Electron Counting Statistics and Coherent States of Electric Current

TL;DR

This paper develops a quantum theory for electron counting in transport, revealing how current states can be measured without circuit disruption and analyzing their statistical properties and coherence.

Contribution

It introduces a novel idealized measurement scheme for electron counting and derives statistical distributions for different transport regimes, linking current states to quantum coherence.

Findings

Counting distribution is Gaussian for perfect transmission at finite temperature.

At low temperature and constant bias, the distribution is binomial.

Identifies current pulses that minimize noise and resemble quantum coherent states.

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.