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We theoretically study a charge qubit interacting with electrons in asemi-infinite 1D wire. The system displays the physics of the Fermi edgesingularity. Our results generalize known results for the Fermi-edge system tothe regime where excitations induced by the qubit can resolve the spatialstructure of the scattering region. We find resonant features in the qubittunneling rate as a function of the qubit level splitting. They occur atinteger multiples of h times v_F/l. Here v_F is the Fermi velocity of theelectrons in the wire, and l is the distance from the tip of the wire to thepoint where it interacts with the qubit. These features are due to a singlecoherent charge fluctuation in the electron gas, with a half-wavelength thatfits into l an integer number of times. As the coupling between the qubit andthe wire is increased, the resonances are washed out. This is a clear signatureof the increasingly violent Fermi-sea shake-up that accompanies strongcoupling.

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