Aspects of dissipation effects in experiments on macroscopic quantum tunnelling in Josephson junctions

Summary The effect of dissipation in experiments on macroscopic quantum tunnelling in Josephson tunnel junctions are discussed. The frequency-dependent, nonlinear dynamic resistance of the junction makes it difficult to understand which effective linear resistance has to be chosen to compare the experimental results with the theory developed in the framework of the RSJ model. Various experiments reported in the literature lead to different conclusions and are presently discussed. Recently obtained experimental results on the thermal regime allow us to propose a new experimental strategy which ultimately should remove any ambiguity on the possibility to observe MQT process in the presence of dissipation in Josephson structures. To speed up publication, the authors have agreed not to receive proofs which have been supervised by the Scientific Committee.     

Experiments on macroscopic quantum tunnelling in Josephson structures: Influence of the uncertainty of junction parameters

Summary Some of the most interesting experiments on MQT, based on the Josephson effect, are considered in order to understand whether a definite experimental proof of the phenomenon exists. We have investigated the effects of some spurious situations related to the uncertainty on the determination of the relevant junction parameters, which can simulate the same effects of MQT. As a result we have seen that probably all the experimental data cannot be completely interpreted within the classical framework. However some ambiguities remain particularly for what concerns the implications of dissipation in the phenomenon.     

Electron-phonon interaction function by numerical analysis of superconducting tunnelling experimental data

Summary A new method of numerical analysis is presented which allows the determination of the electron-phonon interaction functionα ²(ω)F(α) using the experimental data obtained from a superconducting tunnel junction. This method utilizes the dispersion relation for Δ(ω) (complex energy gap function) proposed by Galkin, D'yachenko and Svistunov. The method and the hypotheses which allow the numerical solution of the first-kind integral equation derived from the Eliashberg equations are shown and discussed. Δ(ω) andα ²(ω)F(α) of Pb are obtained by applying this method to the tunnel data of an Al−Al₂O₃-Pb (superconducting electrode) junction. The results are discussed with particular reference to the stability and convergence of the method applied.

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Riassunto Si presenta un nuovo metodo di analisi numerica che, utilizzando la relazione di dispersione per Δ(ω), energy gap function, proposta da Galkin, D'yachenko and Svistunov, permette di determinare da dati sperimentali ottenuti su giunzioni tunnel superconduttive la funzione interazione elettrone-fononeα ²(ω)F(α) per l'elettrodo superconduttore. Il metodo stesso è discusso e si evidenziano le ipotesi che permettono la soluzione numerica dell'equazione integrale di prima specie derivata dalle equazioni di Eliashberg. Le Δ(ω) edα ²(ω)F(α) ottenute applicando tale metodo ai dati relativi ad una giunzione Al−Al₂O₃−Pb (elettrodo superconduttore) sono presentate e discusse con particolare riferimento alla stabilità e convergenza del metodo.

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Резюме Предлагается новый метод численного анализа, который позволяет определить функцию электрон-фононного взаимодействияα ²(ω)F(α), используя экспериментальные данные, полученные для сверхпроводяшего туннельного перехода. Этот метод использует дисперсионное соотнощение длл Д(щ), предложенное Галкиным, Яшенко и Свистуновым. Обсуждается предложенный метод и подтверждаются гипотезы, которые розволяют численно рещить интегральное уравнение первого рода, выведенное из уравнений Элиащберга. Испрльзуя этот метод для туннельных данных в Al−Al₂O₃−Pb переходе, получаются Δ(ω) иα ²(ω)F(α). Полученные результаты обсуждаются с точки зрения устойчивости и сходимости предложенного метода.

     

Retrapping mechanism in the switching dynamics of a Josephson junction

Summary The switching dynamics of a Josephson junction is discussed in connection with the problem of a Brownian particle in a one-dimensional washboard potential. The particle is supposed to escape from a potential well and results concerning the probability of retrapping in another well before the transition into the running state are obtained for the first time. The analysis is restricted to the very-low-damping case and the ?first-passage time? technique is used.

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Riassunto Si discute la dinamica del decadimento dello stato a tensione nulla di una giunzione Josephson nell'ambito del problema del moto browniano. Il potenziale è unidimensionale periodico ed inclinato e sono permessi molti stati metastabili. Si considera la probabilità d'intrappolamento in una buca di potenziale di una particella proveniente da uno stato metastabile a potenziale piú alto.

