# Charge transfer statistics and qubit dynamics at tunneling Fermi-edge singularity

## TL;DR

This paper models charge transfer and qubit dynamics at the Fermi-edge singularity, revealing how transient current oscillations and shot noise relate to qubit coherence and charge statistics in a quantum dot system.

## Contribution

It introduces an exactly solvable model linking qubit evolution to charge transfer statistics, including Fano factors, in a tunneling quantum dot system with Coulomb interactions.

## Key findings

- Sub and super Poisson shot noise explained by transient dynamics.
- Super Poisson signals indicate non-monotonous transient current.
- Large time limit shows fractional Poissonian behavior without fractional charge tunneling.

## Abstract

Tunneling of spinless electrons from a single-channel emitter into an empty collector through an interacting resonant level of the quantum dot (QD) is studied, when all Coulomb screening of charge variations on the dot is realized by the emitter channel and the system is mapped onto an exactly solvable model of a dissipative qubit. In this model we describe the qubit density matrix evolution with a generalized Lindblad equation, which permit us to count the tunneling electrons and therefore relate the qubit dynamics to the charge transfer statistics. In particular, the coefficients of its generating function equal to the time dependent probabilities to have the fixed number of electrons tunneled into the collector are expressed through the parameters of a non-Hermitian Hamiltonian evolution of the qubit pure states in between the successive electron tunnelings. From the long time asymptotics of the generating function we calculate Fano factors of the second and third order (skewness) and establish their relation to the extra average and cumulant, respectively, of the charge accumulated in the transient process of the empty QD evolution beyond their linear time dependence. It explains the origin of the sub and super Poisson shot noise in this system and shows that the super Poisson signals existence of a non-monotonous oscillating transient current and the qubit coherent dynamics. The mechanism is illustrated with particular examples of the generating functions, one of which coincides in the large time limit with the $1/3$ fractional Poissonian realized without the real fractional charge tunneling.