Reply to the comment on "Theoretical analysis of the transmission phase shift of a quantum dot in the presence of Kondo correlations"

In their comment, Aharony, Entin-Wohlman, Oreg and von Delft claimed that the expression we obtained for the phase of the S-matrix does not give back the correct result notably in the U=0 limit of the single level Anderson model (SLAM). Their comment, however, misses the point of our argument, namely, that the SLAM is insufficient to describe the interferometry experiment. Instead, the quantum dot needs to be viewed as a multi-level artificial atom, and the interferometry experiment as a scattering experiment off the atom. The description is subject, in particular, to such scattering theorems as the generalized Levinson theorem. As a result, we show how there exists a factor of 2 difference between the phase of the S-matrix responsible for the shift in the Aharonov-Bohm (AB) oscillations, and the one controlling the conductance. We point out how the results obtained this way are in remarkably good quantitative agreement with measurements performed by AB interferometry for the conductance as well as for the phase shift.