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Резюме В связи с проблемой броуновской частицы в одномерном потенциале обсуждается динамика переключения перехода Джозефсона. Предполагается, что частица освобождается из потенциальной ямы, и впервые определяется вероятность повторного захвата в другую яму перед переходом в движущееся состояние. Анализ ограничивается случаем очень малого затухания и используется техника ?двремени первого хода?.

     

YBCO/Nb bulk junctions: Observation of the Josephson effect

Summary The fabrication procedure of reliable YBCO-based bulk junctions with a Nb film as a counterelectrode is described. Typical currentvoltage characteristics are presented, clearly showing the presence of the Josephson effect.     

Nb/BiSCCO point conctact junctions

Summary Preparation procedure and sample characterization of 112 BiSCCO pellets exhibiting high-T _c superconductivity are discussed. TypicalI–V and dV/dI curves of Nb/BiSCCO point conctact junctions at various temperatures are presented.     

Aspects of macroscopic quantum tunnelling in small Josephson junctions

Summary We study the effect of temperature on the lifetime of the resonant macroscopic quantum tunnelling voltage state. In view of experiments we consider a merit factor in order to balance between measuring extremely small signals of longer duration or larger signals of shorter duration.     

Effects of junction parameters on the resonant macroscopic quantum tunnelling in small Josephson junctions

Summary Within the well-established quantum picture of a Josephson junction, it has been shown that the possibility of a resonant macroscopic quantum tunnelling can produce sharp voltage peaks in the current-voltage characteristics. We investigate the effects of the junction parametrs and bias conditions on the step amplitude, in view of an experimental check of the proposed phenomenon.     

Comments on an experiment of resonant tunnelling between macroscopically distinct quantum levels

Summary In an important experiment performed on a SQUID system, Rouse, Han and Lukens report the first observation of resonant tunnelling between macroscopically distinct quantum levels. We support the experiment with the first theoretical approach for the phenomenon.     

Comments on experiments about the supercurrent decay of josephson junctions

Summary The subtle problems lying in the interpretation of data on the supercurrent decay of underdamped Josephson junction are approached. An analysis of the unavoidable correlation among the free fitting parameters is presented. As a result we find that even the most appropriate approach to this problem leads to a certain unavoidable ambiguity in the interpretation of the data.     

BCS quasi-particle tunnelling current in Josephson tunnel junctions

Summary The recent improvements in the fabrication technology have succeeded in obtaining high-quality Josephson tunnel junctions. TheI–V characteristics of these junctions exhibit now lesser and lesser differences from the theoretical predictions. The various figures of merit, so far introduced to qualify the junctions, appear now focused on too limited aspects and a direct comparison with the detailed prediction of the theory is in order. For this awaken interest in the detailed predictions of the BCS theory, we have revisited the relevant formulae for the quasi-particle tunnelling current. A detailed discussion of the analytical transformation necessary for a simple numerical evaluation of this current is reported. SeveralI–V curves are obtained using the parameter values corresponding to the case of Nb-based junctions, which is the actual running technology. Peculiar interesting aspects are outlined.     

The role of the surface depression of the pair potential on the Josephson and quasi-particle tunnelling in high-T c superconductors

Summary We discuss the influence of the intrinsic surface depression of the order parameter on the temperature dependence of the Josephson critical currentI _c(T) and, tentatively, on the quasi-particle tunnelling conductance in a superconductor with a very short coherence length. The comparison with the experiments shows that the presence of a surface-depressed pair potential can explain the large deviations of theI _c(T) from the ideal BCS behaviour that we recently observed in Bi₂Sr₂CaCu₂O_8+x Josephson break junctions and could mimic the presence of a broadening in the Superconductor-Insulator-Normal tunnelling conductance of the same high-T _c superconductor. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Primary and secondary isotope effect on tunnelling in malonaldehyde using a quantum mechanical scheme

Primary and secondary isotope effect on tunnelling in malonaldehyde is investigated with reduced-dimensional quantum mechanical models in the saddle-point normal coordinates, where the Hamiltonian takes the imaginary-frequency normal model as the reaction coordinate and uses the relaxed potentials to approximate the normal modes not explicitly included. Our two-dimensional (2D) results of the ground-state tunnelling splitting (Δ₀), as well as the ratio of the Δ₀ in malonaldehyde to that in its isotopologues, are in reasonably good agreement with available experimental data. The experimental deduction about the appreciable impact of secondary isotope effect on tunnelling is further confirmed. Moreover, we find that in most isotopologues, the fundamental excitation of the ring-deformation normal mode, explicitly included in the 2D model, shows a large enhancement of tunnelling relative to the Δ₀.     

