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arXiv:cond-mat/0611783 · Physical Review Letters

Stochastic Dynamics of a Josephson Junction Threshold Detector

Eugene V. Sukhorukov, Andrew N. Jordan

Published Mar 29, 2007• 53 citations
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Abstract

We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. The activation rate dependence on the third current cumulant includes an additional term originating from the backaction of the measurement circuit.

DOI
10.1103/physrevlett.98.136803

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We generalize the stochastic path integral formalism by considering Hamiltonian dynamics in the presence of general Markovian noise. Kramers' solution of the activation rate for escape over a barrier is generalized for non-Gaussian driving noise in both the overdamped and underdamped limit. We apply our general results to a Josephson junction detector measuring the electron counting statistics of a mesoscopic conductor. The activation rate dependence on the third current cumulant includes an additional term originating from the backaction of the measurement circuit.
Motivated by several experimental activities to detect charge noise produced by a mesoscopic conductor with a Josephson junction as on-chip detector, the switching rate out of its zero-voltage state is studied. This process is related to the problem of thermal escape in presence of non-Gaussian fluctuations. In the relevant case of weak higher than second order cumulants, an effective Fokker-Planck equation is derived, which is then used to obtain an explicit expression for the escape rate. Specific results for the rate asymmetry due to the third moment of current noise allow to analyze experimental data and to optimize detection circuits.
I study the dynamics of a Josephson junction serving as a threshold detector of fluctuations which is subjected to a general non-equilibrium electronic noise source whose characteristic is to be determined by the junction. This experimental setup was proposed several years ago as a prospective scheme for determining the full counting statistics of an electronic noise source. Despite intensive theoretical as well as experimental research in this direction the promise has not been quite fulfilled yet and I will discuss what the unsolved issues are. First, I review a general theory for the calculation of the exponential part of the non-equilibrium switching rates of the junction and compare its predictions with previous results found in different limiting cases by several authors. I identify several possible weak points in the previous studies and I report a new analytical result for the linear correction to the rate due to the third cumulant of a non-Gaussian noise source in the limit of a very weak junction damping. The various analytical predictions are then compared with the results of the numerical method developed. Finally, I analyze the status of the experimental data thus far made publicly available with respect to the theoretical predictions and discuss briefly the suitability of the present experimental schemes as regards their potential for measuring the whole of the full counting statistics for non-Gaussian noise sources as well as their relation to the available theories.
Non-Gaussian fluctuations of the electrical current can be detected with a Josephson junction placed on-chip with the noise source. We present preliminary measurements with an NIS junction as a noise source, and a Josephson junction in the thermal escape regime as a noise detector. It is shown that the Josephson junction detects not only the average noise, which manifests itself as an increased effective temperature, but also the noise asymmetry. A theoretical description of the thermal escape of a Josephson junction in presence of noise with a non-zero third cumulant is presented, together with numerical simulations when the noise source is a tunnel junction with Poisson noise. Comparison between experiment and theory is discussed.
We consider the theoretical description of real‐time counting of electrons tunneling through a Coulomb‐blockade quantum dot using a detector with finite bandwidth. By tracing out the quantum dot we find that the dynamics of the detector effectively is non‐Markovian. We calculate the cumulant generating function corresponding to the resulting non‐Markovian rate equation and find that the measured current cumulants behave significantly differently compared to those of a Markovian transport process. Our findings provide a novel interpretation of noise suppression found in a number of systems.
Current-biased Josephson junctions can act as detectors of electromagnetic radiation. At optimal conditions, their sensitivity is limited by fluctuations causing stochastic switching from the superconducting to the resistive state. This work provides a quantitative description of a stochastic switching current detector, based on an underdamped Josephson junction. It is shown that activation of a Josephson plasma resonance can greatly enhance the detector responsivity in proportion to the quality factor of the junction. The ways of tuning the detector for achieving optimal operation are discussed. For realistic parameters of Nb / Al O x / Nb tunnel junctions, the sensitivity and noise-equivalent power (NEP) can reach values of S ≃ 5 × 10 12 (V/W) and NEP ≃ 2 × 10 − 23 ( WHz − 1 / 2 ), respectively. These outstanding characteristics facilitate both bolometric and single-photon detection in microwave and terahertz ranges. Published by the American Physical Society 2024
Quantum transport in mesoscopic conductors is essentially governed by the laws of quantum mechanics. One of the major open questions of quantum mechanics is what happens if noncommuting observables are measured simultaneously. Since current operators at different times do not commute, the high-frequency correlation functions of the current are realization of this fundamental quantum question. We formulate this problem in the context of measurements of finite-frequency current cumulants in a general quantum point contact, which are the subject to ongoing experimental effort. To this end, we present two models of detectors that correspond to a weak time-resolved measurement of the electronic current in a mesoscopic junction. In both cases, the backaction of the detector leads to observable corrections to the current correlations functions involving the so-called noise susceptibilities. As a result, we propose a reinterpretation of environmental corrections to the finite-frequency cumulants as inevitable effect resulting from basic quantum mechanical principles. Finally we make concrete predictions for the temperature, voltage, and frequency dependence of the third cumulant, which could be verified directly using current experimental techniques.