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IEEE Transactions on Magnetics

Thermal activation and macroscopic quantum tunneling in a DC SQUID

Fred Sharifi, J. L. Gavilano, Dale J. Van Harlingen

Published Mar 1, 1989• 3 citations
Publisher

Abstract

The authors report measurements of the transition rate from zero-voltage metastable minima in the two-dimensional potential of a DC SQUID (superconducting quantum interference device) as a function of applied flux and temperature. A crossover is observed from thermally activated escape to macroscopic quantum tunneling at a critical temperature that is a strong function of the bias flux. The macroscopic quantum tunneling rate is substantially reduced by damping, which also broadens the crossover region. The authors unexpectedly observed thermal rates that are significantly suppressed from those predicted by the classical two-dimensional thermal activation model, as if the potential barrier for activation were effectively enhanced. They discuss possible explanations for this result, based on the interaction of the macroscopic degrees of freedom in the device and energy level quantization effects.>

DOI
10.1109/20.92499

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The authors report measurements of the transition rate from zero-voltage metastable minima in the two-dimensional potential of a DC SQUID (superconducting quantum interference device) as a function of applied flux and temperature. A crossover is observed from thermally activated escape to macroscopic quantum tunneling at a critical temperature that is a strong function of the bias flux. The macroscopic quantum tunneling rate is substantially reduced by damping, which also broadens the crossover region. The authors unexpectedly observed thermal rates that are significantly suppressed from those predicted by the classical two-dimensional thermal activation model, as if the potential barrier for activation were effectively enhanced. They discuss possible explanations for this result, based on the interaction of the macroscopic degrees of freedom in the device and energy level quantization effects.>
We have measured the thermally-activated escape rate out of the zero-voltage state of hysteretic dc superconducting quantum interference devices (SQUID's) at 4.2 K. We found evidence that the zero-voltage state of these SQUID's is in general not unique, but can correspond instead to several metastable states. Each of these substates is associated with a given number of flux quanta trapped in the super-conducting loop of the SQUID's. The existence of this multiplicity is a direct consequence of the two-dimensional character of the dc-SQUID dynamics. For a fixed external magnetic flux, each zero-voltage substate is characterized by a particular value of the critical current, the expression of which can be derived from the double-cosine tilted two-dimensional SQUID potential. Experimentally, we observed multiple peaks in the switching-current distribution. Each peak was assigned to a given zero-voltage substate and we measured the dependence of the associated critical currents on the external magnetic flux. A procedure was developed in order to select a given substate among the multiplicity of the zero-voltage state. This allowed a precise measurement of the lifetime of one preselected zero-voltage substate as a function of the barrier height. Good agreement with two-dimensional transition-state theory was obtained.
This thesis is a study of escape from metastable wells in one and two dimensional potentials of superconducting devices. We have measured escape rates due to both thermal activation over the barrier and macroscopic quantum tunneling through the barrier. The measurements were performed for a variety of device parameters, corresponding to different shapes of the potential barrier. We find strong evidence for macroscopic quantum tunneling in both one and two dimensional systems with an escape rate that is very sensitive to the dissipation present in the system. Surprisingly, we have also found a discrepancy between our results and the predictions of Kramers' thermal activation model in certain types of potentials.
The escape probability out of the superconducting state of a hysteretic dc SQUID has been measured at different values of the applied magnetic flux. At low temperatures, the escape current and the width of the probability distribution are temperature independent but they depend on flux. Experimental results do not fit the usual one-dimensional macroscopic quantum tunneling (MQT) law but are perfectly accounted for by the two-dimensional MQT behavior as we propose here. Near zero flux, our data confirms the recent MQT observation in a dc SQUID [Phys. Rev. Lett. 89, 98301 (2002)]].
In a coupled system of one classical and one quantum mechanical degree of freedom, the quantum degree of freedom can facilitate the escape of the whole system. Such unusual escape characteristics have been theoretically predicted as the "Münchhausen effect." We implement such a system by shunting one of the two junctions of a dc SQUID with an additional capacitance. In our experiments, we detect a crossover between quantum and classical escape processes related to the direction of escape. We find that, under varying external magnetic flux, macroscopic quantum tunneling periodically alternates with thermally activated escape, a hallmark of the "Münchhausen effect."
Thermally induced vortex-to-vortex transitions between the zero-quantum vortex state and one- flux-quantum vortex state of a symmetric two-junction dc superconducting quantum interference device (SQUID) have been observed. The characterization of transitions of this type is an essential part of the modeling of Josephson junction logic and memory devices. The transition rates, measured as a function of bias current, applied flux, and temperature, are in excellent agreement with rates predicted by a thermal activation model for two-junction SQUID’s.