Dc Superconducting Quantum Interference Device Research Articles

Current Correlation in Single-Electron Current Mirror Electromagnetically Dual to Josephson Voltage Mirror

The electromagnetic duality between single-electron devices and Josephson devices sometimes helps us to develop new electron devices. In this article, a single-electron turnstile is discussed as a dual device to a dc superconducting quantum interference device (dc-SQUID). From the viewpoint of the device characteristics, a single-electron turnstile has better duality to a dc-SQUID than a single-electron transistor. Next, a current mirror based on single-electron turnstiles is introduced as a dual circuit corresponding to a Josephson voltage mirror. A test circuit of a current mirror was fabricated using electron beam lithography and aluminum shadow evaporation. Although the precise current mirror operation was not obtained, we observed two currents approaching each other. Simulation based on the Monte Carlo method succeeded in reproducing the experimental results. Numerical results indicate that insufficient capacitive coupling, nonnegligible parasitic capacitances, and short array length deteriorate the current mirror operation.

A SQUID-Based Nondestructive Evaluation System for Testing Wires of Arbitrary Length

The high field sensitivity of superconducting quantum interference devices (SQUIDs), especially at low frequencies, makes them ideally suited for applications in nondestructive evaluation. For testing of conducting wires, such as aluminum bond wire, we developed a special cryostat, which allows for pulling a wire of arbitrary length (which is kept at room temperature) through a niobium flux transformer connected to a niobium dc SQUID. The wire is excited by either passing an alternating current through it, or by exciting eddy-currents in the wire. The cryostat is made from a stainless steel inner vessel; the outer tube is from fiberglass. The gradiometric pickup loops are wound on a German-silver tube. As the wire under test is at room temperature, thermal noise produced by the wire is limiting the sensitivity of the system, rather than thermal noise produced by the stainless steel dewar.

Two-mode squeezed states and entangled states of two mechanical resonators

We study a device consisting of a dc superconducting quantum interference device (SQUID) with two sections of its loop acting as two mechanical resonators. An analog of the parametric down-conversion process in quantum optics can be realized with this device. We show that a two-mode squeezed state can be generated for two overdamped mechanical resonators, where the damping constants of the two mechanical resonators are larger than the coupling strengths between the dc-SQUID and the two mechanical resonators. Thus we show that entangled states of these two mechanical resonators can be generated.

CRITICAL CURRENT DEPENDENCE OF STACKED JOSEPHSON JUNCTIONS DC SQUID IN Bi2Sr2CaCu2O8+Δ

We investigate critical current (Ic) modulation of stacked Josephson junctions (SJJs) dc superconducting quantum interference device ( dc SQUID) on a Bi 2 Sr 2 CaCu 2 O 8+δ ( Bi -2212) whisker. A coupled SJJs with a completely perforated hole of 0.1 μ m × 0.2 μ m were fabricated by using a 3-D focused-ion-beam (FIB) etching method. Those dc SQUIDs exhibited uniform multi-branch structures and clearly oscillated critical current under external magnetic fields (He). With applying He, the clear periodic modulation patterns of Ic are obtained and well fitted to the calculated value from the loop area of 0.02 μm2.

Nanosecond quantum state detection in a current-biased dc SQUID

This paper presents our procedure to measure the quantum state of a dc superconducting quantum interference device (SQUID) within a few nanoseconds, using an adiabatic dc flux pulse. Detection of the ground state is governed by standard macroscopic quantum tunneling (MQT) theory, with a small correction due to residual noise in the bias current. In the two-level limit, where the SQUID constitutes a phase qubit, an observed contrast of 0.54 indicates a significant loss in contrast compared to the MQT prediction. It is attributed to spurious depolarization (loss of excited state occupancy) during the leading edge of the adiabatic flux measurement pulse. We give a simple phenomenological relaxation model which is able to predict the observed contrast of multilevel Rabi oscillations for various microwave amplitudes.

Analytical results of the Fokker–Planck equation derived for one superconducting nanowirequantum interference device and for DC SQUID: symmetric devices

We consider a symmetric two-junction superconducting quantum interference device,whose junctions are assumed to be overdamped, and consider the sin Fourier seriesfor their current–phase relations. We take into account the effects of thermalfluctuations by forming a two-dimensional Fokker–Planck equation for the distributionfunction. We judge a series expansion of first order with respect to the componentsof the reduced inductance for the distribution function and obtain relations forcurrent–voltage and the circulating current. We consider the measured resistance of thesuperconducting nanowire quantum interference device with mesoscopic leadsthat Hopkins et al reported in Hopkins et al (2005 Science 308 1762) and Pekkeret al (2005 Phys. Rev. B 72 104517), by defining the loop inductance, and byconsidering appropriate relations for the resistance of nanowires. In fact, we extendthe Chesca formulation (Chesca 1998 J. Low Temp. Phys. 112 165) and give aunification formulation for symmetric nanowire two-junction devices, low and highTc DC superconducting quantum interference devices (SQUIDs) in restricted conditions.

