Superconducting Quantum Interference Device Array Research Articles

The SQUID Controller Unit for the LiteBIRD Space Mission: Description, Functional Tests and Early Performance Assessment

AbstractLiteBIRD is a satellite mission to be launched by JAXA in the early 2030s. It will measure the Cosmic Microwave Background (CMB) primordial B-modes with an unprecedented sensitivity. Microwave radiation will be detected by Transition Edge Sensors (TESs) arrays multiplexed in frequency domain and read by Superconducting QUantum Interference Devices (SQUIDs). The LiteBIRD SQUID Controller Unit (SCU), based on the heritage of the successful design used for the ground-based SPT3G experiment, presents some novel elements that make it suitable for a space-borne application. We compare our first breadboard model with the ground-based, Off-The-Shelf Components (COTS) version, by driving the same SQUID Array Amplifier (SAA) at 4 K, measuring relevant quantities such as noise, gain and bandwidth. We demonstrate that the noise added by our first prototype (including a switching part for redundancy purposes) never exceeds the noise added by the COTS-based electronics board, representing our benchmark. We also present the first noise estimates with the SAA cooled below 1 K, going closer to the conditions expected for LiteBIRD operation.

Design and fabrication of cryogenic multiplexing control chip

This paper presents a design and fabrication process of a cryogenic multiplexing control chip (MCC) for superconducting quantum computers. The working temperature of MCC can be 10 ∼ 30 mK, because it could be integrated with quantum processor in the same package. With a multiplexing ratio of 1:4 and designed working frequency 4–8 GHz, the MCC is a non-reciprocity device which consisted of bandpass filters and isolators, which are based on tunable inductor bridges (TIB). The MCC chip size is 6 × 6 mm2 and includes λ/2 coplanar waveguides resonators, superconducting quantum interference device arrays, capacitors, low pass filters, baluns and bias lines. Adopting self-aligned process of Josephson junctions, the fabrication of MCC constitutes four lithography masks. The modular design of MCC could facilitate the development of large-scale superconducting quantum computers.

The effect of bias current configuration on the performance of SQUID arrays

Designing superconducting electronic devices involves a careful study of all the elements in the circuit, including the superconducting bias leads. In this work, we introduce a theoretical model for two-dimensional (2D) superconducting quantum interference device (SQUID) arrays capable of simulating the voltage-to-magnetic flux response of devices with different bias current configurations. First, we compare uniformly biased and centre biased SQUID arrays by investigating the voltage versus magnetic flux response, maximum transfer function and voltage modulation depth. Then, we calculate the time-averaged fluxoid distributions for one-dimensional (1D) and 2D centre biased arrays. Finally, we study the performance of the two bias current configurations depending on array size, screening parameter, thermal noise strength and kinetic self-inductance fraction. Our calculations reveal: (i) centre biased 1D parallel SQUID arrays present an unusual voltage response caused by the asymmetric fluxoid distribution; (ii) the optimal transfer function of centre biased arrays strongly depends on the number of junctions in parallel; (iii) the performance of centre biased arrays approaches the uniform biased ones when the number of junctions in series exceeds those in parallel; (iv) while the screening parameter and the thermal noise strength clearly affect the device performance, the kinetic to self-inductance fraction seems to play only a secondary role.

Effects of Bias Current Non-Uniformity on the SQUID Array (SQA) Response

The amount of current being received by each junction affects the performance of a parallel coupled Superconducting Quantum Interference Device (SQUID) Array (SQA). Previous modeling utilized a uniform bias current input for each Josephson junction (JJ) in a parallel SQA. In this work we explore the effects of the bias current spreading out non-uniformly in the superconductor as a function of the number of JJ's in parallel. We use a lumped model approach combined with pre-calculated cross-sectional current distribution as a function of controllable film properties.

Numerical Study of SQUID Array Responses Due to Asymmetric Junction Parameters

Superconducting quantum interference device arrays have been extensively studied for their high magnetic field sensitivity. The performance of these devices strongly depends on the characteristic parameters of their Josephson junctions, i.e. their critical currents and shunt resistances. Using a resistively shunted junction model and including thermal noise, we perform a numerical investigation of the effects of asymmetric Josephson junctions by independently studying variations in the critical currents and junction resistances. We compare the voltage response of a dc-SQUID with a 1D parallel SQUID array and study the maximum transfer function dependence on the number of junctions in parallel, the screening parameter and thermal noise strength. Our results show that the maximum transfer function and linearity increase with the number of junctions in parallel for arrays with different junction resistances, in contrast to SQUID arrays with identical junctions or with spreads in the critical currents.

