Rf SQUID Research Articles

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.

Control of the effective value of the critical current of the RF SQUID by the high-frequency electromagnetic field

An analysis of the influence of the high-frequency electromagnetic field on the amplitude-frequency and signal characteristics of RF SQUID and experimental verification are carried out. At low parameter βL, the RF SQUID behavior is well described analytically by the theoretical model. In experiment, basic operation scheme is used in which the interferometer is inductively connected to a resonant circuit driven by RF current at a frequency close to the resonance frequency of the circuit. It is shown that parameter βL, which distinguishes between hysteretic and nonhysteretic regimes, can be effectively adjusted to a desired value by applying the high-frequency field of a certain amplitude and frequency much higher than circuit resonance frequency. A significant increase in the conversion factor and sensitivity of the RF SQUID during this adjustment is discussed.

Development of Flux-Tuneable Inductive Nanobridge SQUIDs for Quantum Technology Applications

Niobium nanobridge SQUIDs have shown exceptional noise performance with potential applications in quantum information processing, weak signal detection and single spin detection where the nanobridge geometry should enable efficient electromagnetic coupling to implanted spins. Combining such devices with dispersive microwave readout circuitry allows the spin sensitivity to be further improved by overcoming the standard thermal limit. Here we report on the fabrication and dispersive microwave readout of an array of niobium nanobridge rf SQUIDs incorporated into a superconducting resonator, including the optimization of the nanobridge fabrication process by electron beam lithography. We show the measured flux-tuneability of the resonance is in good agreement with theory, and we also discuss how the nonlinearity of the weak-link in the resonator structure allows for the mediation of parametric effects to enhance performance.

An RF SQUID readout for a flux qubit-based microwave single photon counter

An analysis of the measurement of the magnetic flux in superconducting qubits based on RF SQUIDs was carried out with an 800 MHz bandwidth low-power-consumption cryogenic high-electron-mobility transistor amplifier. The preliminary experimental results obtained at temperatures 2 K and 4 K for RF SQUIDs in hysteretic, and in two non-hysteretic, regimes with a pump frequency of about 30 MHz are discussed. Parameters of RF SQUIDs in the hysteretic and non-hysteretic modes are analyzed within the framework of the resistively and capacitively shunted junction model for Josephson junctions. Its sensitivity at a temperature of 30 mK and frequency band (speed) are calculated and optimized to read the states of a flux qubit used as a single microwave photon counter. It is shown that an RF SQUID, operated in an adiabatic non-hysteretic mode for qubit readout, allows us to minimize its back-action effect and the dark count rate. This is due to the absence of Josephson generation, the small amplitude of the resonator electromagnetic field, and the selection of the pump frequency that does not coincide with the characteristic frequencies of the flux qubit.

The Simons Observatory: Magnetic Shielding Measurements for the Universal Multiplexing Module

The Simons Observatory (SO) includes four telescopes that will measure the temperature and polarization of the cosmic microwave background using over 60,000 highly sensitive transition-edge bolometers (TES). These multichroic TES bolometers are read out by a microwave RF SQUID multiplexing system with a multiplexing factor of 910. Given that both TESes and SQUIDs are susceptible to magnetic field pickup and that it is hard to predict how they will respond to such fields, it is important to characterize the magnetic response of these systems empirically. This information can then be used to limit spurious signals by informing magnetic shielding designs for the detectors and readout. This paper focuses on measurements of magnetic pickup with different magnetic shielding configurations for the SO universal multiplexing module (UMM), which contains the SQUIDs, associated resonators, and TES bias circuit. The magnetic pickup of a prototype UMM was tested under three shielding configurations: no shielding (copper packaging), aluminum packaging for the UMM, and a tin/lead-plated shield surrounding the entire dilution refrigerator 100 mK cold stage. The measurements show that the aluminum packaging outperforms the copper packaging by a shielding factor of 8-10, and adding the tin/lead-plated 1K shield further increases the relative shielding factor in the aluminum configuration by 1-2 orders of magnitude.

