Statistics of charge transfer in a tunnel junction coupled to an oscillator

TL;DR

This paper develops a theoretical framework to analyze charge transfer statistics in a tunnel junction coupled to a quantum oscillator, providing insights into current fluctuations and quantum-object dynamics.

Contribution

It introduces a charge projection technique and charge specific density matrix to evaluate joint quantum and charge transfer statistics in nanoelectromechanical systems.

Findings

Derived the joint probability distribution of quantum state and charge state.

Analyzed the influence of a harmonic oscillator on junction current and noise.

Provided a method to evaluate current fluctuations in quantum-electromechanical systems.

Abstract

The charge transfer statistics of a tunnel junction coupled to a quantum object is studied using the charge projection technique. The joint dynamics of the quantum object and the number of charges transferred through the junction is described by the charge specific density matrix. The method allows evaluating the joint probability distribution of the state of the quantum object and the charge state of the junction.The statistical properties of the junction current are derived from the charge transfer statistics using the master equation for the charge specific density matrix. The theory is applied to a nanoelectromechanical system, and the influence on the average current and the current noise of the junction is obtained for coupling to a harmonic oscillator.