Current noise spectrum in a solvable model of tunneling Fermi-edge singularity

TL;DR

This paper models tunneling in a quantum dot system as an exactly solvable dissipative qubit, analyzing charge transfer statistics and revealing bifurcation phenomena in the current noise spectrum.

Contribution

It introduces a solvable model of tunneling Fermi-edge singularity mapped onto a dissipative qubit, enabling exact analysis of charge transfer and noise characteristics.

Findings

Derived exact charge transfer statistics using generalized Bloch equations.

Calculated the steady current noise spectrum and identified bifurcation of zero-frequency minimum.

Demonstrated the impact of qubit coherent dynamics on noise spectrum features.

Abstract

We consider tunneling of spinless electrons from a single channel emitter into an empty collector through an interacting resonant level of the quantum dot (QD). When all Coulomb screening of sudden charge variations of the dot during the tunneling is realized by the emitter channel, the system is mapped onto an exactly solvable model of a dissipative qubit. The qubit density matrix evolution is described with a generalized Bloch equation which permits us to count the tunneling electrons and find the charge transfer statistics. The two generating functions of the counting statistics of the charge transferred during the QD evolutions form its stationary and empty state have been expressed through each other. It is used to calculate the spectrum of the steady current noise and demonstrate occurrence of the bifurcation of its single zero-frequency minimum into two finite-frequency dips due to the qubit coherent dynamics.