SQUIDs would be possible. Therefore, the MW-MUX with our materials would not suffer from the low frequency noise due to TLS.