Fermi edge singularity and finite frequency spectral features in a semi-infinite 1D wire

TL;DR

This paper explores how a charge qubit interacts with electrons in a semi-infinite 1D wire, revealing resonant features linked to the Fermi edge singularity and spatial structure of scattering, with results extending known theories.

Contribution

It generalizes Fermi edge singularity results to include spatially resolved excitations and identifies resonant tunneling features related to the wire's length and electron velocity.

Findings

Resonant features in qubit tunneling rate at multiples of h*v_F/l

Resonances due to coherent charge fluctuations fitting into the wire length

Strong coupling washes out resonances, indicating Fermi-sea shake-up

Abstract

We theoretically study a charge qubit interacting with electrons in a semi-infinite 1D wire. The system displays the physics of the Fermi edge singularity. Our results generalize known results for the Fermi-edge system to the regime where excitations induced by the qubit can resolve the spatial structure of the scattering region. We find resonant features in the qubit tunneling rate as a function of the qubit level splitting. They occur at integer multiples of h times v_F/l. Here v_F is the Fermi velocity of the electrons in the wire, and l is the distance from the tip of the wire to the point where it interacts with the qubit. These features are due to a single coherent charge fluctuation in the electron gas, with a half-wavelength that fits into l an integer number of times. As the coupling between the qubit and the wire is increased, the resonances are washed out. This is a clear signature of the increasingly violent Fermi-sea shake-up that accompanies strong coupling.