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IEEE Transactions on Magnetics

A simple method of RF-SQUID analysis and its application to a SQUID with a separate driving coil

S.S. Tinchev, K. K. Likharev, Oleg V. Snigirev

Published Jan 1, 1979• 2 citations
Publisher

Abstract

A simple method is developed for analysis of rf SQUIDs operating in the hysteretic mode, for arbitrary values of rf detuning and plateau number. For plateaus with large numbers, the reactive component of the interferometer flux is shown to be essential. The results of theoretical analysis are confirmed by experiments with a 10 MHz point-contact SQUID. The new method is applied to studies of a SQUID with a separate coil for driving flux. The response curve slope in such SQUID can be somewhat larger than that in the conventional rf SQUID. The balanced SQUID circuits are also discussed.

DOI
10.1109/tmag.1979.1060232

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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)

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Superconductor Science and Technology•Jan 6, 2023•7 citations
A simple method is developed for analysis of rf SQUIDs operating in the hysteretic mode, for arbitrary values of rf detuning and plateau number. For plateaus with large numbers, the reactive component of the interferometer flux is shown to be essential. The results of theoretical analysis are confirmed by experiments with a 10 MHz point-contact SQUID. The new method is applied to studies of a SQUID with a separate coil for driving flux. The response curve slope in such SQUID can be somewhat larger than that in the conventional rf SQUID. The balanced SQUID circuits are also discussed.
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.
In this paper a discussion is given of the noise sources and sensitivity limits of the rf biased SQUID. Both the low critical current inductive and the higher critical current hysteretic devices are considered. The intrinsic SQUID noise is treated by considering the internal flux response of a SQUID ring to an applied rf flux. While approximate, this approach yields the most direct picture of the nature of the intrinsic noise. Circuit optimization procedures for maximizing SQUID performance under various operating conditions are also outlined. Finally the effects of non-ideal weak link behavior upon SQUID operation are treated. (Author)
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 analysis of the influence of the high-frequency electromagnetic field on the amplitude-frequency and signal characteristics of RF SQUID and experimental verification are carried out. At low parameter βL, the RF SQUID behavior is well described analytically by the theoretical model. In experiment, basic operation scheme is used in which the interferometer is inductively connected to a resonant circuit driven by RF current at a frequency close to the resonance frequency of the circuit. It is shown that parameter βL, which distinguishes between hysteretic and nonhysteretic regimes, can be effectively adjusted to a desired value by applying the high-frequency field of a certain amplitude and frequency much higher than circuit resonance frequency. A significant increase in the conversion factor and sensitivity of the RF SQUID during this adjustment is discussed.
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)
Abstract An analysis of the measurement of the magnetic flux in superconducting qubits based on RF SQUIDs was carried out with an 800 MHz bandwidth low-power-consumption cryogenic high-electron-mobility transistor amplifier. The preliminary experimental results obtained at temperatures 2 K and 4 K for RF SQUIDs in hysteretic, and in two non-hysteretic, regimes with a pump frequency of about 30 MHz are discussed. Parameters of RF SQUIDs in the hysteretic and non-hysteretic modes are analyzed within the framework of the resistively and capacitively shunted junction model for Josephson junctions. Its sensitivity at a temperature of 30 mK and frequency band (speed) are calculated and optimized to read the states of a flux qubit used as a single microwave photon counter. It is shown that an RF SQUID, operated in an adiabatic non-hysteretic mode for qubit readout, allows us to minimize its back-action effect and the dark count rate. This is due to the absence of Josephson generation, the small amplitude of the resonator electromagnetic field, and the selection of the pump frequency that does not coincide with the characteristic frequencies of the flux qubit.