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arXiv:2512.08072 · Low Temperature Physics

Control of the effective value of the critical current of the RF SQUID by the high-frequency electromagnetic field

V. I. Shnyrkov, V. Yu. Lyakhno, A. A. Kalenyuk, D. G. Mindich, O. O. Leha, Andrii P. Shapovalov

Published Jun 1, 2024• 0 citations
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Abstract

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.

DOI
10.1063/10.0026089

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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.
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.
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)
Radio frequency superconducting quantum interferometers (RF-SQUIDs) are structural elements of nonlinear media used in superconducting metamaterials and superconducting low-noise parametric amplifiers. An expression for the effective Josephson inductance as a function of the external microwave signal power in a two-tone excitation mode is derived. This formula is applied to calculate the effective inductance of a Josephson junction embedded in an RF-SQUID under microwave radiation. The analytically calculated dependences of the resonant frequency and effective Josephson inductance of a non-hysteresis RF-SQUID on microwave power are in good agreement with experimental results.
Experimental results on some radio-frequency superconducting quantum interference device (rf-SQUID) signal properties are presented. The quantum interferometer was made of ceramic YBa2Cu3O7−x and was due to a low critical current operated in the inductance or nonhysteretic mode. With bias current as reference, amplitude variation, and phase shift of the voltage over the tank circuit coupled to the SQUID were measured simultaneously. It is shown that there is qualitative agreement between calculations based on the resistivity shunted junction model and the data. Moreover, using phase detection, signal instabilities predicted for the rf-SQUID inductance mode were observed. These signal instabilities may be exploited to enhance the transfer coefficient for measured flux-to-output signal.
We have studied the basic characteristics of a radio frequency superconducting quantum interference device (rf SQUID) involving two Josephson junctions connected in series, the case for the widely used grain boundary junction (GBJ) rf SQUID. It is found that the SQUID properties are determined mainly by the weaker junction when the critical current of the weaker junction is much lower than that of the other junction. Otherwise, the effect of the other junction is not negligible. We also find that only when the hysteresis parameter β is less than 1−α, where α is the critical current ratio of the two junctions, will the SQUID operate in the nonhysteretic mode.