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Input impedance of a single-contact SQUID

S.S. Tinchev

Published Oct 1, 1982• 0 citations
OpenAlex

Abstract

The performance of an rf SQUID is analyzed when the pumping frequency ..omega.. is comparable to the resonant frequency R/L of the interferometer. The SQUID input impedance is measured for different values of the parameter q = ..omega..L/R< or =..pi../4, input signal frequency, and pump frequency mismatch relative to the resonant frequency of the oscillating SQUID circuit. It is shown that the input resistance and input inductance of the squId may be either positive or negative.

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arXiv:1311.2063•EPJ Quantum Technology•Mar 7, 2014•29 citations
The performance of an rf SQUID is analyzed when the pumping frequency ..omega.. is comparable to the resonant frequency R/L of the interferometer. The SQUID input impedance is measured for different values of the parameter q = ..omega..L/R< or =..pi../4, input signal frequency, and pump frequency mismatch relative to the resonant frequency of the oscillating SQUID circuit. It is shown that the input resistance and input inductance of the squId may be either positive or negative.
A simple method is developed for analysis of the RF SQUID in regime, where the bias frequency ω is comparable to the natural R/L frequency of the SQUID ring. The input impedance of the RF SQUID is calculated for various values of the parametersq = \omega L/R\leq \leq \pi/4, signal frequency and detuning of the rf bias frequency from tank circuit resonant frequency. It is shown, that both the input resistance and the input inductance may be positive or negative. Measurement of the real part of the input impedance of a hysteretic RF SQUID are described. The experimental data are in qualitative agreement with the prediction of the theory.
Using a superconducting ring containing a Nb point contact inductively coupled to a resonant circuit fed with an rf current source, (typical rf SQUID configuration) we have measured the tank voltage as a function of frequency in the regimeLI_{c}< \Phi_{0}/2\pi. ForLI_{c} \ll \Phi_{0}/2\pi, the curves of tank voltage versus drive current for various values of external flux\Phi_{x}through the ring agree with the calculations of Hansma. For higher critical currents, there is an asymmetry in these curves for frequencies above and below ω0, the resonant frequency of the circuit. Calculations using an expanded theory including the effects of a conductanceG_{o}(1+\alpha \cos \phi)and of screening flux give good agreement with the data. In principle α can be determined from these measurements, however the\cos \phiterm and the screening flux produce qualitatively similar effects. A quantitative determination of α requires a precise knowledge of Go/Ic. Using values of Goand Icfrom independent impedance measurements, the data yield a negative value of α in agreement with another experiment.
An experimental method to measure the imaginary and real part of the input impedance of an rf biased SQUID is described. The experimental results are in good agreement with the predictions of a detailed theoretical model of the rf SQUID, recently published. In particular it seems confirmed that the real part of the input impedance has a negative value which depends on the square of the input signal frequency. This effect must be taken into account whenever a SQUID is used to measure high frequency signals.
A superconducting ring containing a Nb point contact inductively coupled to a resonant circuit fed with an rf current source (typical rf SQUID configuration) was used to measure the tank voltage as a function of frequency in the regime LI/sub c/ less than PHOI/sub 0//2..pi... For LI/sub c/ much less than PHI/sub 0//2..pi.., the curves of tank voltage versus drive current for various values of external flux PHI/sub x/ through the ring agree with the calculations of Hansma. For higher critical currents, there is an asymmetry in these curves for frequencies above and below ..omega../sub 0/, the resonant frequency of the circuit. Calculations using an expanded theory including the effects of a conductance G/sub 0/(1 + ..cap alpha.. cos phi) and of screening flux give good agreement with the data. In principle, ..cap alpha.. can be determined from these measurements, but the cos phi term and the screening flux produce qualitatively similar effects. A quantitative determination of ..cap alpha.. requires a precise knowledge of G/sub 0//I/sub c/. Using values of G/sub 0/ and I/sub c/ from independent impedance measurements, the data yield a negative value of ..cap alpha.., in agreement with another experiment. (auth)
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.
A Superconducting QUantum Interference Device (SQUID) modulated by a fast oscillating magnetic flux can be used as a parametric amplifier, providing gain with very little added noise. Here, we develop linearized models to describe the parametrically flux-pumped SQUID in terms of an impedance. An unpumped SQUID acts as an inductance, the Josephson inductance, whereas a flux-pumped SQUID develops an additional, parallel element which we have coined the “pumpistor.” Parametric gain can be understood as a result of a negative resistance of the pumpistor. In the degenerate case, the gain is sensitive to the relative phase between the pump and signal. In the nondegenerate case, gain is independent of this phase. We develop our models first for degenerate parametric pumping in the three-wave and four-wave cases, where the pump frequency is either twice or equal to the signal frequency, respectively. We then derive expressions for the nondegenerate case where the pump frequency is not a multiple of the signal frequency, for which it becomes necessary to consider idler tones that occur. For the nondegenerate three-wave case, we present an intuitive picture for a parametric amplifier containing a flux-pumped SQUID where current at the signal frequency depends upon the load impedance at an idler frequency. This understanding provides insight and readily testable predictions of circuits containing flux-pumped SQUIDs.