Design and Fabrication of Two-stage SQUID for Transition Edge Sensor

The X-ray transition edge sensor (TES) modeled by calorimeter is extremely sensitive to temperature changes when operating at a voltage bias in the temperature region, and is widely used for the detection of particles and photons from submicron frequency to gamma rays. Superconducting quantum interference device (SQUID) is the key to TES current signal readout, we have designed a two-stage SQUID amplifier circuit. First-stage sensor SQUID uses first-grade gradiometer with high input mutual inductance about 176.2 , it increases the coupling sensitivity with the TES detector and has stronger resistance to external interference. Second-stage SQUID array(SSA) adopts 32 single SQUIDs in series, which has low magnetic flux noise and high magnification. We have verified the characteristics of this two-stage circuit and demonstrated that it has a lower magnetic flux noise.

A SQUID controller unit for space-based TES sensor readout

We have developed a Superconducting Quantum Interference Device (SQUID) controller unit for Transition Edge Sensors (TES) readout, designed to be used in a space mission. The unit is made of 8 boards and each board can condition four SQUID array amplifiers. The board design is inspired by a similar one developed for ground based experiments, but specific changes have been made to adopt Components Off The Shelf (COTS) with space grade equivalents, to implement redundancy and cross-strapping capabilities. The design also includes the thermal path to lift the heat off the boards towards an in-house designed monolithic aluminum rack.

Low Noise Frequency-Domain Multiplexing of TES Bolometers Using SQUIDs at Sub-Kelvin Temperature

Digital Frequency-Domain Multiplexing (DfMux) is a technique that uses MHz superconducting resonators and Superconducting Quantum Interference Device (SQUID) arrays to read out sets of transition edge sensors. DfMux has been used by several Cosmic Microwave Background experiments, including most recently POLARBEAR-2 and SPT-3 G with multiplexing factors as high as 68, and is the baseline readout technology for the planned satellite mission LiteBIRD. Here, we present recent work focused on improving DfMux readout noise, reducing parasitic impedance, and improving sensor operation. We have achieved a substantial reduction in stray impedance by integrating the sensors, resonators, and SQUID array onto a single-carrier board operated at 250 mK. This also drastically simplifies the packaging of the cryogenic components and leads to better-controlled crosstalk. We demonstrate a low readout noise level of 8.6 mathrm{pA/Hz}1^{1/2}, which was made possible by operating the SQUID array at a reduced temperature and with a low dynamic impedance. This is a factor of two improvement compared to the achieved readout noise level in currently operating Cosmic Microwave Background experiments using DfMux and represents a critical step toward maturation of the technology for the next generation of instruments.

Evaluation of Self-Field Effects in Magnetometers Based on Meander-Shaped Arrays of Josephson Junctions or SQUIDs Connected in Series.

Arrays of superconducting quantum interference devices (SQUIDs) are highly sensitive magnetometers that can operate without a flux-locked loop, as opposed to single SQUID magnetometers. They have no source of ambiguity and benefit from a larger bandwidth. They can be used to measure absolute magnetic fields with a dynamic range scaling as the number of SQUIDs they contain. A very common arrangement for a series array of SQUIDs is with meanders as it uses the substrate area efficiently. As for most layouts with long arrays, this layout breaks the symmetry required for the elimination of adverse self-field effects. We investigate the scaling behavior of series arrays of SQUIDs, taking into account the self-field generated by the bias current flowing along the meander. We propose a design for the partial compensation of this self-field. In addition, we provide a comparison with the case of series arrays of long Josephson junctions, using the Fraunhofer pattern for applications in magnetometry. We find that compensation is required for arrays of the larger size and that, depending on the technology, arrays of long Josephson junctions may have better performance than arrays of SQUIDs.