Low Frequency Noise Characteristic in HTS Step-Edge Junction Rf SQUID

Rf SQUIDs have been fabricated on MgO substrate using step-edge YBCO junction. Ion beam etching as a post fabrication trimming process is routinely used to reduce (trim) the critical current of the junction for noise optimization. The white noise of SQUIDs with inductance, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = 157 pH can be reduced to 55 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">μ</i> Φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1/2</sup> after the trimming process. However, 1/f noise at low frequency has been found to be degraded after the trimming. Rf SQUIDs with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> = 130 pH were fabricated and measured. A similar noise performance was achieved in these SQUIDs down to 5 Hz without the need of trimming. The 1/f noise was found to be better than that of the trimmed SQUIDs.

Superconducting microwave resonators with non-centrosymmetric nonlinearity

We investigated both theoretically and experimentally open-ended coplanar waveguide resonators with rf SQUIDs embedded in the central conductor at different positions. These rf SQUIDs can be tuned by an external magnetic field and thus may exhibit the non-centrosymmetric nonlinearity of type with suppressed Kerr nonlinearity. We demonstrated that this nonlinearity allows for efficient mixing of and λ modes in the cavity and thus enables various parametric effects with three wave mixing. These effects are the second harmonic generation, the halftone generation, the parametric amplification in both degenerate and non-degenerate regimes and deamplification in degenerate regime.

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.

Harmonic Analysis and Self-Tuning Control Combining Wavelet Analysis and Identification for High-Tc RF SQUID

High-T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> radio-frequency (rf) superconducting quantum interference devices are well understood and widely used in many areas of low-field measurement because of their high sensitivity and high resolution. Harmonic analysis has proven to be an efficient way for finding the optimum working point. However, there is a precondition for using harmonic analysis, which is not well understood so far. In this article, it is shown that the precondition can be fulfilled in the typical range of parameters and under our experimental conditions by using a direct mathematical derivation. It is demonstrated that the improvement of wavelet analysis in mean square error (MSE) is more than 50% for harmonic analysis. In addition, identification by forgetting factor recursive least square is a helpful way for self-tuning controller who gives fast tracking, small MSE and high coefficient of determination (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) for harmonic analysis of different experimentally measured signals.

Estimation of Critical Current of HTS RF-SQUID

The operation of the RF SQUID is restricted by the condition that the inductance parameter β L must be in the range of 1−3. However, since both ends of the Josephson junction (JJ) of RF-SQUID are shorted, it is difficult to non-destructively estimate the critical current (IC ). Thus, we proposed a technique for the non-destructive measurement of the IC of a high-temperature superconducting (HTS) RF-SQUID ring by evaluating the behaviour of the flux in superconducting thin films using a SQUID magnetometer. A superconducting ring sample with JJ was placed below the HTS SQUID magnetometer and cooled down to 77 K. The change in the SQUID output was monitored on application of the magnetic field. When increasing the field, the waveforms indicated that the screening current of the ring sample exceeded the I C of the JJ, and the JJ became a normal-conducting state. As a result, we estimated the IC of the JJ of this sample as 134 μA using the values of mutual inductance and the coupling coefficient α between the coil and the sample.

Harmonic Analysis of High-Tc Rf SQUID to Determine the Optimum Working Condition for Its Automatic Application

High-Tc radio-frequency (rf) SQUIDs are well researched and have been utilized in a range of applications. The rf SQUID operating in a nonhysteretic mode has been elaborated theoretically in a few of literatures, among which an effective method of harmonic analysis was presented to find its optimum working point. A suitable flux-to-voltage curve of the rf SQUID should be acquired before applying the harmonic analysis method, but the approach of getting the suitable curve is unclear. This article carried out an analysis with respect to the three harmonics, which primarily affect the waveform of flux-to-voltage curves and came to the condition, which need be satisfied to acquire the desirable kind of curves. In which, the one with the largest value of its maximum transfer function could be considered as working in the optimum condition. Three rf SQUIDs were employed in experiment to demonstrate the detailed procedure of determining their optimum working conditions, which were the rf frequencies and the attenuator voltages of their tank circuits. Judging from the experimental results, the method proposed in this article is very effective, the optimum working conditions of the three rf SQUIDs can be accurately obtained. The findings would be instructional for automatically setting the working conditions of high-Tc rf SQUIDs in practical applications.

