Abstract:
We describe a method for calculating the counting statistics of electronic transport through nanoscale devices with both sequential and cotunneling contributions. The method is based upon a perturbative expansion of the von Neumann equation in Liouvillian space, with current cumulants calculated from the resulting nonMarkovian master equation without further approximation. As application, we consider transport through a single quantum dot and discuss the effects of cotunneling on noise and skewness, as well as the properties of various approximation schemes.

Abstract:
In order to fully characterize the noise associated with electron transport, with its severe consequences for solid-state quantum information systems, the theory of full counting statistics has been developed. It accounts for correlation effects associated with the statistics and effects of entanglement, but it remains a non-trivial task to account for interaction effects. In this article we present two examples: we describe electron transport through quantum dots with strong charging effects beyond perturbation theory in the tunneling, and we analyze current fluctuations in a diffusive interacting conductor.

Abstract:
Motivated by recent real-time electron counting experiments, we evaluate the full counting statistics (FCS) for the probability distribution of the electron number inside a quantum dot which is weakly coupled to source and drain leads. A non-Gaussian exponential distribution appears when there is no dot state close to the lead chemical potentials. We propose the measurement of the joint probability distribution of current and electron number, which reveals correlations between the two observables. We also show that for increasing strength of tunneling, the quantum fluctuations qualitatively change the probability distribution of the electron number. In this paper, we derive the cumulant generating functions (CGFs) of the joint probability distribution for several cases. The Keldysh generating functional approach is adopted to obtain the CGFs for the resonant-level model and for the single-electron transistor in the intermediate conductance regime. The general form for the CGF of the joint probability distribution is provided within the Markov approximation in an extension of the master equation approach [D. A. Bagrets, and Yu. V. Nazarov, Phys. Rev. B {\bf 67}, 085316 (2003)].

Abstract:
We make use of the first-quantized wave-packet formulation of the full counting statistics to describe charge transport of noninteracting electrons in a mesoscopic device. We derive various expressions for the characteristic function generating the full counting statistics, accounting for both energy and time dependence in the scattering process and including exchange effects due to finite overlap of the incoming wave packets. We apply our results to describe the generic statistical properties of a two-fermion scattering event and find, among other features, sub-binomial statistics for nonentangled incoming states (Slater rank 1), while entangled states (Slater rank 2) may generate super-binomial (and even super-Poissonian) noise, a feature that can be used as a spin singlet-triplet detector. Another application is concerned with the constant-voltage case, where we generalize the original result of Levitov-Lesovik to account for energy-dependent scattering and finite measurement time, including short time measurements, where Pauli blocking becomes important.

Abstract:
In this paper we derive the Clauser-Horne (CH) inequality for the full electron counting statistics in a mesoscopic multiterminal conductor and we discuss its properties. We first consider the idealized situation in which a flux of entangled electrons is generated by an entangler. Given a certain average number of incoming entangled electrons, the CH inequality can be evaluated for different numbers of transmitted particles. Strong violations occur when the number of transmitted charges on the two terminals is the same ($Q_1=Q_2$), whereas no violation is found for $Q_1\ne Q_2$. We then consider two actual setups that can be realized experimentally. The first one consists of a three terminal normal beam splitter and the second one of a hybrid superconducting structure. Interestingly, we find that the CH inequality is violated for the three terminal normal device. The maximum violation scales as 1/M and $1/M^2$ for the entangler and normal beam splitter, respectively, 2$M$ being the average number of injected electrons. As expected, we find full violation of the CH inequality in the case of the superconducting system.

Abstract:
We employ a single-charge counting technique to measure the full counting statistics (FCS) of Andreev events in which Cooper pairs are either produced from electrons that are reflected as holes at a superconductor/normal-metal interface or annihilated in the reverse process. The FCS consists of quiet periods with no Andreev processes, interrupted by the tunneling of a single electron that triggers an avalanche of Andreev events giving rise to strongly super-Poissonian distributions.

Abstract:
Non-equilibrium bosonization technique is used to study current fluctuations of interacting electrons in a single-channel quantum wire representing a Luttinger liquid (LL) conductor. An exact expression for the full counting statistics of the transmitted charge is derived. It is given by Fredholm determinant of the counting operator with a time dependent scattering phase. The result has a form of counting statistics of non-interacting particles with fractional charges, induced by scattering off the boundaries between the LL wire and the non-interacting leads.

Abstract:
We consider the transport of electrons passing through a mesoscopic device possessing internal dynamical quantum degrees of freedom. The mutual interaction between the system and the conduction electrons contributes to the current fluctuations, which we describe in terms of full counting statistics. We identify conditions where this discriminates coherent from incoherent internal dynamics, and also identify and illustrate conditions under which the device acts to dynamically bunch transmitted or reflected electrons, thereby generating super-Poissonian noise.

Abstract:
A theory of electron counting statistics in quantum transport is presented. It involves an idealized scheme of current measurement using a spin 1/2 coupled to the current so that it precesses at the rate proportional to the current. Within such an approach, counting charge without breaking the circuit is possible. As an application, we derive the counting statistics in a single channel conductor at finite temperature and bias. For a perfectly transmitting channel the counting distribution is gaussian, both for zero-point fluctuations and at finite temperature. At constant bias and low temperature the distribution is binomial, i.e., it arises from Bernoulli statistics. Another application considered is the noise due to short current pulses that involve few electrons. We find the time-dependence of the driving potential that produces coherent noise-minimizing current pulses, and display analogies of such current states with quantum-mechanical coherent states.

Abstract:
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.