Session Z2: Detection of Non-Gaussian Noise in Mesoscopic Systems

Detection of the third moment of shot noise by a Josephson junction

We use a hysteretic Josephson junction as an on-chip detector of shot noise of a tunnel junction. The detectable bandwidth is determined by the plasma frequency of the detector, which is about 50 GHz in the experiments that we report. The second moment of shot noise manifests itself as increased effective temperature of junction switching. The third moment results in a measurable change of the switching rate when reversing polarity of the current through the noise source. We have successfully analyzed the observed asymmetry using a phenomenological model. We compare our results to the more quantitative theories as well. Experiments on quantum point contacts and further work on tunnel junctions are in progress.   

Asymmetric noise probed with a Josephson junction

Using a Josephson junction, we have measured the fluctuations of the current through a tunnel junction. The current noise adds to the bias current of the Josephson junction and affects its switching out of the supercurrent branch. The experiment is carried out in a regime where switching is determined by thermal activation. The variance of the noise results in an elevated effective temperature, whereas the third moment, related to its asymmetric character, leads to a difference in the switching rates observed for opposite signs of the current through the tunnel junction. Measurements are compared quantitatively with recent theoretical predictions.   

Fluctuation-induced switching and the switching path distribution.

Fluctuation-induced switching is at the root of diverse phenomena currently studied in Josephson junctions, nano-mechanical systems, nano-magnets, and optically trapped atoms. In a fluctuation leading to switching the system must overcome an effective barrier, making switching events rare, for low fluctuation intensity. We will provide an overview of the methods of finding the switching barrier for systems away from thermal equilibrium. Generic features of the barrier, such as scaling with the system parameters, will be discussed. We will also discuss the motion of the system in switching and the ways of controlling it. Two major classes of systems will be considered: dynamical systems, where fluctuations are induced by noise, and birth-death systems. Even though the motion during switching is random, the paths followed in switching form a narrow tube in phase space of the system centered at the most probable path. The paths distribution is generally Gaussian and has specific features, which have been seen in the experiment [1]. Finding the most probable path itself can be reduced to solving a problem of Hamiltonian dynamics of an auxiliary noise-free system. The solution also gives the switching barrier. The barrier can be found explicitly close to parameter values where the number of stable states of the system changes and the dynamics is controlled by a slow variable. The scaling of the barrier height depends on the type of the corresponding bifurcation. We show that, both for birth-death and for Gaussian noise driven systems, the presence of even weak non-Gaussian noise can strongly modify the switching rate. The effect is described in a simple explicit form [2,3]. Weak deviations of the noise statistics from Gaussian can be sensitively detected using balanced dynamical bridge, where this deviation makes the populations of coexisting stable states different from each other; a realization of such a bridge will be discussed. We will also discuss the sharp anisotropy of fluctuations induced by Poisson noise in overdamped systems and how it is changed with decreasing damping. \\[4pt] [1] H. B. Chan, M. I. Dykman, and C. Stambaugh , Phys. Rev. Lett. \textbf{100}, 130602 (2008). \\[0pt] [2] M. I. Dykman, I. B. Schwartz, A. S. Landsman, Phys. Rev. Letts. \textbf{101, }078101 (2008). \\[0pt] [3] L. Billings, M. I. Dykman, and I. B. Schwartz, Phys. Rev. E \textbf{78} (2008).   

Theory of Mesoscopic Threshold Detectors of non-Gaussian Noise

Recently, measurements of current fluctuations arising from the charge discreteness (shot noise) have become an invaluable tool in mesoscopic physics, the most noticeable achievement being the measurement of quasi-particle charge in the fractional quantum Hall state. Typically, shot noise experiments report measurements of the zero-frequency noise power, which is a characteristic of the Gaussian component of current fluctuations. A natural generalization of the noise power, the counting statistics of charge transmitted through a system, is interesting in itself, because it contains complete information about the electron transport on a long time scale. However, the measurement of non-Gaussian noise effects presents an experimental challenge because of the limitations imposed by the central limit theorem. This difficulty can be partly overcome by placing an auxiliary mesoscopic system (detector) very close to the noise source and arranging strong coupling to the noise. This leads to the idea of a threshold detector, which is able to measure rare current fluctuations. Its basic principle is analogous to a pole vault: A detection event occurs when the measured system variable exceeds a given threshold value. A natural candidate for such a threshold detector is a metastable system operating on an activation principle. By measuring the rate of switching out of the metastable state, information about the statistical properties of the noise driving the system may be extracted.~ This requires solving the Kramers' problem of noise-activated escape from a metastable state beyond the Gaussian noise approximation and investigating how the measurement circuit affects threshold detection.   

Theory of Josephson junction detectors of higher order noise cumulants

A promising strategy pursued at various laboratories to measure higher order cumulants of the electrical current of nanoscopic devices employs on-chip Josephson junction detectors. The non-Gaussian nature of the noise generated by electronic nanostructures modifies the switching rate of the Josephson junction out of the zero voltage state, and the noise cumulants can be extracted from this modification. When the decay of the metastable zero voltage state occurs by noise activation to the top of the barrier of the Josephson potential, the third noise cumulant gives rise to an asymmetry of the rate when the bias current is inverted. In the range of decay by macroscopic quantum tunneling (MQT) through the barrier potential, the forth noise cumulant leads to an enhancement of the MQT rate. The theoretical methods to describe a Josephson junction noise detector in these parameter regimes are outlined and associated experimental strategies are discussed.