Small capacitance self-shunted MoRe–Si(W)–MoRe junctions for SQUIDs applications

MoRe–Si(W)–MoRe planar Josephson junctions with a hybrid barrier layer made of amorphous silicon doped with tungsten at relatively high tungsten concentrations (~ 11%) are experimentally studied. Small intrinsic (natural) capacitance and shunting by tungsten nanoclusters give an advantage to MoRe–Si(W)–MoRe junctions against traditional superconductor–insulator–superconductor (SIS) planar junctions as candidates for innovative superconducting electronics. It is shown that the use of such junctions with a Si(W) barrier layer thickness of 15–30 nm can substantially enhance the sensitivity of both RF and DC SQUIDs.

Quantized Single-Ion-Channel Hodgkin-Huxley Model for Quantum Neurons

The Hodgkin-Huxley model describes the behavior of the cell membrane in neurons, treating each part of it as an electric circuit element, namely capacitors, memristors, and voltage sources. We focus on the activation channel of potassium ions, due to its simplicity, while keeping most of the features displayed by the original model. This reduced version is essentially a classical memristor, a resistor whose resistance depends on the history of electric signals that have crossed it, coupled to a voltage source and a capacitor. Here, we will consider a quantized Hodgkin-Huxley model based on a quantum memristor formalism. We compare the behavior of the membrane voltage and the potassium channel conductance, when the circuit is subjected to AC sources, in both classical and quantum realms. Numerical simulations show an expected adaptation of the considered channel conductance depending on the signal history in all regimes. Remarkably, the computation of higher moments of the voltage manifest purely quantum features related to the circuit zero-point energy. Finally, we study the implementation of the Hodgkin-Huxley quantum memristor as an asymmetric rf SQUID in superconducting circuits. This study may allow the construction of quantum neuron networks inspired in the brain function, as well as the design of neuromorphic quantum architectures for quantum machine learning.

On the possibility of faster detection of magnetic flux changes in a single-photon counter by RF SQUID with MoRe–Si(W)–MoRe junction

The nonhysteretic mode of a RF SQUID with a MoRe–Si(W)–MoRe Josephson junction is analyzed in order to detect the states of a single-photon counter based on a superconducting quantum interferometer with a discrete Hamiltonian. The absorption of a photon with 10 GHz frequency brings the counter to the excited level causing tunnelling into the adjacent potential well and a change in the magnetic flux in the interferometer, which can be detected by the SQUID magnetometer. Measurement of a quantum system requires minimization of the back action of the signal read-out channel at the counter, high sensitivity, and speed of the magnetometer. The MoRe–Si(W)–MoRe contacts are optimized for various concentrations of tungsten (W) in silicon (Si) and barrier layer thickness. It is shown that using MoRe–Si(W)–MoRe contacts with a tungsten concentration of approximately 11% for the RF SQUID at excitation frequencies of ∼1 GHz makes it practically an ideal parametric upward frequency shifter with noise determined by the cooled amplifier.

Tunable Superconducting Cavity using Superconducting Quantum Interference Device Metamaterials

Here we consider a tunable superconducting cavity that can be used either as a tunable coupler to a qubit inside the cavity or as a tunable low noise, low temperature, RF filter. Our design consists of an array of radio-frequency superconducting quantum interference devices (rf SQUIDs) inside a superconducting cavity. This forms a tunable metamaterial structure which couples to the cavity through its magnetic plasma frequency. By tuning the resonant frequency of the metamaterial through an applied magnetic flux, one can tune the cavity mode profile. This allows us to detune the cavity initially centered at 5.593 GHz by over 200 MHz. The maximum quality factor approaches that of the empty cavity, which is 4.5 × 106. The metamaterial electromagnetic response is controlled via a low-frequency or dc magnetic flux bias, and we present a control line architecture that is capable of applying sufficient magnetic flux bias with minimal parasitic coupling. Together this design allows for an in-situ tunable cavity which enables low-temperature quantum control applications.

