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Physical Review Letters

Effects of Dissipation and Temperature on Macroscopic Quantum Tunneling

Sean Washburn, R. A. Webb, Richard F. Voss, S. M. Faris

Published Jun 24, 1985• 199 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.54.2712

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Measurements of the tunneling rate \ensuremathΓ\ensuremath{\Gamma}\ensuremathΓ 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 \ensuremathΓ\ensuremath{\Gamma}\ensuremathΓ in agreement with dissipative calculations of the macroscopic-quantum-tunneling rate. As temperature increases, ln[\ensuremathΓ(T)\ensuremathΓ(0)]\ensuremath∝T2\mathrm{ln}[\frac{\ensuremath{\Gamma}(T)}{\ensuremath{\Gamma}(0)}]\ensuremath{\propto}{T}^{2}ln[\ensuremathΓ(0)\ensuremathΓ(T)​]\ensuremath∝T2 as recently predicted.
The probability distributions for switching out of the superconducting state of low-cur-rent-density 1-\ensuremath{\mu}m Nb Josephson junctions with capacitance \ensuremath{\approx} 0.1 pF have been measured as a function of temperature TTT down to 3 mK. Below 100 mK the distribution widths become independent of TTT. The results are in excellent agreement with predictions for the quantum tunneling of the (macroscopic) junction phase that include the reduction of tunneling rates due to dissipation.
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.
Josephson junctions based on Nb/AlOx/Nb trilayer technology have demonstrated excellent quality, exhibiting very low dissipation in the subgap region. This property is very important for all those experiments which have to deal with the quantum behavior of macroscopic variables in Josephson devices. In view of performing an experiment of macroscopic quantum coherence with a Josephson device, we measured the escape temperature and the return current of several junctions fabricated with different processes and having different characteristics, by cooling them from 4.2 to 0.3 K. We show that, for what concerns the process of escape from the zero-voltage state, no difference can be found among different junctions. On the other hand, the dissipation properties are strongly influenced by the current density, with lower current density resulting in lower intrinsic dissipation.
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."
Measurements of temperature dependence of the return current in high quality Nb/AlOx/Nb Josephson junctions are presented. From the experimental data, we obtain the effective resistance, i.e., the effective dissipation, for the retrapping process, according to the generalized resistively shunted junction model proposed by Chen, Fisher, and Leggett. We present a careful analysis, based on a comparison between the measured temperature dependencies of both the return and the quasiparticle tunneling current. We find that the junction subgap conductance, which includes the quasiparticle and the quasiparticle-pair interference terms, is responsible for the return process. The measurements have been performed on various samples, in a wide range of critical current densities from 50 to 2250 A/cm2, covering different damping regimes and spanning over the high and low temperature limits. Junctions with low critical current density show ideal dissipation which makes the return current scale with temperature according to the BCS exponential behavior without flattening out effects. This result may be relevant for the possible use of Nb/AlOx/Nb junctions in macroscopic quantum coherence experiments, which strongly require a very low dissipation.