Potential Characterization of a Double SQUID Device for Quantum Computing Experiments

We report on experiments performed on a system consisting of a double SQUID (superconducting quantum interference device) built with gradiometer geometry. Two single-turn coils provide two independent control fluxes: one of these allows biasing the device and tilting the potential, while the other changes the barrier height of the potential. When the dynamics of the inner dc SQUID can be neglected, the free energy of the double SQUID, as a function of the internal magnetic flux, is just the corrugated parabola of an rf SQUID whose local minima represent metastable states for the system. Our analysis instead is substantially concerned with the interesting phenomenology generated by the static configurations of an internal two-junction interferometer and by the tunability of the internal loop inductance. Two readout systems are employed to thoroughly characterize the dynamics of our system. We investigate the dynamical response at temperatures low enough (tens of mK) to minimize the effects of thermal fluctuations concentrating the analysis on the aspects that could be relevant for macroscopic quantum coherence and computing. The results indicate that from the finite inductance of the inner loop originates a potential well generating competing processes with the tunneling between the two main wells of the rf-SQUID potential.

Characteristics of Switchable Superconducting Flux Transformer with DC Superconducting Quantum Interference Device

We have investigated the flux transfer characteristics of a switchable flux transformer comprising a superconducting loop and a DC superconducting quantum interference device (DC-SQUID). This system can be used to couple multiple flux qubits with a controllable coupling strength. Its characteristics were measured using a flux input coil and a DC-SQUID for readout coupled to the transformer loop in a dilution refrigerator. The observed characteristics are consistent with the calculation results. We have demonstrated the reversal of the slope of the characteristics and the complete switching off of the transformer, which are useful features for its application as a controllable coupler for flux qubits.

Solid-State Qubits with Current-Controlled Coupling

The ability to switch the coupling between quantum bits (qubits) on and off is essential for implementing many quantum-computing algorithms. We demonstrated such control with two flux qubits coupled together through their mutual inductances and through the dc superconducting quantum interference device (SQUID) that reads out their magnetic flux states. A bias current applied to the SQUID in the zero-voltage state induced a change in the dynamic inductance, reducing the coupling energy controllably to zero and reversing its sign.

Low temperature magnetic susceptometer based upon a dc superconducting quantum interference device

A low temperature magnetic susceptometer was constructed by combining an Oxford Instruments Heliox probe sorption pumped He3 cryostat with a Quantum Design model 5000 dc superconducting quantum interference device sensor, giving an effective temperature range from 300mKto4.2K. The smallest resolvable change in magnetic moment detected by this system was found to be Δ∼1×10−12JT−1 (1×10−9emu).

Hard Magnetic Dots for Flux Bias of DC SQUIDs

In this paper, we demonstrate that perpendicularly magnetized sub- and micrometer-sized magnetic dots, with a high coercivity and nearly complete remanence, can be used to provide the flux bias for dc superconducting quantum interference devices (SQUIDs). The radius of a submicrometer Co-Pd magnetic dot has been optimized with respect to the surrounding superconducting circuitry to generate the phase shift of approximately pi/2 in it. In this way, it is possible to bias a dc SQUID to the steepest part of its voltage-flux characteristic without using an additional coil and current source. Furthermore, it has been shown that the flux bias can also be achieved using a micrometer-sized Co-Pd dot, upon saturation, by placing a dc SQUID on top of the dot. Given that the underlying principles of flux biasing do not require any particular superconducting pairing scheme (s- or d-wave), these hybrid superconductor/ferromagnet structures can be used as to design a dc SQUID with a complete flux self-biasing

Cooperative dynamics in coupled noisy dynamical systems near a critical point: The dc superconducting quantum interference device as a case study

Dynamical systems that operate near the onset of coupling-induced oscillations can exhibit enhanced sensitivity to external perturbations under suitable operating parameters. This cooperative behavior and the attendant enhancement in the system response (quantified here via a signal-to-noise ratio at the fundamental of the coupling-induced oscillation frequency) are investigated in this work. As a prototype, we study an array of dc superconducting quantum interference device (SQUID) rings locally coupled, unidirectionally as well as bidirectionally, in a ring configuration; it is well known that each individual SQUID can be biased through a saddle-node bifurcation to oscillatory behavior. We show that biasing the array near the bifurcation point of coupling-induced oscillations can lead to a significant performance enhancement.