On the measurement of electron tunnelling time

A suggestion to experimentally measure the electron tunnelling time by observing the tunnelling current cut-off as a function of the magnetic field intensity in semiconductor pn tunnel junctions, when they are placed in a crossed electric and magnetic field configuration, has been made in this paper. A simple and a rigorous quantum mechanical analysis to justify the above proposition have been presented. An order of agreement between the tunnelling time values derived from the published experimental data and our theoretical prediction has been noticed.     

High-quality YBCO d.c. SQUIDs based on bicrystal substrates

Summary An analysis of superconducting transport properties and magnetic behaviour of d.c. SQUIDs employing YBCO bicrystal grain boundary junctions (GBJs) has been performed. GBJs have been obtained by deposition of ac-axis-oriented YBCO film on a SrTiO₃ bicrystal substrate by ICM sputtering technique. Experimental measurements on a YBCO d.c. SQUID with a misorientation angle θ=20° are reported. The SQUID shows a critical temperatureT _c∼89 K and a high critical current densityJ _c∼3·10⁶ A/cm² atT=4.2 K. Current-voltage characteristics are close to the behaviour predicted by the resistively shunted junction (RSJ) model and the temperature dependenceJ _c(T) shows a linear behaviour at small reduced temperatures and a depressedJ _c value close toT _c. High-quality flux-voltage curves have been found upT=87 K over a large range of magnetic field. The high reproducibility and the good control of transport properties by the variation of θ make YBCO bicrystal GBJs very useful for applications in electronics. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Generation of subharmonic shapiro steps in ladder arrays of overdamped superconducting junctions

Summary Subharmonic Shapiro Steps (SSS) are usually observed in 2D arrays of superconducting junctions when their dynamical states are perturbed by factors like disorder, frustration, current inhomogeneities and so on. In order to clarify the conditions under which SSS can be generated we decided to investigate arrays of very simple shape like the ladder ones. In particular we have studied the influence of the frustration (i.e. of an external magnetic field) on the time evolution of the vortex configuration and the commensurability of the latter with the geometry and the dimension of the array. Ladders, parallel or perpendicular to the bias current, turn out to be systems where the properties of the square arrays can be suitably tested. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Crossover between the extremely low damping and moderate underdamped regime in the thermal activation theory: Preliminary experimental results

Summary The problem of the decay of metastable state due to thermal activation is studied. Experimental data referring to the supercurrent decay of an underdamped Josephson junction are compared with Kramers theory and its recent improvements. Significative aspects of the crossover region between the extremely underdamped regime and the moderate underdamped one are discussed.     

2D superconducting junction networks as detectors of radiation

Summary We present a careful study of the behaviour of the below-gap photoresponse in 2D arrays of superconducting junctions. We have included the effects of the temperature, not only through the white-noise current term, but also through theT-dependence of the junction coupling energy. In order to render our model more realistic we also consider the correction due to the self-field generated by the screening currents. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Temperature dependence of the superconducting energy gap from conductance curves

Summary An analytic relationship between the values of the applied voltages which produce a maximum in the differential conductance and the energy gap is derived for BCS isotropic superconductors. The different methods of deduction of the temperature dependence of the gap in high-T _c superconductors are analysed.     

Enhanced coherence of a quantum doublet coupled to Tomonaga-Luttinger liquid leads

We use boundary field theory to describe the phases accessible to a tetrahedral qubit coupled to Josephson junction chains acting as Tomonaga-Luttinger liquid leads. We prove that, in a pertinent range of the fabrication and control parameters, an attractive finite coupling fixed point emerges due to the geometry of the composite Josephson junction network. We show that this new stable phase is characterized by the emergence of a quantum doublet which is robust not only against the noise in the external control parameters (magnetic flux, gate voltage) but also against the decoherence induced by the coupling of the tetrahedral qubit with the superconducting leads. We provide protocols allowing to read and to manipulate the state of the emerging quantum doublet and argue that a tetrahedral Josephson junction network operating near the new finite coupling fixed point may be fabricated with today?s technologies.