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Physical Review Letters

Observation of Energy Levels Quantization in Underdamped Josephson Junctions above the Classical-Quantum Regime Crossover Temperature

P. Silvestrini, Vittorio Giulio Palmieri, B. Ruggiero, M. Russo

Published Oct 20, 1997• 108 citations
Publisher

Abstract

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 ( $dI/dt$ up to 25 A/sec) in order to induce nonstationary conditions in the energy potential describing the junction dynamics.

DOI
10.1103/physrevlett.79.3046

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We present a clear observation of the presence of energy levels quantization in high quality Nb\ensuremath−AlOx\ensuremath−Nb\mathrm{Nb}\ensuremath{-}{\mathrm{AlO}}_{x}\ensuremath{-}\mathrm{Nb}Nb\ensuremath−AlOx​\ensuremath−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.
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We have investigated the dynamics of underdamped Josephson junctions with a relatively small Josephson coupling EJ{E}_{J}EJ​. In addition to the usual crossover between macroscopic quantum tunneling and thermally activated (TA) behavior we observe, for the first time, the transition from TA behavior to underdamped phase diffusion. Above the crossover temperature, the threshold for switching into the finite-voltage state becomes extremely sharp. We propose a (TTT, EJ{E}_{J}EJ​) phase diagram with various regimes and show that for a proper description of it, dissipation and level quantization in a metastable well are crucial.
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..
A single flux quantum (SFQ) circuit to measure quantized energy levels in a Josephson junction has been proposed and implemented, which allows us to perform high-speed and low-noise measurements of the escape rate in Josephson junctions. By using this technique, the measurement of escape rate has been carried out at 4.2 K, the temperature three times higher than the crossover temperature. The test results show periodic dependence of the escape rate on the junction bias current, which is caused by the energy quantization effect in the Josephson junction.
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 ${T}_{1}\ensuremath{\approx}4\phantom{\rule{0.3em}{0ex}}\mathrm{ns}$.