High slew rate, ultrastable direct-coupled readout for dc superconducting quantum interference devices

A very fast and thermostable readout electronics for dc superconducting quantum interference devices (SQUIDs) is presented. The authors have applied a concept which gives them the opportunity to combine several, at first sight contradictory, important parameters for the SQUID system user. With their flux-locked-loop electronics they could reach more than 16MΦ0∕s slew rate while using a 1.3m cable between the electronics and a conventional low transition temperature SQUID (with a maximum peak-peak voltage of the flux-to-voltage transfer function of ⩾63μV). By making use of thermocurrent compensation in the first stage of the amplifier they have achieved a thermal drift of about 5nV∕K for a temperature range between 0 and 65°C. The system demonstrated a white noise voltage level of ∼0.32nV∕Hz1∕2, with a flicker noise corner frequency of about 0.1Hz.

Ultra-low-drift and very fast dc SQUID readout electronics

High-slew rate and thermo-stable readout electronics for dc superconducting quantum interference devices (SQUIDs) is presented. This electronics represents an optimum combination of the most important parameters for the SQUID-system user. In the new flux-locked loop (FLL) - unit design we have decreased a voltage white noise level down to the 0.32 nV/Hz½, with a flicker noise corner frequency of ∼0.1 Hz. By making use of electro-thermal feedback in the first stage amplifier, and multi-loop conventional feedback throughout the whole amplifier we have achieved a very low thermal drift <10 nV/K for T = 20 - 65 °C. FLL gain stability is improved down to ∼1% for the temperature range 10 - 60 °C and for 5 V (peak-peak) ± 30% of the power supplier voltage range. The maximum gain bandwidth product of the FLL-unit was increased 10 times up to ∼5 GHz. In turn, we could reach more than 10 Mϕ0/s slew rate while using a conventional LTS SQUID (connected to the FLL by a 1.2 meterlength twisted pair), with a maximum voltage of the field-to-flux transfer function of ⩾60 µV (peak-peak). At the same time, we reduced by 40% the number of chips used in the FLL unit.

Digitally controlled high-performance dc SQUID readout electronics for a 304-channel vector magnetometer

Recently, we have developed a family of dc superconducting quantum interference device (SQUID) readout electronics for several applications. These electronics comprise a low-noise preamplifier followed by an integrator, and an analog SQUID bias circuit. A highly-compact low-power version with a flux-locked loop bandwidth of 0.3 MHz and a white noise level of 1 nV/√Hz was specially designed for a 304-channel low-Tc dc SQUID vector magnetometer, intended to operate in the new Berlin Magnetically Shielded Room (BMSR-2). In order to minimize the space needed to mount the electronics on top of the dewar and to minimize the power consumption, we have integrated four electronics channels on one 3 cm × 10 cm sized board. Furthermore we embedded the analog components of these four channels into a digitally controlled system including an in-system programmable microcontroller. Four of these integrated boards were combined to one module with a size of 4 cm × 4 cm × 16 cm. 19 of these modules were implemented, resulting in a total power consumption of about 61 W. To initialize the 304 channels and to service the system we have developed software tools running on a laptop computer. By means of these software tools the microcontrollers are fed with all required data such as the working points, the characteristic parameters of the sensors (noise, voltage swing), or the sensor position inside of the vector magnetometer system. In this paper, the developed electronics including the software tools are described, and first results are presented.

Decoherence processes in a current biased dc SQUID

A current biased dc superconducting quantum interference device behaves as an anharmonic quantum oscillator controlled by a bias current and an applied magnetic flux. We consider here its two level limit consisting of the two lower energy states \ensuremath{\mid}0⟩ and \ensuremath{\mid}1⟩. We have measured energy relaxation times and microwave absorption for different bias currents and fluxes in the low microwave power limit. Decoherence times are extracted. The low frequency flux and current noise have been measured independently by analyzing the probability of current switching from the superconducting to the finite voltage state, as a function of applied flux. The high frequency part of the current noise is derived from the electromagnetic environment of the circuit. The decoherence of this quantum circuit can be fully accounted for by these current and flux noise sources.

