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Japanese Journal of Applied Physics

Voltage versus Flux Relation of DC Superconducting Quantum Interference Device Using Three Josephson Junctions

Keiji Enpuku, Hideki Doi

Published Apr 1, 1994• 13 citations
Publisher

Abstract

It has been shown that the voltage versus flux (V-Φ) relation of dc superconducting quantum interference devices (SQUIDs) operating at T=77 K is degraded considerably by thermal noise. Since degradation of modulation voltage in the V-Φ relation becomes more significant when inductance increases, a very restricted range of inductance exists which can be used at T=77 K. In order to reduce the degradation due to thermal noise and to enable the use of large inductances, a new SQUID using three Josephson junctions (3J-SQUID) is proposed. Numerical simulation shows that inductance of 3J-SQUID can be increased to twice as large as that of the conventional case without degrading modulation voltage. It is also shown that modulation voltage is highly improved by damping resistance parallel to inductance. As a result, we can expect to use inductances as large as L<500 pH if 3J-SQUID with damping resistance is employed. Large inductances available in 3J-SQUID will be useful in realizing efficient coupling of external magnetic field to the SQUID inductance.

DOI
10.1143/jjap.33.1856

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It has been shown that the voltage versus flux (V-Φ) relation of dc superconducting quantum interference devices (SQUIDs) operating at T=77 K is degraded considerably by thermal noise. Since degradation of modulation voltage in the V-Φ relation becomes more significant when inductance increases, a very restricted range of inductance exists which can be used at T=77 K. In order to reduce the degradation due to thermal noise and to enable the use of large inductances, a new SQUID using three Josephson junctions (3J-SQUID) is proposed. Numerical simulation shows that inductance of 3J-SQUID can be increased to twice as large as that of the conventional case without degrading modulation voltage. It is also shown that modulation voltage is highly improved by damping resistance parallel to inductance. As a result, we can expect to use inductances as large as L<500 pH if 3J-SQUID with damping resistance is employed. Large inductances available in 3J-SQUID will be useful in realizing efficient coupling of external magnetic field to the SQUID inductance.
Effects of thermal noise on the characteristics of the dc superconducting quantum interference device (SQUID) have been studied. Numerical simulation on the SQUID characteristics operating at T=77 K has been performed by taking into account the thermal noise. It is shown that the voltage versus flux relation of the dc SQUID is degraded considerably with the thermal noise. The degradation becomes significant when the inductance of the SQUID increases. Due to this degradation, there exists significant limitation for the range of the inductance available at T=77 K, unlike the case at T=4.2 K. The maximum inductance should be around 200 pH in order to avoid significant degradation of the transfer function. This limited value of the inductance must be taken into account when we realize the SQUID coupled to an input coil. The analytical expression for the degradation of the transfer function due to the thermal noise is also obtained. The theoretical result explains experimental results reported recently.
Properties of white noise of a high-Tc dc superconducting quantum interference device (SQUID) have been studied using numerical simulation. It is shown that thermal noise at T=77 K significantly affects the noise properties of the SQUID. As a result, dependencies of noise properties on inductance become quite different from conventional results at T=4.2 K. In contrast to the case T=4.2 K, the voltage noise of the SQUID at T=77 K depends very weakly on the inductance, while the transfer function degrades rapidly with inductance. Consequently, rapid degradation of flux noise with inductance, as compared with the case T=4.2 K, is caused mainly by that of the transfer function. These simulation results explain reasonably experimental results reported recently. Therefore, it is necessary to improve the transfer function for the improvement of noise properties in the case of large inductances. Numerical simulation shows that a method for improving the transfer function using resistively shunted inductance or three Josephson junctions, which was proposed by the authors, is also useful for improving noise properties in the case of large inductances.
Two methods are proposed in order to improve the voltage modulation depth of high-T/sub c/ DC SQUIDs in the case of large inductances. One is a damping resistance parallel to the inductance, and the other is a new SQUID using three junctions, which we call 3J-SQUID. Numerical simulation shows the usefulness of the present method. Moreover. It is shown that the improvement of the voltage modulation depth results in the improvement of magnetic flux noise in the white noise region. Therefore, the present method will enable the use of large inductances. The usefulness of the present method is also confirmed partly by experimental results.>
Direct current-superconducting quantum interference devices (SQUIDs) characterized by asymmetric Josephson junctions have never been used for applications. In order to demonstrate their potential advantages, a throughout numerical analysis of different asymmetric configurations has been carried out. A damping resistance has been included in the SQUID circuit and the thermal noise associated with junction and damping resistances has been considered in the numerical model. Magnetic modulations and flux noise spectral densities have been computed as a function of many parameters (bias current, asymmetry, SQUID inductance, and damping resistance) and the performance of symmetric and asymmetric devices have been compared. The results show that, by properly optimizing the SQUID design, asymmetric SQUIDs are characterized by higher magnetic flux to voltage transfer coefficient and lower flux noise. As a result, asymmetric configurations can be very useful in all the applications where high sensitivity is required.
We have fabricated and characterized the noise performance of well-coupled Nb-Pb alloy edge junction dc superconducting quantum interference devices (SQUIDs) with a resistively shunted inductance. The extra damping resistor removes the resonances in the current-voltage characteristics resulting in a very low value of the extrinsic energy sensitivity in flux-locked-loop operation. Numerical simulations, with the junction capacitance included, indicate that the damping resistance does not degrade noise performance until it is significantly less than the junction-shunting resistance. We also tested different SQUID designs and demonstrated that a large SQUID inductance, proposed earlier to be desirable when resistively shunted, can seriously affect the low-frequency flux noise.
An analytical expression for the stationary probability distribution of the DC superconducting quantum interference device (SQUID) with a resistively shunted inductance driven by thermal noise is derived from the two-dimensional Fokker–Planck equation. The effects on the SQUID characteristics subject to a large thermal fluctuation with a noise parameter Γ>0.20 are discussed by taking into account the thermal noise in the accuracy of numerical simulation. This theory is valid for a reduced inductance β⩽1. The analytical formulae for the SQUID characteristics, e.g. the circulating current, the average voltage and the voltage modulation, are obtained and discussed. The theory shows that the voltage modulation increases with the shunted inductance more efficiently for a large inductance parameter β and small fluctuation parameter Γ.