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Applied Physics Letters

Fine structure of voltage levels in the I-V characteristics of the rf SQUID’s

Eshel Ben‐Jacob, D. Abraham

Published Nov 15, 1981• 9 citations
Publisher

Abstract

Results of digital numerical calculations of the rf-(SQUID) superconducting quantum interference device dynamics and I-V characteristics are presented. Fine structure of voltage levels in the I-V characteristics were found. We have introduced thermal noise effects via Langevin term in the equations of motion. The thermal noise causes transitions between the voltage levels. In the case of a SQUID with an underdamped junction, negative slope can be observed, which is due to to the transition to the lower voltage levels.

DOI
10.1063/1.92576

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Journal of Applied Physics•May 1, 2001•15 citations
Results of digital numerical calculations of the rf-(SQUID) superconducting quantum interference device dynamics and I-V characteristics are presented. Fine structure of voltage levels in the I-V characteristics were found. We have introduced thermal noise effects via Langevin term in the equations of motion. The thermal noise causes transitions between the voltage levels. In the case of a SQUID with an underdamped junction, negative slope can be observed, which is due to to the transition to the lower voltage levels.
The electrical equations of a resonant circuit fed with a radio-frequency current and inductively coupled to a weakly superconducting loop have been derived. The current-voltage characteristic of the rf superconducting quantum interference device can then be calculated and studied as a function of the junction resistance or of the resonance frequency, enabling its behavior to be better understood. As shown by Kurkijärvi, the large positive slope of the steps and the rounding of the characteristic result from thermal noise. However, in order to explain quantitatively the experimental results concerning, namely, point contact weak links which are generally oxidized or which have several contact points, it is useful to remark that the connection between the two superconductors constituting the Josephson junction may be made from n resistive paths. The mean thermal energy of the fluctuating flux is then close to nkbT instead of kbT if the inductances linking the contact points are large enough, that is, on the order of 10−11 H.
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.
We measured the amplitude–frequency characteristics of radio frequency superconducting quantum interference devices (rf SQUIDs) over a temperature range between 65 and 79 K. Using the expressions derived from the recently developed rf SQUID theory, valid also at large thermal fluctuations, we determined from these data the basic parameters of high-transition-temperature superconductor (HTS) rf SQUIDs. These parameters were: (a) the high-frequency coupling coefficient between the rf SQUID and the tank circuit resonator, k, (b) the SQUIDs hysteretic parameter, β, (c) the critical current of the Josephson junction, Ic, (d) its normal resistance, Rn, and (e) its noise parameter, Γ. We found a good agreement with the values of β(Ic) and Rn determined directly after destructively opening the SQUID loop. In accordance with the theoretical predictions, our experimental results show that at large thermal fluctuation levels (T≅77 K), rf SQUIDs with large loop inductance operate in nonhysteretic mode up to β values exceeding 3. Furthermore, we have shown that the optimal energy sensitivity is attained in the nonhysteretic mode at a value of β distinctly higher than 1. A quantitative comparison of white noise predicted by the theory with that obtained from the experiment showed a reasonable agreement. We also discussed the contribution of the phase information to the SQUID’s signal and noise at optimum operation conditions, when a mixer was used as a signal detector.
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.
The time-dependent characteristics of a radio frequency superconducting quantum interference device (rf SQUID) involving two Josephson junctions connected in series are studied. First the dynamics of the total flux is given. Then the intrinsic flux noises in both nonhysteretic and hysteretic modes are investigated. The result shows that it is necessary to properly reduce the critical current ratio of the two junctions for low intrinsic noise level. When the critical current ratio is properly reduced, the intrinsic flux noise level of a two-junction rf SQUID is generally close to or slightly larger than that of a single junction rf SQUID, but no more than one order-of-magnitude.
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.