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International Journal of Modern Physics B

Macroscopic Quantum Tunneling in Josephson Junctions and Squids

C. Granata, E. Esposito, B. Ruggiero, M. Russo, P. Silvestrini

Published Apr 20, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1142/s0217979299001296

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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.
Macroscopic quantum effects in Josephson systems have recently attracted interest in the scientific community both for the physics involved and in view of applications. Here we present experiments on the presence of energy level quantization at temperatures above the classical-quantum regime crossover temperature in different Josephson junctions. This has been possible by extending the measurements of the escape rate out of the zero-voltage state at higher sweeping bias rate (dI/dt up to 100 A/sec) in order to induce nonstationary conditions in the energy potential describing the junction dynamics. Our measurements allow us to obtain as fitting parameter the "effective" resistance to be used in the RSJ model which is compatible with the subgap resistance at very low voltage. The very low dissipation level obtained at low temperatures renders our results quite interesting in view of applications in the quantum limit.
We present a clear observation of the presence of energy levels quantization in high quality $\mathrm{Nb}\ensuremath{-}{\mathrm{AlO}}_{x}\ensuremath{-}\mathrm{Nb}$ underdamped Josephson junctions at temperatures above the quantum crossover temperature. This has been possible by extending the measurements of the escape rate out of the zero-voltage state at higher sweeping frequency ( dI/dtdI/dtdI/dt up to 25 A/sec) in order to induce nonstationary conditions in the energy potential describing the junction dynamics.
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..
We report on the first measurements of the intrinsic dissipation in a macroscopic system cooled at very low temperature (35 mK) and operating in the quantum regime. The system under study is an rf SQUID with a high quality Josephson junction. Below 50 mK the tunneling probability of escape from a metastable well vs applied flux presents a series of maxima due to energy level quantization. From the shape of the tunneling probability we can evaluate the intrinsic dissipation related to the overall system as well as the coherence time related to the Rabi oscillations in a future macroscopic quantum coherence experiment.
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."
We have studied the temperature dependence of escape phenomena in various underdamped Josephson junctions (JJs). The junctions had different Josephson coupling energies E J which were relatively small, but larger than the charging energy E C . Upon increasing the temperature T , we first observe the usual cross-over between macroscopic quantum tunnelling and thermally activated (TA) behaviour at temperatures k B T ∼ ℏω p , where ω p is the plasma frequency of the junction. Increasing T further, the width of the switching current distribution has, counterintuitively, a non-monotonic temperature dependence. This can be explained by the novel cross-over from TA behaviour to underdamped phase diffusion. We show that this cross-over is expected to occur at temperatures such that k B T ∼ E J (1 − 4/π Q ) 3 /2, where Q is the quality factor of the junction at the plasma frequency, in agreement with experiment. Our findings can be compared with detailed model calculations which take into account dissipation and level quantization in a metastable well. Particular attention is paid to the sample with the smallest E J , which shows extensive phase diffusion even at the lowest temperatures. This sample consists of a dc-SQUID and a single JJ close to each other, such that the SQUID acts as a tunable inductive protection for the single junction from fluctuations of a dissipative environment. By varying the flux through the dc-SQUID, we present, for the first time, experimental evidence of the escape of a JJ from the phase diffusion regime to the free running state in a tunable environment. We also show that in the zero voltage state the losses mainly occur at frequencies near the plasma resonance.