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Physical Review Letters

Quantitative Study of the Effect of the Environment on Macroscopic Quantum Tunneling

D. B. Schwartz, B. Sen, Charles N. Archie, James E. Lukens

Published Oct 7, 1985• 172 citations
Publisher

Abstract

Data are presented on the temperature-dependent escape rates of a macroscopic system, a SQUID containing a highly damped Josephson junction, from its metastable state. These data provide the first quantitative confirmation of recent predictions of the exponential effects of temperature and damping on quantum tunneling in macroscopic systems in contrast to previously reported discrepancies. Predicted quantum corrections to thermally activated escape at high temperatures are not observed.

DOI
10.1103/physrevlett.55.1547

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Data are presented on the temperature-dependent escape rates of a macroscopic system, a SQUID containing a highly damped Josephson junction, from its metastable state. These data provide the first quantitative confirmation of recent predictions of the exponential effects of temperature and damping on quantum tunneling in macroscopic systems in contrast to previously reported discrepancies. Predicted quantum corrections to thermally activated escape at high temperatures are not observed.
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A macroscopic variable, the phase difference across a Josephson junction, is shown to obey quantum mechanics by observing the phenomena of energy-level quantization and quantum tunneling.The relevant parameters of the junction were determined .!.!! .ill!:!, in the thermal regime from the dependence of the escape rate on bias current and from resonant activation in the presence of microwaves.The first observation of quantized energy levels for this system is reported.The positions of these energy levels are in quantitative agreement with the quantum mechanical predictions based on the measured junction parameters.A model is presented that predicts correctly the observed resonance shapes.The measured value of the escape rate out of the zero-voltage state for an underdamped (Q -30) junction was found to be independent of temperature at low temperatures.This low temperature escape rate was in excellent agreement with the prediction for macroscopic quantum tunneling, with no adjustable parameters.Jolw rJt..
The escape rate of an underdamped ($Q\ensuremath{\approx}30$), current-biased Josephson junction from the zero-voltage state has been measured. The relevant parameters of the junction were determined in situ in the thermal regime from the dependence of the escape rate on bias current and from resonant activation in the presence of microwaves. At low temperatures, the escape rate became independent of temperature with a value that, with no adjustable parameters, was in excellent agreement with the zero-temperature prediction for macroscopic quantum tunneling.
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.
Experiments to investigate the quantum behavior of a macroscopic degree of freedom, namely the phase difference across a Josephson tunnel junction, are described. The experiments involve measurements of the escape rate of the junction from its zero voltage state. Low temperature measurements of the escape rate for junctions that are either nearly undamped or moderately damped agree very closely with predictions for macroscopic quantum tunneling, with no adjustable parameters. Microwave spectroscopy reveals quantized energy levels in the potential well of the junction in excellent agreement with quantum-mechanical calculations. The system can be regarded as a "macroscopic nucleus with wires."