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.

Theory of a quantum artificial neuron based on superconducting devices

An artificial neuron using superconducting devices, so-called rf SQUID, working at the quantum-mechanical domain is studied. It is shown that quantum rf SQUID regarded as flux qubit can act as an artificial neuron with sigmoid function generated by coherent quantum-mechanical transitions between wells in double well potential representing rf SQUID.

A micro-SQUID with dispersive readout for magnetic scanning microscopy

We have designed and characterized a micro-SQUID with dispersive readout for use in low temperature scanning probe microscopy systems. The design features a capacitively shunted RF SQUID with a tunable resonance frequency from 5 to 12 GHz, micrometer spatial resolution, and integrated superconducting coils for local application of magnetic fields. The SQUID is operated as a nonlinear oscillator with a flux- and power-dependent resonance frequency. Measurements for device characterization and noise benchmarking were carried out at 4 K. The measured flux noise above 10 kHz at 4 K is 80 nΦ0 Hz−1∕2 at a bandwidth of 200 MHz. Estimations suggest that one can benefit from parametric gain based on inherent nonlinearity of the Josephson junction and reduce the flux noise to 30 nΦ0Hz–1∕2 at 100 mK, which corresponds to 10.6 μBHz–1∕2 for a magnetic moment located at the center of the pickup loop.

HTS YBCO Resonator Configuration With a Coplanar Optimized Flux Concentrator Strongly Coupled to rf SQUID

We developed a novel magnetic coupling module formed of a monolayer superconducting flux concentrator, which is integrated with a coplanar resonator strongly coupled to HTS rf-SQUID. Three types of resonators, including a long stripline resonator between input loop and pick-up loop of the flux concentrator, a complementary split ring resonator (CSRR), and also a spiral shape inside the input loop are explored. The resonance quality factors as well as the coupling to the SQUID of different patterns of these three types of the resonators is evaluated using Finite Element Method (FEM) simulations. Several readout methods to couple the electronic system to the resonators are tested, including inductive (coil) and capacitive (transmission line) couplings, and the optimum readout is reported for each of the resonators. Among the evaluated resonator types, a spiral shape resonator with optimal design showing the highest quality factor (5900) together with the strongest coupling to the SQUID (-0.5 dB) at resonance frequency of 836 MHz, is fabricated using 200 nm thick superconducting YBCO on a 1 mm thick crystalline LaAlO3 substrate. The flux concentrator of the module is optimized by the variation of its linewidths and also its input loop radius to obtain maximum flux transformation efficiency.

Detecting fractional Josephson effect through 4π phase slip

Fractional Josephson effect is a unique character of Majorana Fermions in topological superconductor system. This effect is very difficult to detect experimentally because of the disturbance of quasiparticle poisoning and unwanted couplings in the superconductor. Here, we propose a scheme to probe the fractional DC Josephson effect of a semiconductor nanowire-based topological Josephson junction through 4π phase slip. By exploiting a topological RF SQUID system we find that the dominant contribution for Josephson coupling comes from the interaction of Majorana Fermions, resulting in a resonant tunneling with 4π phase slip. Our calculations with experimentally reachable parameters show that the time scale for detecting the phase slip is two orders of magnitude shorter than the poisoning time of nonequilibrium quasiparticles. Additionally, with a reasonable nanowire length the 4π phase slip could overwhelm the topological trivial 2π phase slip. Our work is meaningful for exploring the effect of modest quantum fluctuations of the phase of the superconductor on the topological system, and provide a new method for quantum information processing.