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Physical review. B, Condensed matter

Effects of the phase-dependent dissipative term on the supercurrent decay of Josephson junctions

P. Silvestrini

Published Sep 1, 1992• 10 citations
Publisher

Abstract

We study the decay of the zero-voltage state of an underdamped Josephson junction, including in the equivalent circuit model the interference cos\ensuremath{\varphi} term. From a theoretical point of view, we provide an expression for the lifetime of the metastable state, which takes into account the dependence on the voltage of both the quasiparticles tunneling and the interference-term conductances. We also present a comparison of the theory with our experimental results, which clearly indicates the importance of these intrinsic mechanisms of dissipation on the supercurrent decay. We show that the interference term must be included in the theory if agreement between theory and data is to be achieved within the experimental uncertainty.

DOI
10.1103/physrevb.46.5470

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We study the decay of the zero-voltage state of an underdamped Josephson junction, including in the equivalent circuit model the interference cos\ensuremath{\varphi} term. From a theoretical point of view, we provide an expression for the lifetime of the metastable state, which takes into account the dependence on the voltage of both the quasiparticles tunneling and the interference-term conductances. We also present a comparison of the theory with our experimental results, which clearly indicates the importance of these intrinsic mechanisms of dissipation on the supercurrent decay. We show that the interference term must be included in the theory if agreement between theory and data is to be achieved within the experimental uncertainty.
The decay of the zero-voltage state is studied, including quasi-particle tunneling and the interference cos phi term in the equivalent circuit model. As a result of the approach used, the effective resistance for describing the junction dissipation, which was an arbitrary parameter in the resistively shunted junction (RSJ) model, can now be obtained in terms of the measurable junction parameters and bias conditions. This allows a direct comparison of data with theory. The very good agreement between data and theory confirms the essential correctness of the authors' assumptions. The data also provide an excellent experimental test of the thermal activation theory in underdamped physical systems.>
The effect of the voltage-dependent junction resistance R/sub j/ on the critical current decay of Josephson junctions was studied. In the thermal regime, the author has obtained a simple expression for the lifetime of the zero-voltage state which takes into account the nonlinear dependence of R/sub j/ on the voltage, removing an assumption of the resistivity shunted junction model (RSJ), which assumes an ohmic shunt resistance to describe the junction dissipation. These results are confirmed by experimental data which also show the relevance of the intrinsic dissipation due to the presence of quasiparticles. This latter aspect is relevant, because it allows extremely underdamped systems to be obtained at low temperatures. These conditions are particularly interesting to study a macroscopic quantum aspect, namely the effects of the presence of quantized energy levels on the supercurrent decay. The dependence of this latter effect on the junction resistance is also briefly discussed.
We present an experimental study of the effective dissipation relevant in the thermally activated supercurrent decay of extremely underdamped Josephson junctions. Data referring to the supercurrent decay of Nb/AlOx/Nb{\mathrm{N}\mathrm{b}/\mathrm{A}\mathrm{l}\mathrm{O}}_{x}/\mathrm{Nb}Nb/AlOx​/Nb Josephson junctions are compared with the Kramers theory. Our measurements allow us to obtain the ``effective'' resistance to be used in the resistively shunted junction model that results to be the subgap resistance due to the presence of thermally activated quasiparticles. The extremely low dissipation level obtained at low temperatures renders our result quite interesting in view of experiments in the quantum limit.
This chapter considers one important physical example of that kind, quantum dissipative decay of a metastable state. It demonstrates how to evaluate the quantum decay rate of a metastable state for a quantum particle in the presence of dissipation. In the presence of phase fluctuations, however, such current states become unstable and decay simply because the “particle” can escape from the local potential minimum either by thermal activation or by quantum tunneling. The chapter also considers sufficiently low temperatures in which case the decay is due to quantum tunnelling. Classical process of thermally activated decay of supercurrent in Josephson junctions was first demonstrated in 1974, and the results turned out to be in a good agreement with theoretical predictions. Later experiments allowed to quantitatively verify a number of important theoretical predictions, for example, ones concerning the effect of temperature and damping on the quantum decay rate.
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.
Quasiparticle tunneling across a Josephson junction sets a limit for the lifetime of a superconducting qubit state. We develop a general theory of the corresponding decay rate in a qubit controlled by a magnetic flux. The flux affects quasiparticles tunneling amplitudes, thus making the decay rate flux-dependent. The theory is applicable for an arbitrary quasiparticle distribution. It provides estimates for the rates in practically important quantum circuits and also offers a new way of measuring the phase-dependent admittance of a Josephson junction.