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IEICE Electronics Express

Adjustable SQUID-resonator direct coupling in microwave SQUID multiplexer for TES microcalorimeter array

Yuki Nakashima, Fuminori Hirayama, Satoshi Kohjiro, Hirotake Yamamori, Shuichi Nagasawa, Noriko Y. Yamasaki, Kazuhisa Mitsuda

Published Jan 1, 2017• 11 citations
Publisher

Abstract

We have succeeded in the first demonstration of a simple and accurate resonator-superconducting quantum interference device (SQUID) coupling for microwave SQUID multiplexers. A simple theory shows our direct coupling with adjustable fractional inductance in the SQUID loop can decrease the deviation of resonance frequencies from designed values in contrast to a conventional inductive coupling. Our direct coupling provides the individual coupling that can be optimized with keeping identical structure, shape, and dimension of the SQUID among all pixels on the same chip. It covers experimentally three or potentially more factors of a frequency band that is larger than that of cryogenic high electron mobility transistor amplifiers. The deviation of experimental fractional inductance from the designed one is less than −3/+10%.

DOI
10.1587/elex.14.20170271

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We have succeeded in the first demonstration of a simple and accurate resonator-superconducting quantum interference device (SQUID) coupling for microwave SQUID multiplexers. A simple theory shows our direct coupling with adjustable fractional inductance in the SQUID loop can decrease the deviation of resonance frequencies from designed values in contrast to a conventional inductive coupling. Our direct coupling provides the individual coupling that can be optimized with keeping identical structure, shape, and dimension of the SQUID among all pixels on the same chip. It covers experimentally three or potentially more factors of a frequency band that is larger than that of cryogenic high electron mobility transistor amplifiers. The deviation of experimental fractional inductance from the designed one is less than −3/+10%.
Resonant frequencies and SQUID inductancesLSin a microwave SQUID multiplexer are studied for the purpose of reliable design applicable for a future large-format array of transition edge sensors (TESs). The key element of the multiplexer chip is a quarter-wave-length resonator terminated by a dissipationless rf SQUID connected to TES. For the resonator, we found that a small correction to the effective length of the resonators made the designed resonant frequencies fit the experimental one over the whole readout band of 4-8 GHz covered by our cryogenic amplifier. We also found that microstrip-type SQUIDs with vertical loops are suitable for accurate design of small inductanceLS<; 10<; pH to operate the rf SQUID in dissipationless regime. Based on these well-designed resonators and SQUIDs, we have successfully demonstrated the multiplexing of three pulsed signals with 1-ms width and spacing given at the input ports of three SQUIDs. The equivalent noise current refer to the SQUID input is not dominated by SQUIDs and estimated to be 200-270 pA/ √Hz, whose improvement approach is quantitatively discussed.
We present a hybrid microwave superconducting quantum interference device (SQUID) multiplexer that combines two frequency-division multiplexing techniques to allow multiplexing a given number of cryogenic detectors with only a fraction of frequency encoding resonators. Similar to conventional microwave SQUID multiplexing, our multiplexer relies on inductively coupling non-hysteretic, unshunted rf-SQUIDs to superconducting microwave resonators as well as applying flux ramp modulation for output signal linearization. However, instead of utilizing one resonator per SQUID, we couple multiple SQUIDs to a common readout resonator and encode the SQUID input signals in sidebands of the microwave carrier by varying the flux ramp modulation frequency for each SQUID. We prove the suitability of our approach using a prototype device and argue by means of fundamental information theory that our approach is particularly suited for reading out large cryogenic bolometer arrays.
We report on the study of a microwave superconducting quantum interference device (SQUID) multiplexer (MW-Mux) with current noise lower than that of our typical transition-edge sensor (TES) X-ray microcalorimeter. A large mutual inductance, between SQUID loop and input inductor connected to a TES X-ray microcalorimeter in series, realizes such low current noise referred to the SQUID input, but also can cause undesirable resonances which affect the SQUID performances. In this paper, we have developed the MW-Mux with mutual inductance of about 370 pH, which is six times larger than that of the previous one, by adopting a spiral input coil longer than a half wavelength at the readout microwave frequency. Its characteristics are evaluated, and the results have shown that the distortion of the SQUID characteristics and the degradation of its noise performance are not clearly observed. Finally, we have developed an MW-Mux microstrip SQUID with a low current noise of <; 20 pA/√(Hz) which is below the typical noise of our TES X-ray microcalorimeter, 30 pA/√(Hz).
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.
We describe a superconducting quantum interference device (SQUID) multiplexer operated at microwave frequencies. The outputs of multiple SQUIDs are simultaneously modulated at different frequencies and summed into the input of one high electron mobility transistor (HEMT). The large bandwidth and dynamic range provided by HEMT amplifiers should make it possible to frequency-division multiplex a large number of SQUIDs in one output coaxial cable. We measure low SQUID noise (∼0.5μΦ0∕Hz at 4K) and demonstrate the multiplexed readout of two direct current (dc) SQUIDs at different resonant frequencies. In this work, dc SQUIDs are used, but this approach is equally applicable to radio-frequency SQUIDs.
Understanding the coupling mechanism between SQUID (superconducting quantum interference device) loop and resonator in high-frequency SQUIDs is essential for the application of these devices in sensitive magnetometers or controllable microwave devices. We have investigated, therefore, two kinds of planar microstrip tank circuit resonators: (1) S-shaped λ/2-resonators with direct or indirect coupling to the SQUID loop with optional flux-focussing pads and (2) conventional rf-washer-SQUID structures for which we have found resonant modes of the washer providing a coupling to the SQUID loop. A lumped element representation of SQUID loop and resonator is presented in order to describe the effective SQUID-resonator coupling in case of direct or indirect coupling. According to this approach, the square of the effective coupling constant k in both cases is equal to the ratio of the magnetic energy stored in the SQUID loop to that stored in the resonator. For the indirect coupled S-shaped λ/2-resonators, k can be described in terms of a geometry-defined mutual inductance. The predictions of the lumped element description are compared with simulations using a standard full-wave analysis computer program in order to quantify the effect of the different layouts on microwave current distribution and on k. A method for the determination of k by simulation is described, leading to useful design rules for the optimization of high-frequency SQUIDs. The simulation results will also be compared with experimental data.