SQUID Loop Research Articles

Design dependence of noise in Nb-based dc SQUIDs

Noise in superconducting quantum interference devices (dc SQUIDs) with different design, based on Nb/AlOx/Nb technology, has been systematically measured at temperature T = 4.2 K. We demonstrate that for all our devices the power spectral density of the white noise (above a frequency of about 1 kHz) is determined by the shunt resistors, reaching about 5 times Planck’s constant. The low-frequency noise level was measured for washer- and multi-loop-type SQUIDs with systematically varied effective area, SQUID loop perimeter, and inductance. We show that at 1 Hz the noise spectral density is approximately 40 times higher than the white noise level and its scaling with washer width and effective area is negligible. These results are incompatible with several models of the flicker noise source. Possible origins of this noise are discussed.

Effects of strong capacitive coupling between meta-atoms in rf SQUID metamaterials

We consider, for the first time, the effects of strong capacitive and inductive coupling between radio frequency superconducting quantum interference devices (rf SQUIDs) in an overlapping metamaterial geometry when driven by rf flux at and near their self-resonant frequencies. The equations of motion for the gauge-invariant phases on the Josephson junctions in each SQUID are set up and solved. Our model accounts for the high-frequency displacement currents through capacitive overlap between the wiring of SQUID loops. We begin by modeling two overlapping SQUIDs and studying the response in both the linear and nonlinear high-frequency driving limits. By exploring a sequence of more and more complicated arrays, the formalism is eventually extended to the N×N×2 overlapping metamaterial array, where we develop an understanding of the many ( 8N2−8N+3 ) resulting resonant modes in terms of three classes of resonances. The capacitive coupling gives rise to qualitatively new self-resonant responses of rf SQUID metamaterials, and is demonstrated through analytical theory, numerical modeling, and experiment in the 10–30 GHz range on capacitively and inductively coupled rf SQUID metamaterials.

Comparison of Double Relaxation Oscillation SQUIDs and DC-SQUIDs of Large Stewart-McCumber Parameter

Increasing the flux-to-voltage transfer coefficient of the SQUID output voltage is necessary to release the constraint on the preamplifier input noise. As one of the approaches to increase the transfer coefficient, we have been using a double relaxation oscillation SQUID (DROS) having a transfer coefficient of about 10 times larger than those of DC-SQUIDs. Traditionally, DC-SQUIDs were operated in the non-hysteretic condition with the Stewart-McCumber parameter (β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ) less than 1. In this study, we fabricated hysteretic DC-SQUIDs with the β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> ranging from 2.5 and compared the transfer coefficient and the system noise of DC-SQUIDs and DROSs. Both DROS and DC-SQUID have the same structure and design parameters for the SQUID loop inductance, resonance-damping circuits in the SQUID loop, and input coil. All the SQUIDs were fabricated in the same wafer using the Nb/AlO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> /Nb junction process. The transfer coefficients of DROSs were about 1 mV/Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , regardless of SQUID parameters. For DC-SQUIDs, the transfer coefficients were sensitive to the β <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> and the operating margin was narrower than that of DROS. The white noise of both SQUIDs in the flux-locked loop mode was around 1.5 μΦ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> /√Hz at 100 Hz, measured with a preamplifier of input voltage noise of 1 nV/√Hz. DC-SQUIDs had mostly a narrower operating margin against the bias current, and the modulation voltage was smaller than DROS. In a near-optimized operating condition, both DROS and hysteretic DC-SQUID showed comparable noise performance.

Design of a High-Tc SQUID Planer Gradiometer and Evaluation of Sensitivity Distribution

When using SQUID magnetic sensors to inspect metallic contaminants in magnetic matrices, such as battery components, it is advantageous to use a gradiometer rather than a magnetometer because a higher signal-to-noise ratio can be obtained. In this study, we reviewed the design of directly coupled SQUID gradiometers and optimized their pickup loops. Several gradiometers with pickup loops of different sizes were fabricated. To evaluate these gradiometers, we applied a small magnetic field produced by a magnetic field coil with a small diameter (effective diameter: 0.65 mm) to them. The sensitivity distribution of these gradiometers was evaluated using a special mechanism that allows for complete scanning over the device substrate. As a result, the magnitude of the peak value could be explained by an inductance imbalance between the pickup loop and the SQUID. Finally, we could find the optimal pickup coil design conditions. Furthermore, we could capture the sensitivity distribution of a small SQUID loop placed in the center of the device.