Demonstration of MHz frequency domain multiplexing readout of 37 transition edge sensors for high-resolution x-ray imaging spectrometers

We report on the development and demonstration of MHz frequency domain multiplexing (FDM) technology to readout arrays of cryogenic transition edge sensor (TES) x-ray microcalorimeters. In our FDM scheme, TESs are AC biased at different resonant frequencies in the low MHz range through an array of high-Q LC resonators. The current signals of all TESs are summed at superconducting quantum interference devices (SQUIDs). We have demonstrated multiplexing for a readout of 31 pixels using room temperature electronics, high-Q LC filters, and TES arrays developed at SRON, and SQUID arrays from VTT. We repeated this on a second setup with 37 pixels. The summed x-ray spectral resolutions @ 5.9 keV are ΔE31pix MUX=2.14 ± 0.03 eV and ΔE37pix MUX=2.23 ± 0.03 eV. The demonstrated results are comparable with other multiplexing approaches. There is potential to further improve the spectral resolution, to increase the number of multiplexed TESs, and to open up applications for TES x-ray microcalorimeters.

Development of series SQUID array with on-chip filter for TES detector

A cold preamplifier based on superconducting quantum interference devices (SQUIDs) is currently the preferred readout technology for the low-noise transition edge sensor (TES). In this work, we have designed and fabricated a series SQUID array (SSA) amplifier for the TES detector readout circuit. In this SSA amplifier, each SQUID cell is composed of a first-order gradiometer formed using two equally large square washers, and an on-chip low pass filter (LPF) as a radio-frequency (RF) choke has been developed to reduce the Josephson oscillation interference between individual SQUID cells. In addition, a highly symmetric layout has been designed carefully to provide a fully consistent embedded electromagnetic environment and achieve coherent flux operation. The measured results show smooth V–Φ characteristics and a swing voltage that increases linearly with increasing SQUID cell number N. A white flux noise level as low as 0.28 μ Φ 0/Hz1/2 is achieved at 0.1 K, corresponding to a low current noise level of 7 pA/Hz1/2. We analyze the measured noise contribution at mK-scale temperatures and find that the dominant noise derives from a combination of the SSA intrinsic noise and the equivalent current noise of the room temperature electronics.

Synchronization transitions in a hyperchaotic SQUID trimer.

The phenomena of intermittent and complete synchronization between two out of three identical, magnetically coupled Superconducting QUantum Interference Devices (SQUIDs) are investigated numerically. SQUIDs are highly nonlinear superconducting oscillators/devices that exhibit strong resonant and tunable response to applied magnetic field(s). Single SQUIDs and SQUID arrays are technologically important solid-state devices, and they also serve as a testbed for exploring numerous complex dynamical phenomena. In SQUID oligomers, the dynamic complexity increases considerably with the number of SQUIDs. The SQUID trimer, considered here in a linear geometrical configuration using a realistic model with experimentally accessible control parameters, exhibits chaotic and hyperchaotic behavior in wide parameter regions. Complete chaos synchronization as well as intermittent chaos synchronization between two SQUIDs of the trimer is identified and characterized using the complete Lyapunov spectrum of the system and appropriate measures. The passage from complete to intermittent synchronization seems to be related to chaos-hyperchaos transitions as has been conjectured in the early days of chaos synchronization.

Modeling Large Two-Dimensional Superconducting Quantum Interference Device Arrays With Josephson Junction Opens and Shorts

In this paper we explore the effects of open and shorted Josephson Junctions (JJs) on the current-voltage (I-V) curve, and the voltage-field (V-B) curve of two-dimensional high temperature superconductor (HTS) Gaussian distributed Superconducting Quantum Interference Device (SQUID) Arrays (SQAs). We examine two cases here. The first case involves having a portion of the parallel rows of junctions containing either a single open or shorted junction. The second case involves an array having large blocks of open JJs. The large blocks represent a large damaged area on an array.

Fabrication and experimental analysis of series superconducting quantum inteference device array

