Wave-packet Formalism of Full Counting Statistics

TL;DR

This paper develops a wave-packet formalism for full counting statistics in mesoscopic electron transport, revealing how entanglement influences charge noise and extending existing models to include energy dependence and finite measurement times.

Contribution

It introduces a wave-packet approach to full counting statistics, accounting for energy, time dependence, and exchange effects, and explores entanglement's impact on charge noise.

Findings

Entangled states can produce super-binomial noise.

Wave-packet formalism captures energy and time dependence.

Generalizes Levitov-Lesovik formula for finite measurement times.

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.