Full counting statistics of nano-electromechanical systems

We develop a theory for the full counting statistics (FCS) for a class of nanoelectromechanical systems (NEMS), describable by a Markovian generalized master equation. The theory is applied to two specific examples of current interest: vibrating C60 molecules and quantum shuttles. We report a numerical evaluation of the first three cumulants for the C60-setup; for the quantum shuttle we use the third cumulant to substantiate that the giant enhancement in noise observed at the shuttling transition is due to a slow switching between two competing conduction channels. Especially the last example illustrates the power of the FCS.Comment: 7 pages, 3 figures; minor changes - final version as published in Europhys. Let

The influence of charge detection on counting statistics

We consider the counting statistics of electron transport through a double quantum dot with special emphasis on the dephasing induced by a nearby charge detector. The double dot is embedded in a dissipative enviroment, and the presence of electrons on the double dot is detected with a nearby quantum point contact. Charge transport through the double dot is governed by a non-Markovian generalized master equation. We describe how the cumulants of the current can be obtained for such problems, and investigate the difference between the dephasing mechanisms induced by the quantum point contact and the coupling to the external heat bath. Finally, we consider various open questions of relevance to future research.Comment: 15 pages, 2 figures, Contribution to 5-th International Conference on Unsolved Problems on Noise, Lyon, France, June 2-6, 200

Non-equilibrium Entanglement and Noise in Coupled Qubits

We study charge entanglement in two Coulomb-coupled double quantum dots in thermal equilibrium and under stationary non-equilibrium transport conditions. In the transport regime, the entanglement exhibits a clear switching threshold and various limits due to suppression of tunneling by Quantum Zeno localisation or by an interaction induced energy gap. We also calculate quantum noise spectra and discuss the inter-dot current correlation as an indicator of the entanglement in transport experiments.Comment: 4 pages, 4 figure

Frequency-dependent counting statistics in interacting nanoscale conductors

We present a formalism to calculate finite-frequency current correlations in interacting nanoscale conductors. We work within the n-resolved density matrix approach and obtain a multi-time cumulant generating function that provides the fluctuation statistics, solely from the spectral decomposition of the Liouvillian. We apply the method to the frequency-dependent third cumulant of the current through a single resonant level and through a double quantum dot. Our results, which show that deviations from Poissonian behaviour strongly depend on frequency, demonstrate the importance of finite-frequency higher-order cumulants in fully characterizing interactions.Comment: 4 pages, 2 figures, improved figures & discussion. J-ref adde

Rights Myopia in Child Welfare

For decades, legal scholars have debated the proper balance of parents\u27 rights and children\u27s rights in the child welfare system. This Article argues that the debate mistakenly privileges rights. Neither parents\u27 rights nor children\u27s rights serve families well because, as implemented, a solely rights-based model of child welfare does not protect the interests of parents or children. Additionally, even if well-implemented, the model still would not serve parents or children because it obscures the important role of poverty in child abuse and neglect and fosters conflict rather than collaboration between the state and families. In lieu of a solely rights-based model, this Article proposes a problem-solving model for child welfare and explores one embodiment of such a model, family group conferencing. This Article concludes that a problem-solving model holds significant potential to address many of the profound theoretical and practical shortcomings of the current child welfare system

Electron Waiting Times in Mesoscopic Conductors

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a cross-over from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with energy level statistics and random matrix theory.Comment: 4+ pages, 3 figure

Strong quantum memory at resonant Fermi edges revealed by shot noise

Studies of non-equilibrium current fluctuations enable assessing correlations involved in quantum transport through nanoscale conductors. They provide additional information to the mean current on charge statistics and the presence of coherence, dissipation, disorder, or entanglement. Shot noise, being a temporal integral of the current autocorrelation function, reveals dynamical information. In particular, it detects presence of non-Markovian dynamics, i.e., memory, within open systems, which has been subject of many current theoretical studies. We report on low-temperature shot noise measurements of electronic transport through InAs quantum dots in the Fermi-edge singularity regime and show that it exhibits strong memory effects caused by quantum correlations between the dot and fermionic reservoirs. Our work, apart from addressing noise in archetypical strongly correlated system of prime interest, discloses generic quantum dynamical mechanism occurring at interacting resonant Fermi edges.Comment: 6 pages, 3 figure

Factorial cumulants reveal interactions in counting statistics

Full counting statistics concerns the stochastic transport of electrons in mesoscopic structures. Recently it has been shown that the charge transport statistics for non-interacting electrons in a two-terminal system is always generalized binomial: it can be decomposed into independent single-particle events and the zeros of the generating function are real and negative. Here we investigate how the zeros of the generating function move into the complex plane due to interactions and demonstrate that the positions of the zeros can be detected using high-order factorial cumulants. As an illustrative example we consider electron transport through a Coulomb blockade quantum dot for which we show that the interactions on the quantum dot are clearly visible in the high-order factorial cumulants. Our findings are important for understanding the influence of interactions on counting statistics and the characterization in terms of zeros of the generating function provides us with a simple interpretation of recent experiments, where high-order statistics have been measured.Comment: 12 pages, 7 figures, Editors' Suggestion in Phys. Rev.

Current noise in a vibrating quantum dot array

We develop methods for calculating the zero-frequency noise for quantum shuttles, i.e. nanoelectromechanical devices where the mechanical motion is quantized. As a model system we consider a three-dot array, where the internal electronic coherence both complicates and enriches the physics. Two different formulations are presented: (i) quantum regression theorem, and (ii) the counting variable approach. It is demonstrated, both analytically and numerically, that the two formulations yield identical results, when the conditions of their respective applicability are fulfilled. We describe the results of extensive numerical calculations for current and current noise (Fano factor), based on a solution of a Markovian generalized master equation. The results for the current and noise are further analyzed in terms of Wigner functions, which help to distinguish different transport regimes (in particular, shuttling vs. cotunneling). In the case of weak inter-dot coupling, the electron transport proceeds via sequential tunneling between neighboring dots. A simple rate equation with the rates calculated analytically from the P(E)-theory is developed and shown to agree with the full numerics.Comment: 22 two-column pages, 9 figure

Shot noise of a quantum shuttle

We formulate a theory for shot noise in quantum nanoelectromechanical systems. As a specific example, the theory is applied to a quantum shuttle, and the zero-frequency noise, measured by the Fano factor F, is computed. F reaches very low values (F~0.01) in the shuttling regime even in the quantum limit, confirming that shuttling is universally a low noise phenomenon. In approaching the semiclassical limit, the Fano factor shows a giant enhancement (F~100) at the shuttling threshold, consistent with predictions based on phase-space representations of the density matrix.Comment: 4 pages, 2 figures; minor formal changes - updated figures and references; final version as published in Phys. Rev. Let