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Journal of Applied Physics

Influence of the tank circuit noise on the dc impedance of the rf-biased R-SQUID

Heikki Seppä

Published May 1, 1989• 1 citation
Publisher

Abstract

The tank circuit noise in an rf-biased R-SQUID noise thermometer is shown to have a small but a detectable influence on the dc impedance of the resistively shunted Josephson junction. The result supplements earlier calculations which have been used to explain some of the experimentally observed characteristics of the dc impedance.
DOI
10.1063/1.342634

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The dc -impedance of an rf-biased R-SQUID is studied analytically for the nonhysteretic regime. A mathematical analysis of the intrinsic behavior of an R-SQUID, including the mutual interaction between the tank circuit and the SQUID loop, is presented. The results obtained give good agreement with some experimentally observed features. Although the main aim of the present paper was to find an analytic solution for the dc -impedance of an R-SQUID, the results given here can also be used to estimate the R-SQUID parameters and to optimize the performance of a R-SQUID noise thermometer. The theory presented here also provides a good basis for modelling the noise properties of a Josephson junction noise thermometer.
The impedance and noise of a resistive superconductive quantum interference device (R-SQUID) have been measured as a function of the dc and rf currents applied to it. The Josephson junction was adjustable so that data were also taken for several values of the junction critical current. The results were compared with the predictions of a resistively shunted junction (RSJ) model which takes into account the influence of the Josephson junction on the impedance and noise. The agreement was found to be quite good and demonstrates that the noise in the circuit is well understood. Use of the R-SQUID as a noise thermometer below 1 K is assessed in terms of corrections due to the RSJ model. It is demonstrated how the dc and rf currents may be adjusted so that the total noise of the R-SQUID is reduced to within 0.1% of the Johnson noise generated by the resistor alone. Under these conditions, the R-SQUID may be used as a noise thermometer to determine thermodynamic temperature to this inaccuracy from 6 to 700 mK.
We have measured with high accuracy (100 ppm) and high precision (5--10 ppm) the impedance of a rf-driven resistive superconducting quantum interference device (SQUID) as a function of the amplitude and frequency of the radio-frequency (rf) bias, as a function of the current bias, and as a function of several other circuit parameters. We have developed the coupled differential equations for the resistive SQUID and for the rf tank circuit. The fit of the solutions of these equations to the data for nonhysteretic junctions is excellent. We were unable to develop solutions for the hysteretic case and thus simply present examples of typical data obtained in order to illustrate the differences with the nonhysteretic case. The relationship of this study to noise thermometry using resistive SQUID's is indicated.
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Noise characteristics of dc SQUIDs in large β regimes have been studied experimentally in the case when a SQUID inductance is resistively shunted. Here, β=2L I 0/Φ0 is the modulation parameter, L is the SQUID inductance, I 0 is the critical current of the Josephson junction and Φ0 is the flux quantum. It is shown experimentally that the performance of the SQUID does not degrade significantly even for large β values; for example, the minimum energy resolution of the SQUID is as small as ε=25h and the flux region where ε<50h is as wide as 0.1Φ0, even for the case β=12, where h is the Planck constant. The experimental results agree quantitatively with the theoretical ones.