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arXiv:2504.20398 · Journal of Applied Physics

Noise limits for dc SQUID readout of high-Q resonators below 300 MHz

Victoria Ankel, C. Bartram, J. Begin, C. Bell, L. Brouwer, Saptarshi Chaudhuri, John L. Clarke, Hsiao-Mei Cho, J. Corbin, W. Craddock, S. Cuadra, A. Droster, Malcolm Durkin, J. Echevers, J. T. Fry, Gene C Hilton, K. D. Irwin, A. Keller, R. Kolevatov, A. Kunder, Dale Li, N. Otto, K. M. W. Pappas, N. M. Rapidis, Chiara P. Salemi, Daniel R. Schmidt, Maria Simanovskaia, Jyotirmai Singh, P. Stark, Claudia D. Tesche, Joel N. Ullom, Leila R. Vale, E. C. van Assendelft, K. van Bibber, Michael R. Vissers, K. Wells, J. Wiedemann, L. A. Winslow, D. M. Wright, Andrew K. Yi, Betty Young

Published Sep 4, 2025• 0 citations

Abstract

We present the limits on noise for the readout of cryogenic high-Q resonators using dc Superconducting Quantum Interference Devices (SQUIDs) below 300 MHz. This analysis uses realized first-stage SQUIDs (previously published), whose performance is well described by Tesche–Clarke (TC) theory, coupled directly to the resonators. We also present data from a prototype second-stage dc SQUID array designed to couple to this first-stage SQUID as a follow-on amplifier with high system bandwidth. This analysis is the first full consideration of dc SQUID noise performance referred to a high-Q resonator over this frequency range and is presented relative to the standard quantum limit. We include imprecision, backaction, and backaction–imprecision noise correlations from TC theory, the noise contributed by the second-stage SQUIDs, wiring, and preamplifiers, and optimizations for both on-resonance measurements and off-resonance scan sensitivity. This architecture has modern relevance due to the increased interest in axion searches and the requirements of the DMRadio-m3 axion search, which uses dc SQUIDs in this frequency range.

DOI: 10.1063/5.0280831

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SQUID Readout of a High-

Q

Superconducting

LC

Resonator

We demonstrate the readout of a superconducting

LC

resonator, with

Q \approx 2 \times 10^{6}

at approximately 250 kHz, using a dc SQUID followed by a SQUID series-array amplifier readout chain. We find that

Q

depends on the SQUID flux-bias point, increasing near the shallow-slope point of the SQUID modulation curve and decreasing near the steep-slope point, consistent with the previously observed SQUID damping effects. From this variation, we infer the SQUID effective input impedance. We further infer the effective temperature of the resonator circuit from the resonance peak in the noise spectrum and show that it also depends on the SQUID flux-bias point, suggesting a possible contribution from SQUID back-action noise. This system provides a working prototype for future experiments based on lumped-element resonators with SQUID readout, in particular low-mass axion searches within the DMRadio program.

We describe a low-noise, two-stage dc Superconducting QUantum Interference Device (SQUID) amplifier that is designed for applications requiring high bandwidth and dynamic range. The output signal of a low-noise SQUID in the input stage coherently modulates a series array of identical SQUIDs in the output stage via a common modulation line. The input stage is designed so its output signal does not produce multiple modulation periods in the output stage. The output stage is designed to have sufficient gain so the output noise is dominated by the amplified noise of the input SQUID and exceeds the noise of a preamplifier in the room temperature readout electronics. The SQUID amplifier may therefore be operated without flux modulation or any impedance matching network, resulting in a large dynamic range and high bandwidth.

Superconducting quantum interference device (SQUID) is a sensitive detector of magnetic flux signals. Up to now, the main application of SQUIDs has been measurements of magnetic flux signals in the frequency range from near DC to several MHz. Recently, cryogenic low-noise radio-frequency (RF) amplifiers based on DC SQUID are under development aiming to detect RF signals with sensitivity approaching quantum limit. In this paper, we review the recent progress of cryogenic low-noise RF amplifiers based on SQUID technology.

Direct-current superconducting quantum interference devices (dc-SQUIDs) are one of the most sensitive magnetic detectors. These sensors are extensively used in the readout of superconducting transition edge sensors (TESs), which are used for the detection of weak signals. A cosmic microwave background (CMB) polarization telescope operating in 22-48 GHz is currently under developing. The TESs calorimeter of the telescope will be readout by a time-division multiplexer (TDM) SQUID readout system. We develop a two-stage dc-SQUID amplifier circuit, comprising an input-stage SQUID with 4 SQUID cells and a series SQUID array (SSA) with 100 SQUID cells. This configuration has been shown to achieve extremely high signal gain while effectively controlling system noise. We assess the system noise at

300

mK

in an adiabatic demagnetisation refrigerator (ADR). The the measured magnetic flux noise of the two-stage SQUID circuit system is approximately

0.3

μΦ_{0}/\sqrt{Hz}

at

10

kHz

. The current noise equivalent to the input coil of input SQUID is about

2.4

pA/\sqrt{Hz}

. This result meets the low-noise readout requirements of the CMB TES and other applications with TES detectors.

An improved read-out electronics without flux modulation for dc superconducting quantum interference devices (dc SQUIDs) is presented where the preamplifier is directly coupled to the SQUID. Compared to our previous designs, the 1/f voltage and current noise levels of the preamplifier were reduced by about a factor of 4 (rms) by using bipolar matched transistors instead of operational amplifiers at the input. Three types of flux-locked-loop electronics were developed and successfully tested: a low-power (120 mW) version for large multichannel arrays, a high-speed version with a 15 MHz bandwidth and a very fast (300 ns) reset mode, and a low-noise (0.44 nV/Hz) version with a fast and precise bias reversal circuit. The flux-locked-loop electronics are compatible with each other, so that only one type of low-power (180 mW) control unit is required to operate them. All essential specifications of practical SQUID systems (noise, dynamic behavior, and temperature stability) were determined by using liquid-helium and liquid-nitrogen cooled SQUIDs, respectively.