Fermi edge singularity and finite-frequency spectral features in a semi-infinite one-dimensional wire

Abstract

We theoretically study a charge qubit interacting with electrons in a semi-infinite one-dimensional 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 $h{v}_{F}/l$. 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 the constructive interference of the amplitudes for creating single coherent left- or right-moving charge fluctuation (plasmon) in the electron gas. 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, associated with the creation of many plasmons whose individual energies are too low to meet the resonance condition.