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Science

Quantum Mechanics of a Macroscopic Variable: The Phase Difference of a Josephson Junction

John L. Clarke, Andrew N. Cleland, Michel Devoret, Daniel Esteve, John M. Martinis

Published Feb 26, 1988• 359 citations
Publisher

Abstract

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."

DOI
10.1126/science.239.4843.992

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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."
Experiments are described that demonstrate the quantum behavior of a macroscopic degree of freedom, namely the phase difference \ensuremath{\delta} across a current-biased Josephson tunnel junction. The behavior of \ensuremath{\delta} was deduced from measurements of the escape rate \ensuremath{\Gamma} of the junction from its zero-voltage state. The relevant parameters of the junction, that is, its critical current and shunting admittance, were determined in situ in the thermal regime from the dependence of \ensuremath{\Gamma} on bias current and from resonant activation in the presence of microwaves. It was found that the shunting capacitance was dominated by the self-capacitance of the junction while the shunting conductance was dominated by the bias circuitry. For an underdamped junction in the quantum regime, \ensuremath{\Gamma} became independent of temperature at low temperatures with a value that, with no adjustable parameters, was in excellent agreement with predictions for macroscopic quantum tunneling at T=0. When the critical current was reduced with a magnetic field so that the junction remained in the thermal regime at low temperatures, \ensuremath{\Gamma} followed the predictions of the thermal model, thereby showing the influence of extraneous noise to be negligible. In a further series of experiments, the existence of quantized energy levels in the potential well of the junction was demonstrated spectroscopically. The positions of the energy levels agreed quantitatively with quantum-mechanical predictions involving junction parameters measured in the thermal regime. The relative heights and widths of the resonances are in reasonable agreement with the predictions of a simple model.
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.
We report experiments on energy level quantization in Nb/AlOx/Nb Josephson junctions while measurements on SQUIDs are in progress. Data on the presence of energy level quantization are shown at temperatures above the classical-quantum regime crossover temperature. This has been possible by extending the measurements of the rate of the escape from the zero-voltage state at higher sweep bias rate in order to induce non-stationary conditions in the energy potential describing the junction dynamics. Data are compatible with extremely low "effective" dissipation in our system. Theoretical predictions on quantum effects related to the presence of non-stationary conditions in the potential associated to a rf SQUID are reported in view of new possible experiments.