Superconducting quantum interference device (SQUID) has been used as an extremely sensitive flux sensor up to now. Series SQUID array (SSA) is made up of several identical element-SQUIDs in series, in which each element-SQUID is coupled with the same set of input coils by mutual inductance to realize the amplified output of the input current. From the noise viewpoint, each element-SQUID in SSA is independent of each other, resulting in the total voltage noise across the array rising linearly with the square root of the number of element-SQUIDs. From the perspective of input signals, since the signals come from the same set of input coils, the voltage output of the array is enlarged with the proportion of element-SQUID number, N. Taken together, the signal-to-noise ratio of SSA is increased by <inline-formula><tex-math id="M4">\begin{document}$\sqrt{ {N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210467_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210467_M4.png"/></alternatives></inline-formula> times, or the flux noise of SSA is reduced by 1/<inline-formula><tex-math id="M5">\begin{document}$\sqrt{ {N}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210467_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210467_M5.png"/></alternatives></inline-formula> times compared with that of an element-SQUID ideally. However, with the increase in the number of element-SQUIDs in series, the chip design of SSA becomes more complicated, which puts forward higher requirements for the consistency and stability of its fabrication process. Besides, there exists a certain flux coherence between element-SQUIDs in SSA, whose normal operation depends on the working state of each element-SQUID in the array. In this paper, the fabrication of series SQUID array is carried on the autonomous superconducting micro-nano process platform, with a yield rate reaching over 80% on a 4-inch standard silicon wafer. Two kinds of SSAs with 200 and 800 element-SQUIDs, respectively, are integrated in a meandering way on a chip in a millimeter area. Home-made directly-coupled readout circuit is used to obtain the characteristics of SSA. The experimental results reveal that the flux noise at best working point is as low as 0.5μ<inline-formula><tex-math id="M6">\begin{document}$\varPhi _{\text{0}}/\sqrt{\text{Hz}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210467_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210467_M6.png"/></alternatives></inline-formula> and the current sensitivity is about 35 μA/<i>Φ</i><sub>0</sub>, thus, the equivalent input current noise is achieved at a level of 18 pA/<inline-formula><tex-math id="M7">\begin{document}$ \sqrt{\text{Hz}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210467_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210467_M7.png"/></alternatives></inline-formula>. Additionally, the dependence of relevant parameters in array on the number of element-SQUIDs is verified, which is consistent with theoretical expectation basically. These show that the reliability of device design and the consistency of fabrication process perform well, thus laying the technical foundation for developing the low-noise SQUID amplifier and the multiplexed readout of low-impedance detectors.

Simulation-based Analysis of Magnetogastrography Sensor Configurations for Characterizing Gastric Slow Wave Dysrhythmias.

The routine diagnosis of gastric motility disorders represents a significant problem to current clinical practice. Magnetogastrography (MGG) provides a non-invasive option for assessing gastric slow wave (SW) dysrhythmias that are associated with motility disorders. However, its ability to characterize SW propagation is impaired by the limited spatial coverage of existing superconducting quantum interference devices (SQUIDs). Recently developed optically-pumped magnetometers can potentially substitute SQUIDs and enable subject-specific MGG arrays with greater spatial coverage. This study developed simulations of gastric MGG to determine the distribution of the magnetic fields (MFs) generated by SWs above the torso, and investigated the impact of several realistic dysrhythmic patterns of propagation. The distribution of MFs was found to vary significantly for different patterns of SW propagation, with ectopic dysrhythmia displaying the greatest difference from normal. Notably, some important proportion of the MFs lay outside the coverage of an existing experimental SQUID array used in gastrointestinal research for some simulated SW propagation patterns, such as retrograde activity. Results suggest that MGG measurements should be made over the entire frontal face of the torso to capture all of the strongest MFs generated by SWs.Clinical relevance- This provides a guide for the placement of MGG sensors for the capture of both normal and dysrhythmic gastric slow wave propagation.

Micrometer Scale Y–Ba–Cu–O SQUID Arrays Fabricated With a Focused Helium Ion Beam

We present the fabrication and testing of microarrays of superconducting quantum interference devices (SQUIDs) fabricated from the high-transition temperature superconductor YBa $_2$ Cu $_3$ O $_{7-\delta }$ (YBCO). The arrays consisted of 84 SQUIDs, each with loop area 25 $\mu \text{m}^{2}$ , connected electrically in series with a meander line structure. The entire array was contained in an area of just $\text{100}\,\mu \text{m}\times \text{100}\,\mu \text{m}$ . The Josephson junctions in the arrays were directly written into YBCO thin films with ion irradiation from a focused helium ion beam. We found that the electrical properties can be controlled by changing the diameter of the ion beam through selection of either a 20 or 5 $\mu \text{m}$ beam aperture. In particular, larger aperture or beam size results in a weaker link junction with higher operating temperature and smaller critical voltage. The voltages across the dc-biased arrays were measured as a function of magnetic field. The data exhibited maximum voltage modulations of 300 $\mu \text{V}$ at 65 K and 1 mV at 52 K for the 20 and 5 $\mu \text{m}$ beam aperture, respectively. The magnetic field periodicity for both arrays was approximately 30 $\mu$ T per flux quantum.

