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Applied Superconductivity

Measurements of thermal switching between metastable flux states in a RF-SQUID with intermediate damping

Maria Gabriella Castellano, Roberto Leoni, G. Torrioli, C. Cosmelli, F. Chiarello, P. Carelli

Published Jul 1, 1997• 3 citations
Publisher
DOI
10.1016/s0964-1807(98)00061-1

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Soviet Journal of Low Temperature Physics•Feb 1, 1985•18 citations
We present an analysis and numerical study of a dc superconducting quantum interference device (SQUID) with a damped loop inductance. We find a previously unreported regime of voltage-flux bistability due to the damping resistor when the SQUID is biased below the zero-field critical current. We determine the region where this phenomenon can be found in the parameter space defined by the damping resistance and the inductance parameter. We show that switching between the bistable states can be controlled by external flux pulses and by adding thermal noise to the model, we have determined the maximum noise level at which the bistability can be seen.
Abstract This work investigates the distribution of flux states of hysteretic dc superconducting quantum interference devices (SQUIDs) obtained from standard current ramp measurement at 2.50 and 0.35 K. Each flux state corresponds to a specific number of flux quanta trapped in the superconducting loop, associated with a metastable state in the two-dimensional potential energy of the hysteretic SQUID. The flux states can be distinguished by the multiple switching currents. The observed distribution is different from the distribution caused only by thermal excitation at a specific temperature. There are notable systematic deviations between the measurement results of three samples and the standard Boltzmann distribution, which can be clearly identified from the ratios between the proportions of different flux states. A formula resembling the Boltzmann distribution, involving multiple effective temperatures, is proposed to provide a better fit to the measured results. The finding suggests that the observed distribution of flux states is established during the SQUID’s transition from the dissipative state to the zero-voltage state, and multiple equivalent temperatures may be involved in the process.
The mechanisms of the decay of metastable current states in the superconducting loop of an rf SQUID in the hysteresis state are studied. Clamped point contacts are used as the Josephson weak link. The first derivative of the radio-frequency IVC dVT/dIRF, which gives the dependence of the decay probability density on the amplitude of the oscillations of the magnetic flux in the ring, was measured experimentally. Studies of the temperature dependence of the width of the probability distribution in the interval from 4.2 to 0.5 K show that for most high-resistance Nb–Nb, Nb–Ag–Nb contacts the quantum mechanisms of decay become dominant at a temperature of the order of 2 K. The experimentally measured parameters of the decay probability distribution in the quantum limit are compared with the theoretical values calculated based on the theory of macroscopic quantum tunneling in the limit of strong and weak dissipation. The experimental magnitude of the width of the probability density as well as the characteristic quantum temperature exceed the theoretical values, which can be explained by the deviation of the current-phase dependence of the contact from a sinusoidal dependence. In addition, some contacts apparently correspond to the case of an intermediate magnitude of dissipation. When the frequency of the rf oscillations changed from 30 to 6 MHz, the width of the distribution remained unchanged, which follows from the theory of quantum tunneling decay of the metastable current state in the loop in the limit of strong damping. At low temperatures (T ∼ 50 K) and for a sufficiently small damping coefficient, anomalous peaks were observed in the probability density with an amplitude of the rf oscillations significantly smaller than the critical magnitude of the magnetic flux in the loop.