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Physica Scripta

Observation of the Temporal Decoupling Effect on the Macroscopic Quantum Tunneling of a Josephson Junction

D Esteve, John M. Martinis, C. Urbina, Emmanuel Turlot, Michel Devoret, Hermann Grabert, Sebastian Linkwitz

Published Jan 1, 1989• 96 citations
Publisher

Abstract

We have measured the Macroscopic Quantum Tunneling (M.Q.T.) rate out of the zero voltage state of a Josephson junction shunted by a delay line terminated by a resistor. As the length of the line is increased in situ , thereby increasing the delay with which the resistor damps the junction, the M.Q.T. rate increases until it almost recovers its value in the absence of damping: This constitutes the temporal decoupling effect. We compare our results to the theoretical predictions.

DOI
10.1088/0031-8949/1989/t29/022

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We have measured the Macroscopic Quantum Tunneling (M.Q.T.) rate out of the zero voltage state of a Josephson junction shunted by a delay line terminated by a resistor. As the length of the line is increased in situ , thereby increasing the delay with which the resistor damps the junction, the M.Q.T. rate increases until it almost recovers its value in the absence of damping: This constitutes the temporal decoupling effect. We compare our results to the theoretical predictions.
The tunneling probability for a system modelling macroscopic quantum tunneling is computed. We consider an open quantum system with one degree of freedom consisting of a particle trapped in a cubic potential interacting with an environment characterized by a dissipative and a diffusion parameter. A representation based on the energy eigenfunctions of the isolated system, i. e. the system uncoupled to the environment, is used to write the dynamical master equation for the reduced Wigner function of the open quantum system. This equation becomes very simple in that representation. The use of the WKB approximation for the eigenfunctions suggests an approximation which allows an analytic computation of the tunneling rate, in this real time formalism, when the system is initially trapped in the false ground state. We find that the decoherence produced by the environment suppresses tunneling in agreement with results in other macroscopic quantum systems with different potentials. We confront our analytical predictions with an experiment where the escape rate from the zero voltage state was measured for a current-biased Josephson junction shunted with a resistor.
We have carried out systematic Macroscopic Quantum Tunneling (MQT) experiments on Nb/Al-AlO_x/Nb Josephson junctions (JJs) of different areas. Employing on-chip lumped element inductors, we have decoupled the JJs from their environmental line impedances at the frequencies relevant for MQT. This allowed us to study the crossover from the thermal to the quantum regime in the low damping limit. A clear reduction of the crossover temperature with increasing JJ size is observed and found to be in excellent agreement with theory. All junctions were realized on the same chip and were thoroughly characterized before the quantum measurements.
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."
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.
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.
Measurements of the tunneling rate $\ensuremath{\Gamma}$ out of the zero-voltage state for several Nb edge junctions with differing shunt capacitances are described. At zero temperature, increasing the shunt capacitance lowers $\ensuremath{\Gamma}$ in agreement with dissipative calculations of the macroscopic-quantum-tunneling rate. As temperature increases, $\mathrm{ln}[\frac{\ensuremath{\Gamma}(T)}{\ensuremath{\Gamma}(0)}]\ensuremath{\propto}{T}^{2}$ as recently predicted.