Improving the sensitivity of ahigh-Tc SQUID at MHz frequency using a normal metal transformer

Superconducting quantum interference devices (SQUIDs) can be used to detectthe signals of nuclear quadrupole resonance (NQR). The NQR frequencies ofsome interesting materials are in the order of MHz. However, the sensitivity of ahigh-Tc SQUID is normally not enough to detect the weak NQR signals. To improve the sensitivity of ahigh-Tc SQUID at MHz frequency, we used a transformer made of normal copper wire.The transformer was composed of a pickup coil, an input coil and a capacitor.The pickup coil was used to detect the magnetic field; the input coil was used tocouple the field to the SQUID; and the capacitor was used to create a resonantfrequency. By using the normal metal transformer, the magnetic field resolution of thehigh-Tc dc SQUID was improved by about 38.8 times (from 220 to5.67 fT Hz−1/2) at 954 kHz.

Low-noise ultra-high-speed dc SQUID readout electronics

User-friendly ultra-high-speed readout electronics for dc superconducting quantuminterference devices (SQUIDs) are presented. To maximize the system bandwidth, theSQUID is directly read out without flux modulation. A composite preamplifier is usedconsisting of a slow dc amplifier in parallel with a fast ac amplifier. In this way, excellent dcprecision and a high amplifier bandwidth of 50 MHz are achieved, simultaneously. A virtual50 Ω amplifier input resistance with negligible excess noise is realized by activeshunting, i.e., by applying feedback from preamplifier output to inputvia a high resistance. The white voltage and current noise levels are0.33 nV Hz−1 and 2.6 pA Hz−1/2, respectively. The electronics is fully computer controlled via a microcontroller integratedinto the flux-locked loop (FLL) board. Easy-to-use software makes the variouselectronic settings accessible. A wide bias voltage range of 1.3 mV enables thereadout of series SQUID arrays. Furthermore, additional current sources allowthe operation of two-stage SQUIDs or transition edge sensors. The electronicswas tested using various SQUIDs with input inductances between 30 nH and1.5 µH. Typically, the maximum FLL bandwidth was 20 MHz, which is close to the theoreticallimit given by transmission line delay within the FLL. Slew rates of up to4.6 Φ0 µs−1 were achieved with series SQUID arrays. Current noise levels as low as0.47 pA Hz−1/2 and coupled energysensitivities between 90 h and 500 h were measuredat 4.2 K, where h is the Planck constant. The noise did not degrade when the system bandwidth was increased tothe maximum value of about 20 MHz. With a two-stage set-up, intrinsic white energy sensitivities of30 h and 2.3 h were measured at 4.2 and 0.3 K, respectively.

Control System for Readout Electronics of Multi-Channel Magnetocardiographs Using High-Temperature DC Superconducting Quantum Interference Devices

We aimed to develop a control system for multichannel magnetocardiography (MCG) based on a high-temperature DC superconducting quantum interference device (high-Tc SQUID). To create this system, we used one oscillator as an AC bias controller to operate a multichannel high-Tc SQUID. To optimize the SQUID parameters (such as the AC bias, offset voltage), two new control sequences based on a cross-correlation method and a fast Fourier transform method were developed. Using the AC bias controller and the sequences, the typical white noise level of the SQUID was about 50–60 fT Hz-1/2 around 100 Hz. Multichannel MCG signals were detected clearly in the system with the SQUIDs. We conclude that our control system with one oscillator and new protocols can reliably operate a multichannel SQUID.

Superconducting quantum interference device with frequency-dependent damping: Readout of flux qubits

Recent experiments on superconducting flux qubits, consisting of a superconducting loop interrupted by Josephson junctions, have demonstrated quantum coherence between two different quantum states. The state of the qubit is measured with a superconducting quantum interference device (SQUID). Such measurements require the SQUID to have high resolution while exerting minimal backaction on the qubit. By designing shunts across the SQUID junctions appropriately, one can improve the measurement resolution without increasing the backaction significantly. Using a path-integral approach to analyze the Caldeira-Leggett model, we calculate the narrowing of the distribution of the switching events from the zero-voltage state of the SQUID for arbitrary shunt admittances, focusing on shunts consisting of a capacitance ${C}_{s}$ and resistance ${R}_{s}$ in series. To test this model, we fabricated a dc SQUID in which each junction is shunted with a thin-film interdigitated capacitor in series with a resistor, and measured the switching distribution as a function of temperature and applied magnetic flux. After accounting for the damping due to the SQUID leads, we found good agreement between the measured escape rates and the predictions of our model. We analyze the backaction of a shunted symmetric SQUID on a flux qubit. For the given parameters of our SQUID and realistic parameters for a flux qubit, at the degeneracy point we find a relaxation time of $113\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, which limits the decoherence time to $226\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$. Based on our analysis of the escape process, we determine that a SQUID with purely capacitive shunts should have narrow switching distributions and no dissipation.