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We propose a threshold detector for Levy distributed fluctuations based on a Josephson junction. The Levy noise current added to a linearly ramped bias current results in clear changes in the distribution of switching currents out of the zero-voltage state of the junction. We observe that the analysis of the cumulative distribution function of the switching currents supplies information on both the characteristics shape parameter $alpha$ of the Levy statistics and the intensity of the fluctuations. Moreover, we discuss a theoretical model which allows to extract characteristic features of the Levy fluctuations from a measured distribution of switching currents. In view of this results, this system can effectively find an application as a detector for a Levy signal embedded in a noisy background.
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We propose to characterize Levy-distributed stochastic fluctuations through the measurement of the average voltage drop across a current-biased Josephson junction. We show that the noise induced switching process in the Josephson washboard potential can be exploited to reveal and characterize Levy fluctuations, also if embedded in a thermal noisy background. The measurement of the average voltage drop as a function of the noise intensity allows to infer the value of the stability index that characterizes Levy-distributed fluctuations. An analytical estimate of the average velocity in the case of a Levy-driven escape process from a metastable state well agrees with the numerical calculation of the average voltage drop across the junction. The best performances are reached at small bias currents and low temperatures, emph{i.e.}, when both thermally activated and quantum tunneling switching processes can be neglected. The effects discussed in this work pave the way toward an effective and reliable method to characterize Levy components eventually present in an unknown noisy signal.
We demonstrate that by utilizing an over-screened Josephson junction as a noise detector it is possible to achieve the threshold regime, whereby the tails of the fluctuating current distribution are measured. This situation is realized by placing the Josephson junction and mesoscopic conductor in an external circuit with very low impedance. In the underdamped limit, over-screening the junction inhibits the energy diffusion in the junction, effectively creating a tunable activation barrier to the dissipative state. As a result, the activation rate is qualitatively different from the Arrhenius form.
We study mesoscopic fluctuations and weak localization correction to the supercurrent in Josephson junctions with coherent diffusive electron dynamics in the normal part. Two kinds of junctions are considered: a chaotic dot coupled to superconductors by tunnel barriers and a diffusive junction with transparent normal--superconducting interfaces. The amplitude of current fluctuations and the weak localization correction to the average current are calculated as functions of the ratio between the superconducting gap and the electron dwell energy, temperature, and superconducting phase difference across the junction. Technically, fluctuations on top of the spatially inhomogeneous proximity effect in the normal region are described by the replicated version of the sigma-model. For the case of diffusive junctions with transparent interfaces, the magnitude of mesoscopic fluctuations of the critical current appears to be nearly 3 times larger than the prediction of the previous theory which did not take the proximity effect into account.
Inspired by a recent experiment, we study the influence of thermal fluctuations on the $I$-$V$ characteristics of a Josephson junction, coupled to a strongly resistive environment. We obtain analytical results in the limit where the Josephson energy is larger than the charging energy and quasiparticles are absent.
We introduce a new and quantitative theoretical framework for noise spectral analysis using a threshold detector, which is then applied to a superconducting device: the Cavity Bifurcation Amplifier (CBA). We show that this new framework provides direct access to the environmental noise spectrum with a sensitivity approaching the standard quantum limit of weak continuous measurements. In addition, the accessible frequency range of the spectrum is, in principle, limited only by the ring down time of the CBA. This on-chip noise detector is non-dissipative and works with low probing powers, allowing it to be operated at low temperatures ($T<15$mK). We exploit this technique for measuring the frequency fluctuations of the CBA and find a low frequency noise with an amplitude and spectrum compatible with a dielectric origin.
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