A feasible path for the use of ferromagnetic josephson junctions in quantum circuits: The ferro-transmon

We discuss the capabilities of ferromagnetic (F) Josephson junctions (JJs) in a variety of layouts and configurations. The main goal is to demonstrate the potential of these hybrid JJs to disclose new physics and the possibility to integrate them in superconducting classical and quantum electronics for various applications. The feasible path towards the use of ferromagnetic Josephson junctions in quantum circuits starts from experiments demonstrating macroscopic quantum tunneling in NbN/GdN/NbN junctions with ferro-insulator barriers and with triplet components of the supercurrent, supported by a self-consistent electrodynamic characterization as a function of the barrier thickness. This has inspired further studies on tunnel ferromagnetic junctions with a different layout and promoted the first generation of ferromagnetic Al-based JJs, specifically Al/AlOx/Al/Py/Al. This layout takes advantage of the capability to integrate the ferromagnetic layer in the junction without affecting the quality of the superconducting electrodes and of the tunnel barrier. The high quality of the devices paves the way for the possible implementation of Al tunnel-ferromagnetic JJs in superconducting quantum circuits. These achievements have promoted the notion of a novel type of qubit incorporating ferromagnetic JJs. This qubit is based on a transmon design featuring a tunnel JJ in parallel with a ferromagnetic JJ inside a SQUID loop capacitively coupled to a superconducting readout resonator. The effect of an external RF field on the magnetic switching processes of ferromagnetic JJs has been also investigated.

Asymmetric higher-harmonic SQUID as a Josephson diode

We theoretically investigate asymmetric two-junction SQUIDs with different current-phase relations in the two Josephson junctions, involving higher Josephson harmonics. Our main focus is on the "minimal model" with one junction in the SQUID loop possessing the sinusoidal current-phase relation and the other one featuring additional second harmonic. The current-voltage characteristic (CVC) turns out to be asymmetric, $I(-V) \neq -I(V)$. The asymmetry is due to the presence of the second harmonic and depends on the magnetic flux through the interferometer loop, vanishing only at special values of the flux such as integer or half-integer in the units of the flux quantum. The system thus demonstrates the flux-tunable Josephson diode effect (JDE), the simplest manifestations of which is the direction dependence of the critical current. We analyze asymmetry of the overall $I(V)$ shape both in the absence and in the presence of external ac irradiation. In the voltage-source case of external signal, the CVC demonstrates the Shapiro spikes. The integer spikes are asymmetric (manifestation of the JDE) while the half-integer spikes remain symmetric. In the current-source case, the CVC demonstrates the Shapiro steps. The JDE manifests itself in asymmetry of the overall CVC shape, including integer and half-integer steps.

The Role of Coupling Radius in 1-D Parallel and 2-D SQUID and SQIF Arrays

We investigate theoretically the effect of the coupling radius on the transfer function in 1D parallel and 2D SQUID arrays with different number of Josephson junctions in parallel and series at 77 K. Our results show a plateauing of the array maximum transfer function with the number of junctions in parallel. The plateauing defines the array coupling radius which we show increases with decreasing the normalised inductive reactance of the SQUID loop. The coupling radius is found to be independent of the number of junctions in series. Finally, we investigate the voltage versus magnetic field response and maximum transfer function of one 1D and two 2D SQIF arrays with different SQUID loop area distributions.

Phase-dependent microwave response of a graphene Josephson junction

Gate-tunable Josephson junctions embedded in a microwave environment provide a promising platform to in-situ engineer and optimize novel superconducting quantum circuits. The key quantity for the circuit design is the phase-dependent complex admittance of the junction, which can be probed by sensing an rf SQUID with a tank circuit. Here, we investigate a graphene-based Josephson junction as a prototype gate-tunable element enclosed in a SQUID loop that is inductively coupled to a superconducting resonator operating at 3 GHz. With a concise circuit model that describes the dispersive and dissipative response of the coupled system, we extract the phase-dependent junction admittance corrected for self-screening of the SQUID loop. We decompose the admittance into the current-phase relation and the phase-dependent loss and as these quantities are dictated by the spectrum and population dynamics of the supercurrent-carrying Andreev bound states, we gain insight to the underlying microscopic transport mechanisms in the junction. We theoretically reproduce the experimental results by considering a short, diffusive junction model that takes into account the interaction between the Andreev spectrum and the electromagnetic environment, from which we deduce a lifetime of ~17 ps for non-equilibrium populations.

Nonlinear Charge- and Flux-Tunable Cavity Derived From an Embedded Cooper-Pair Transistor

We introduce the cavity-embedded Cooper pair transistor (cCPT), a device which behaves as a highly nonlinear microwave cavity whose resonant frequency can be tuned both by charging a gate capacitor and by threading flux through a SQUID loop. We characterize this device and find excellent agreement between theory and experiment. A key difficulty in this characterization is the presence of frequency fluctuations comparable in scale to the cavity linewidth, which deform our measured resonance circles in accordance with recent theoretical predictions [Brock et al., Phys. Rev. Applied 14, 054026 (2020)]. By measuring the power spectral density of these frequency fluctuations at carefully chosen points in parameter space, we find that they are primarily a result of the $1/f$ charge and flux noise common in solid state devices. Notably, we also observe key signatures of frequency fluctuations induced by quantum fluctuations in the cavity field via the Kerr nonlinearity.

