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IEEE Transactions on Applied Superconductivity

Energy level quantization in underdamped niobium Josephson junctions [Nb/AlO/sub x//Nb]

B. Ruggiero, C. Granata, E. Esposito, Vittorio Giulio Palmieri, Maria Gabriella Castellano, C. Cosmelli, M. Russo, P. Silvestrini

Published Jun 1, 1999• 2 citations
Publisher

Abstract

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.

DOI
10.1109/77.783899

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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 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.
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..
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.
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.
When a Josephson junction in the zero-voltage state is current-biased below its critical current, the rate that it escapes to the finite-voltage state depends on the quantum state of the junction. By employing a slow current sweep, it is possible to observe experimentally the emptying of the thermally populated first excited level as a well-defined feature in the escape rate. This feature provides a simple method of determining the junction's energy relaxation time T1{T}_{1}T1​, a key parameter for evaluating its utility for quantum computation. We discuss the temperature regime where this effect is readily observable and describe how the emptying depends directly on the relaxation time. Our model of the junction dynamics agrees well with the measured escape rate of a $10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}\ifmmode\times\else\texttimes\fi{}10\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ $\mathrm{Nb}\text{\ensuremath{-}}\mathrm{AlOx}\text{\ensuremath{-}}\mathrm{Nb}$ device in the 25 to 300mK300\phantom{\rule{0.3em}{0ex}}\mathrm{mK}300mK temperature range, yielding ${T}_{1}\ensuremath{\approx}4\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.