Full Counting Statistics of Quantum Point Contact with Time-dependent Transparency

TL;DR

This paper investigates the full counting statistics of charge transfer in a quantum point contact with time-dependent transparency and bias, providing numerical solutions and analyzing protocols for minimal excitations and entanglement.

Contribution

It introduces a numerical method to compute FCS for general time-dependent biases and transparencies, and explores protocols for low noise and entanglement generation.

Findings

Numerical solutions for FCS with time-dependent parameters.

Protocols for minimal excitation charge transfer.

Analysis of entanglement-maximizing protocols.

Abstract

We analyse the zero temperature Full Counting Statistics (FCS) for the charge transfer across a biased tunnel junction. We find the FCS from the eigenvalues of the density matrix of outgoing states of one lead. In the general case of a general time-dependent bias and time-dependent transparency we solve for these eigenvalues numerically. We report the FCS for the case of a step pulse applied between the leads and a constant barrier transparency (this case is equivalent to Fermi edge singularity problem). We have also studied combinations of a time-dependent barrier transparency and biases between the leads. In particular we look at protocols which excite the minimal number of excitations for a given charge transfer (low noise electron source) and protocols which maximise entanglement of charge states.