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arXiv:cond-mat/0607020 · Physical Review Letters

Detecting Charge Noise with a Josephson Junction: A Problem of Thermal Escape in Presence of Non-Gaussian Fluctuations

Joachim Ankerhold

Published Jan 16, 2007• 39 citations
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Abstract

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.

DOI
10.1103/physrevlett.98.036601

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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.
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.
The Josephson junction noise detector measures the skewness of non-Gaussian noise via the asymmetry of the rate of escape from the zero-voltage state upon reversal of the bias current. The feedback of this detector on the noise generating device is investigated in detail. Concise predictions are made for a second Josephson junction as noise generating device. The strong nonlinearity of this component implies particularly strong feedback effects, including a change in sign of the rate asymmetry as the applied voltage approaches twice the superconducting gap.
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.
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.
We measure current fluctuations of mesoscopic devices in the quantum regime, when the frequency is of the order of or higher than the applied voltage or temperature. Detection is designed to probe separately the absorption and emission contributions of current fluctuations, i.e. the positive and negative frequencies of the Fourier transformed nonsymmetrized noise correlator. It relies on measuring the quasiparticles photon assisted tunneling current across a superconductor-insulator-superconductor junction (the detector junction) caused by the excess current fluctuations generated by quasiparticles tunneling across a Josephson junction (the source junction). We demonstrate unambiguously that the negative and positive frequency parts of the nonsymmetrized noise correlator are separately detected and that the excess current fluctuations of a voltage biased Josephson junction present a strong asymmetry between emission and absorption.
We study a Josephson junction (JJ) in the regime of incoherent Cooper-pair tunneling, capacitively coupled to a nonequilibrium noise source. The current-voltage (I-V) characteristics of the JJ are sensitive to the excess voltage fluctuations in the source, and can thus be used for wideband noise detection. Under weak driving, the odd part of the I-V can be related to the second cumulant of noise, whereas the even part is due to the third cumulant. After calibration, one can measure the Fano factors for the noise source, and get information about the frequency dependence of the noise.