Counting statistics of transport through Coulomb blockade nanostructures: High-order cumulants and non-Markovian effects

TL;DR

This paper develops a recursive theoretical framework to accurately compute high-order current cumulants in Coulomb blockade nanostructures, accounting for non-Markovian effects, to match recent experimental capabilities.

Contribution

It introduces a general recursive method for calculating zero-frequency current cumulants of any order in systems with strong Coulomb interactions and non-Markovian dynamics.

Findings

Applicable to systems with many states

Handles non-Markovian dynamics

Analyzes properties of high-order cumulants

Abstract

Recent experimental progress has made it possible to detect in real-time single electrons tunneling through Coulomb blockade nanostructures, thereby allowing for precise measurements of the statistical distribution of the number of transferred charges, the so-called full counting statistics. These experimental advances call for a solid theoretical platform for equally accurate calculations of distribution functions and their cumulants. Here we develop a general framework for calculating zero-frequency current cumulants of arbitrary orders for transport through nanostructures with strong Coulomb interactions. Our recursive method can treat systems with many states as well as non-Markovian dynamics. We illustrate our approach with three examples of current experimental relevance: bunching transport through a two-level quantum dot, transport through a nano-electromechanical system with dynamical Franck-Condon blockade, and transport through coherently coupled quantum dots embedded in a dissipative environment. We discuss properties of high-order cumulants as well as possible subtleties associated with non-Markovian dynamics.