High transfer coefficient niobium nano-SQUID integrated with a nanogap modulation flux line

Nano-superconducting quantum interference devices (nano-SQUIDs) with high energy sensitivity and spatial resolution are essential in many applications such as single spin detection, nano-electromechanical vibration detection and microscale magnetic imaging. This paper studies a Dayem-type niobium nano-SQUID using focus ion beam milling technology. The device has two 42 nm × 60 nm nano-bridges and an integrated on-chip Nb modulation flux line located beside the SQUID loop with a 100 nm nanogap. The non-hysteretic temperature range of the nano-SQUID is about 1.4 K from 4.6 K to 6.0 K, which could broaden the operation temperature range of the device. The maximal transfer coefficient V Φ and peak-to-peak voltage ΔV are 8.53 mV/Φ 0 and 430 μV at 4.8 K, respectively.

Analysis of LC-Resonance in DC SQUID Using Dynamic System Model

Direct current superconducting quantum interference device (dc SQUID) can be regarded as a hybrid system with two nonlinear Josephson currents driving a linear network consists of conventional resistors (R), inductors (L), and capacitors (C). There must be LC resonances inside the SQUID loop with influences on its static current-voltage characteristics. To study the working principle of the LC resonance, we build an equivalent dynamic system model transformed directly from the circuit equations of dc SQUID. With dynamic system analyses in both dc and alternating current (ac) domains, we derive the analytical expressions of the resonance point with only the RLC circuit parameters. The analytical derivation proves that the LC resonance inside a symmetrical dc SQUID with resonance frequency ω = 1/√LC results in the flux modulation suppression with I-V curves concentrated on one resonance point. Based on those mathematical expressions, the resonance point is easily indentified from the measured I-V curves, and can be utilized for practical SQUID parameters characterization.

Optimal SQUID Loop Size in Arrays of HTS SQUIDs

Arrays of Superconducting interference devices (SQUIDs) deserve much attention for high frequency magnetic field detection because of the combined advantages of wideband radiofrequency operation and improved dynamic range compared to single SQUID magnetometers. Indeed, in principle the dynamic range should scale as the square root of the number of SQUIDs. It is well-known that the size of a SQUID designed for magnetometry has an optimum resulting from a trade-off between large magnetic flux in its loop and small loop inductance. Among the factors affecting this optimum when using arrays of SQUIDs, we discuss the impact of Josephson junction characteristic dispersion, experimentally observed with high temperature superconductors (HTS) and wideband requirement. Both limit the SQUID size to lower values, in particular for arrays of SQUIDs connected in series.

Characterizing and Optimizing Qubit Coherence Based on SQUID Geometry

The dominant source of decoherence in contemporary frequency-tunable superconducting qubits is 1/$f$ flux noise. To understand its origin and find ways to minimize its impact, we systematically study flux noise amplitudes in more than 50 flux qubits with varied SQUID geometry parameters and compare our results to a microscopic model of magnetic spin defects located at the interfaces surrounding the SQUID loops. Our data are in agreement with an extension of the previously proposed model, based on numerical simulations of the current distribution in the investigated SQUIDs. Our results and detailed model provide a guide for minimizing the flux noise susceptibility in future circuits.

Planar MoRe-based direct current nanoSQUID

We have developed planar nanoSQUID with nanobridge-type Josephson junctions based on the oxidation resistant and high Hc2 MoRe alloy. The objective of the research was to reduce size of the SQUID loop with the aim being to reduce magnetic flux noise and improve the spatial resolution of the SQUID sensors. Employing RF-magnetron sputtering, electron-beam lithography, and reactive ion etching in CHF3 + O2 plasma using Al hard masks, we have realized nanoSQUIDs with Josephson junctions in the form of 30 − 50 nm wide nanobridges and an effective magnetic flux capture radius of ~ 95 nm. The critical temperature of the fabricated devices was Tc = 7.9 K. The I(V)-characteristics demonstrated critical current I0≃ 114 µA at 4.2 K and modulation period in magnetic fields of ~ 700 Oe.