Measurement of Magnetic Particles by Hexagonal Pseudo Seven-Channel HTS SQUID Array

We developed a high-Tc superconducting (HTS) three-channel Superconducting Quantum Interference Device (SQUID) array and applied it to the measurement of a flow of magnetic nano-particles (MNPs).Three magnetometers were positioned in-line with a separation of 2.3 mm. The pick-up loop consisted of a 1 mm × 1 mm square loop; the size of a SQUID washer slit was 5 μm × 60 μm. Using this array, we arranged a hexagonal pseudo seven-channel SQUID array. The signal from the water-diluted MNPs, Resovist, in motion was measured by the array in a DC bias magnetic field and an AC modulation magnetic field. The dependence of the SQUID signal on the angle of the MNP flow to the baseline of the array was measured and discussed. The results suggest that the signal peak values are highly dependent on the flow path angle and that most of the flow path can be identified by the shape of the waveforms. This method is a promising candidate for brain activity investigation of small animals.

Fabrication and Characteristics of All-NbN SQUID Series Array

In this article, an all-NbN superconducting quantum interference device (SQUID) array was developed for future applications by taking advantage of the higher critical temperature of a NbN film compared with Nb. The NbN SQUID array was composed of 100 SQUIDs with equal loop areas connected in series. The array was fabricated on a single-crystal MgO (100) substrate using 3- μ m-diameter NbN/AlN/NbN Josephson junctions. The hysteresis and shielding parameters of the SQUID were 0.67 and 0.15, respectively. The SQUIDs in the array were coherently modulated by injecting current in a common flux control line, which resulted in a modulation voltage of 3.54 mV with consistent periodicity and a flux-to-voltage transfer coefficient of 23 mV/Ф0. Using a flux locked loop circuit, the fabricated NbN SQUID array exhibited excellent performance with a low white flux noise of 1.4 μΦ0/√Hz, which included the preamplifier noise.

SQUID Array With Optimal Compensating Configuration for Magnetocardiography Measurement in Different Environments

We developed a 51-channel magnetocardiography (MCG) system based on weakly damped dc superconducting quantum interference device (SQUID) magnetometers. In previous works, the system consisted of 36 sensing magnetometers, 12 reference magnetometers, and a three-component vector magnetometer. In this paper, we have describe the optimizing processes of software gradiometer configurations in different magnetically shielded rooms (MSRs). Using a simulated MCG signal generated by a small coil driven by electrocardiograph, we have quantitatively evaluated the signal quality through four key performance indices, which are 1) correlation in time domain, 2) correlation in frequency domain, 3) relative heights of different peaks, and 4) magnetic field map of simulating coil. After data processing and analysis of these four parameters, optimized software gradiometers of first or second order can be formed by using specific reference magnetometer signals to compensate the signals of 36 sensing magnetometers in each MSR. Also, the MCG signals of an adult have been detected by using these optimized configurations. The magnetic field maps and typical parameters at T-peak have been extracted and compared, and the results with high consistency confirm the effectiveness of optimization processes.

Chimera States in Networks of Locally and Non-locally Coupled SQUIDs

Planar and linear arrays of SQUIDs (superconducting quantum interference devices) operate as nonlinear magnetic metamaterials in microwaves. Such {\em SQUID metamaterials} are paradigmatic systems that serve as a test-bed for simulating several nonlinear dynamics phenomena. SQUIDs are highly nonlinear oscillators which are coupled together through magnetic dipole-dipole forces due to their mutual inductance; that coupling falls-off approximately as the inverse cube of their distance, i.~e., it is non-local. However, it can be approximated by a local (nearest-neighbour) coupling which in many cases suffices for capturing the essentials of the dynamics of SQUID metamaterials. For either type of coupling, it is numerically demonstrated that chimera states as well as other spatially non-uniform states can be generated in SQUID metamaterials under time-dependent applied magnetic flux for appropriately chosen initial conditions. The mechanism for the emergence of these states is discussed in terms of the multistability property of the individual SQUIDs around their resonance frequency and the attractor crowding effect in systems of coupled nonlinear oscillators. Interestingly, controlled generation of chimera states in SQUID metamaterials can be achieved in the presence of a constant (dc) flux gradient with the SQUID metamaterial initially at rest.