Phase transitions create a domain structure with defects, that has been argued by Zurek and Kibble to depend in a characteristic way on the quench rate. In this letter we present an experiment to measure the ZK scaling exponent σ. Using long symmetric Josephson Tunnel Junctions, for which the predicted index is σ = 0.25, we find σ = 0.27 ± 0.05. Further, we agree with the ZK prediction for the overall normalisation.

We report on the first experimental verification of the Zurek-Kibble scenario in an isolated superconducting ring over a wide parameter range. The probability of creating a single flux quantum spontaneously during the fast normal-superconducting phase transition of a wide Nb loop clearly follows an allometric dependence on the quenching time τ Q , as one would expect if the transition took place as fast as causality permits. However, the observed Zurek-Kibble scaling exponent σ = 0.62 ± 0.15 is two times larger than anticipated for large loops. Assuming Gaussian winding number densities we show that this doubling is well-founded for small annuli.

It has been argued by Zurek and Kibble that the likelihood of producing defects in a continuous phase transition depends in a characteristic way on the quench rate. In this paper we discuss an improved experiment for measuring the scaling exponent for the production of single fluxons in annular symmetric Josephson tunnel junctions. We find Ӎ 0.5 and show how this can arise from the Kibble-Zurek scenario. Further, we report accurate measurements of the temperature dependence of the junction gap voltage, which allow for precise monitoring of the fast temperature variations during the quench.

In parallel with Kibble's description of the onset of phase transitions in the early Universe, Zurek has provided a simple picture for the onset of phase transitions in condensed matter systems, supported by agreement with experiments in 3He and superconductors. We show how experiments with annular Josephson tunnel junctions can, and do, provide further support for this scenario.

We have investigated the static configurations of the phase inside an annular Josephson tunnel junction in the presence of an externally applied magnetic field. We report here a detailed study of the dependence on the magnetic field of the critical current for different annular geometries. The periodic conditions for the phase difference across the barrier are derived from fluxoid quantization. For rings having a radius less than the Josephson penetration depth analytical results are derived which are in excellent agreement with the experimental data. For longer junctions numerical analysis is carried out after the derivation of the appropriate perturbed sine-Gordon equation. We find that a number of different phase profiles may exist for a given applied field which differ according to the number of fluxon-antifluxon pairs present in the line. Experimental data support the theoretical analysis provided self-field effects are taken into account in real devices.

New scaling behavior has been both predicted and observed in the spontaneous production of fluxons in quenched N b − Al/Alox/N b annular Josephson tunnel junctions as a function of the quench time, τQ. The probability f1 to trap a single defect during the N-S phase transition clearly follows an allometric dependence on τQ with a scaling exponent σ = 0.5, as predicted from the Zurek-Kibble mechanism for realistic JTJs formed by strongly coupled superconductors. This definitive experiment replaces one reported by us earlier, in which an idealised model was used that predicted σ = 0.25, commensurate with the then much poorer data. Our experiment remains the only condensed matter experiment to date to have measured a scaling exponent with any reliability.

Chaotic behavior in the rf-biased Josephson junction is studied through digital simulations of the Steward–McCumber model. Chaotic states are characterized by Poincare sections, Liapunov exponents, and power spectra. Models are presented which explain some features of the chaotic spectra. The parameter range over which chaotic behavior occurs is determined empirically for a broad range of dc bias, rf bias, and hysteresis parameters for a fixed rf frequency. It is shown that chaos does not occur if either the dc bias or the rf bias is very large. An attempt is made to explain the boundaries of the chaotic region in terms of simple models for chaotic behavior.

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