Voltage-controlled superconducting magnetic memory

Over the past few decades, superconducting circuits have been used to realize various novel electronic devices such as quantum bits, SQUIDs, parametric amplifiers, etc. One domain, however, where superconducting circuits fall short is information storage. Superconducting memories are based on the quantization of magnetic flux in superconducting loops. Standard implementations store information as magnetic flux quanta in a superconducting loop interrupted by two Josephson junctions (i.e., a SQUID). However, due to the large inductance required, the size of the SQUID loop cannot be scaled below several micrometers, resulting in low-density memory chips. Here, we propose a scalable memory consisting of a voltage-biased superconducting ring threaded by a half-quantum flux bias. By numerically solving the time-dependent Ginzburg-Landau equations, we show that applying a time-dependent bias voltage in the microwave range constitutes a writing mechanism to change the number of stored flux quanta within the ring. Since the proposed device does not require a large loop inductance, it can be scaled down, enabling a high-density memory technology.

Onset of phase diffusion in high kinetic inductance granular aluminum micro-SQUIDs

Superconducting granular aluminum is attracting increasing interest due to its high kinetic inductance and low dissipation, favoring its use in kinetic inductance particle detectors, superconducting resonators or quantum bits. We perform switching current measurements on DC-SQUIDs, obtained by introducing two identical geometric constrictions in granular aluminum rings of various normal-state resistivities in the range from ρn = 250–5550 μΩ cm. The relative high kinetic inductance of the SQUID loop, in the range of tens of nH, leads to a suppression of the modulation in the measured switching current versus magnetic flux, accompanied by a distortion towards a triangular shape. We observe a change in the temperature dependence of the switching current histograms with increasing normal-state film resistivity. This behavior suggests the onset of a diffusive motion of the superconducting phase across the constrictions in the two-dimensional washboard potential of the SQUIDs, which could be caused by a change of the local electromagnetic environment of films with increasing normal-state resistivities.

Controlled Stochastic Amplification of a Weak Signal in a Superconducting Quantum Interferometer

In a single-junction niobium superconducting quantum interferometer (RF SQUID loop), a weak low-frequency harmonic signal is amplified when quasi-white Gaussian noise magnetic flux is applied to the loop; such amplification is due to stochastic resonance (SR). We have experimentally shown that if the suboptimal flux noise intensity is insufficient for SR, the mean rate of transitions between the metastable states of the loop, and thus the signal gain, can be controlled by an additional deterministic alternating magnetic flux with frequency being much higher than that of the useful signal to provide the maximal possible gain. The frequency characteristics of a multi-tone composite signal amplification in the cases of controlled stochastic amplification and “pure” SR are compared to each other.

Phase controllable Josephson junctions for cryogenic memory

Josephson junctions containing ferromagnetic layers have generated interest for application in cryogenic memory. In a junction containing both a magnetically hard fixed layer and soft free layer with carefully chosen thicknesses, the ground-state phase difference of the junction can be controllably switched between 0 and π by changing the relative orientation of the two ferromagnetic layers from antiparallel to parallel. This phase switching has been observed in junctions using Ni fixed layers and NiFe free layers. We present phase-sensitive measurements of such junctions in low-inductance symmetric SQUID loops which simplify analysis relative to our previous work. We confirm controllable 0−π switching in junctions with 2.0 nm Ni fixed layers and 1.25 nm NiFe free layers across multiple devices and using two SQUID designs, expanding the phase diagram of known thicknesses that permit phase control.

Performance Optimization of a Three-Dimensional NanoSQUID Based on Niobium Tunnel Nanojunctions

We report results about an optimized three-dimensional nanoSQUID based on niobium tunnel nanojunctions having the loop suspended to reduce the parasitic capacitance. The SQUID loop has a size of 400 × 600 nm 2 while the dimension of the square tunnel nanojunctions is 150 × 150 nm 2 with a density of the critical current of about 35 × 10 3 A/cm 2 . The nanodevice has been characterized at liquid helium temperature; it has shown nonhysteretic current-voltage characteristics and smooth voltage- magnetic flux characteristics resulting in a very stable operation in a wide range of bias points. The spectral density of the magnetic flux noise in the white region, measured with a two-stage noise measurement setup, was as low as 300 nΦ 0 /Hz 1/2 corresponding to a spin sensitivity of few Bohr magnetons for bandwidth unit.

Analysing magnetism using scanning SQUID microscopy.

Scanning superconducting quantum interference device microscopy (SSM) is a scanning probe technique that images local magnetic flux, which allows for mapping of magnetic fields with high field and spatial accuracy. Many studies involving SSM have been published in the last few decades, using SSM to make qualitative statements about magnetism. However, quantitative analysis using SSM has received less attention. In this work, we discuss several aspects of interpreting SSM images and methods to improve quantitative analysis. First, we analyse the spatial resolution and how it depends on several factors. Second, we discuss the analysis of SSM scans and the information obtained from the SSM data. Using simulations, we show how signals evolve as a function of changing scan height, SQUID loop size, magnetization strength, and orientation. We also investigated 2-dimensional autocorrelation analysis to extract information about the size, shape, and symmetry of magnetic features. Finally, we provide an outlook on possible future applications and improvements.